iff a. K44 Cornell University Library TP 492.5.K44 The thermodynamic properties of ammonia 3 1924 004 586 032 DATE DUE pT.r,'..1 " -f *G7# ~ f n *■■ *— APR^ ir** ism "WW **^pj LiJ,„<2-^L_ * CAVLOflD »RINTEO IN U.S.*. Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004586032 THE THERMODYNAMIC PROPERTIES OF AMMONIA COMPUTED FOR THE USE OF ENGINEERS FROM NEW EXPERI- MENTAL DATA DERIVED FROM INVESTIGATIONS MADE AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY BY FREDERICK G. KEYES and ROBERT B. BROWNLEE FIRST EDITION FIRST THOUSAND NEW YORK JOHN WILEY & SONS, Inc. London: CHAPMAN & HALL, Limited 1916 J k/, «55l Copyright, 191 6, BY FREDERICK G. KEYES AND ROBERT B. BROWNLEE Stanhope jpress F. H.GILSON COMPANY BOSTON, U.S.A. PREFACE These tables of the properties of saturated and superheated ammonia are based for the most part on an experimental investigation carried out during the course of several years in the Research Laboratory of Physical Chemistry of the Massachusetts Institute of Technology. This investi- gation was suggested by Professor Edward F. Miller of the Institute's Mechanical Engineering Department, which generously supplied many of the facilities needed in prosecuting the experimental investigation. The original intention was to determine the vapor-pressure curve and the specific heat-capacity of liquid ammonia with the view of utilizing the results obtained as a partial basis for the computation of a new table of the thermodynamic properties of ammonia which would prove useful in controlling the performance of refrigerating machines. After the completion of the preliminary work, in connection with which the . already existing data had been critically examined, it appeared desir- able to. carry out a more comprehensive experimental investigation. Throughout the whole work we have been indebted to Professor Miller for his advice and support. The experimental work was carried out by Henry A. Babcock, Harvey S. Benson and Robert B. Brownlee, senior and graduate students in the Mechanical Engineering Department, under the direction of Frederick G. Keyes, a member of the Research Laboratory staff. Mr. Babcock took up the portion of the work bearing on the heat-capacity of liquid ammonia. Messrs. Benson and Brownlee began the determination of the vapor-pres- sures, the liquid specific volumes, and the isotherms of the substance and continued this work during the following year. Mr. Brownlee collabo- rated with Mr. Keyes in working over all the data and in constructing the necessary diagrams for the tables. The computation of the tables was carried out by George W. Clark, Instructor in the Mechanical Engineering Department of the Institute. Mr. Clark's task was especially difficult because of the form of the equa- tion of state employed; and it was carried out by him with great skill and intelligence. This part of the work was aided financially by a gen- erous grant from the Rumford Fund of the American Academy. The computed values have been thoroughly and independently checked by F. G. Keyes. The experimental methods employed and the details of the data ob- tained will, it is hoped, soon be ready for publication. It was decided, however, to print the tables in advance of the publication of the experi- iv PREFACE mental research on account of the technical need of more accurate tables than have been hitherto accessible. The treatment of the experimental results obtained and the critical study of other observers' data have resulted in some new methods of examining experimental data which are here presented in considerable detail, for it is hoped that they will be of service to others interested in similar studies. The form of the equation of state employed is very different from those which have hitherto been employed in compu- ting tables. The usual equations employed give the volume explicitly, while the equation used in computing the present tables possesses five values of the volume. The multiple value of the volume is an obvious physical necessity from the point of view of the continuity of the phases; and a careful study of the application of the equation, not only to the vapor phase of ammonia but also to the existing data for several other substances, has shown its use to be justified. The use of the equation for practical purposes has moreover led to the development of special methods of application which greatly lighten the labor involved in com- puting. The tables have been brought into the usual forms convenient for engineering practice. In addition to the tables an accurate "Mollier" diagram has been prepared which has proved to be of very material assistance for rapidly solving engineering problems. Frederick G. Keyes. Robert B. Brownlee. January, 1916. CONTENTS PART I. DISCUSSION OF THE DATA AND COMPUTATIONS Page i. Fundamental Thermodynamic Relations 3 2. Functional Expressions for the Change of Vapor-Pressure with Temperature 8 3. The Vapor-pressure Data for Ammonia 10 4. The Specific Volume of Liquid Ammonia ' 14 5. Equations of State in General 16 6. The Equation of State for Ammonia Vapor 20 7. The Heat of Vaporization of Liquid Ammonia 23 8. The Specific Heat-Capacity of Ammonia Vapor 26 9. The Entropy of Ammonia Vapor 27 10. The Specific Heat-Capacity of Liquid Ammonia 29 PART II. TABLES OF THE THERMODYNAMIC CONSTANTS OF AMMONIA Description of the Tables 34 Table I. Saturated Ammonia. Temperature Table 36 Table II. Saturated Ammonia. Pressure Table 44 Table III. Superheated Ammonia 54 PART I DISCUSSION OF THE DATA AND COMPUTATIONS LIST OF SYMBOLS USED dQ : Element of heat absorbed when the work dW is represented by p dv. dH : Element of heat absorbed when the work dW is represented by d (pv). dU : Increment of the internal energy. 1 : Subscript referring to the vapor phase. 2 . Subscript referring to the liquid phase. s : Subscript referring to the saturation state. p : Pressure (or force per unit area). v : Volume of a unit of weight. T : Temperature reckoned on the absolute scale or on the (substantially equivalent) hydrogen scale. C : Specific heat where the heat element dQ is considered. 7 : Specific heat where the heat element dH is considered. * : Entropy defined as I ■— ■ L : Heat of evaporation of unit-weight of a substance. R : Absolute gas constant defined by pv = RT. & : Correction term of the volume in the equation of state. a and / : Constants of the cohesive pressure term -; ^r in the equation of state. (» - If One 15 calorie = 4.182 joules.* One 15° B.t.u. = 777.17 standard ft. lb. Absolute temperature of the ice-point: 273.1° C. or 459.58° F. * This value is very nearly identical with the mean value, 4.1826 joules, obtained from a recom- putation of Barnes work by A. W. Smith (Phys. Rev., 191 1). The Thermodynamic Properties of Ammonia 1. FUNDAMENTAL THERMODYNAMIC RELATIONS The First Law of Thermodynamics requires that the heat absorbed dQ from the surroundings by a system which undergoes any change in state be equal to the increase dU in its internal energy plus the work dW produced in the surroundings. Since the work commonly consists in a change in volume dv against a pressure p, this relation is commonly ex- pressed by the equation * dQ = dU + pdv. (i)f The quantity dQ, although of infinitesimal magnitude, is not a differ- ential of any finite quantity which, like the internal energy U, is fully determined by the state of the system. It is therefore convenient for many purposes to consider another energy quantity dH which is defined by the equation dH = dU + d(pv) (2) and which therefore is related to dQ in the way expressed by the equation dH = dQ + v dp. The quantity dH is evidently a complete differential, — one whose value is fully determined by the change in state of the system (since the values of dU and d (pv) are so determined). Various useful relations may be deduced from these equations by ex- pressing the state of the substance (constituting the system) in terms of the variables p, v, and T. We shall consider in connection with equation (1) first the case where the independent variables are p and T and then the case where they are v and T. Differentiating equation (1) with respect to T we get ®).- c -($. + '&); * It is customary in writing thermodynamic equations to sometimes insert a factor J or its reciprocal, depending on the units employed. In the equations here presented this factor has not been inserted. The simplification may be obtained by suitably choosing the units. f In representing this heat-quantity Clausius wrote dQ to indicate that the quantity of heat was infinitesimal. However, dQ is not the differential of a known finite quantity Q, and some writers make use of other notations to avoid a misunderstanding of the quantity. The element dH, on the othei hand, is evidently a perfect differential. 3 THE THERMODYNAMIC PROPERTIES OF AMMONIA But and it may dv dU = m\ \dT, i dT+ { dp/7 dp. be easily shown * that f — - j = — T[-pp) dT/ t = (-~j dT+(^j dp, (1) may be written dQ = C p dT-t(^j dp. p ( — ) , and since (4) From (4) may be written the specific heats along the saturation line of either the liquid or vapor,f or Ofl L-11 U dp dT = r (-) KdTj. Vi - v 2 (5) .dp since T^~ (z>i — z> 2 ) = L. Thus the difference in the specific heats dT along the saturation lines of liquid and vapor may be written l^s, L-sj C — C — V\ - Vi [(jf) - (i) ] (6) The specific heat of a liquid as measured is usually that defined by (5), while it is impossible to measure C Sl directly. By means of the equation C-7) _dL m dT L T dp T dT dVi dT, (dvt\ \dTj. one obtains easily from (6) C Sl — C $2 = -™ — -f, • It is evident that since — is negative, C Sl may be negative or positive. If C Sl is negative the vapor would superheat on compression. From (4) the expression for the entropy becomes -if-/^-/^)*^ and accordingly it follows on differentiating that Cp T' dp/, dT/ p (7) (8) The first of these equations differentiating with respect to p and the second with respect to T may be equated, giving the equation (dC P \ ' * 2 " \dp/ T \dT% * Max Planck, "Thermodynamik," 3rd ed., page 128. t The subscript 1 will refer to the vapor phase and 2 to the liquid phase. FUNDAMENTAL THERMODYNAMIC RELATIONS 5 The first of equations (8) is a necessary condition of consistency which applies to tables of thermodynamic properties. For example, the dif- ferences in the total heats at constant pressure are the values of the mean specific heat between the two temperatures at which the difference is taken. This quantity divided by the average absolute temperature should be equal to the difference in the entropies for the corresponding temperatures. The choice of v and T as independent variables leads to a general expres- sion for dQ. For this purpose the definition (— — ) = C v and the equation \dl/ v ( — J = T (t^) —p are needed. Proceeding in the same manner as with equation (4) there is obtained J dp dQ=C v dT+T[^J dv. (9) From this equation it follows at once that the specific heats along the saturation line may be written and the difference of the specific heats becomes c Sl - c H = c„ - c H + T\\ dT )^ 2t - {jf\' d%\ (ll) If C a is replaced by C p one obtains the familiar relation c - c - + r (£). ■(£),: <»> and the difference between C s and C p is evidently c -- c - r (fr)„[i-(fr)J "3) The equation for the entropy and its derivatives becomes $ \dT/ v t' \dv) T \ar/ v (15) Applying to (15) a process similar to that employed with equations (8) leads to the equation (d£A =T (&P\ V dv I T \dTV v 6 THE THERMODYNAMIC PROPERTIES OF AMMONIA Returning to equation (2) it follows as with (4) that dH = C v dT -\t(^ -vjdp (16) *„d «-[& + .(*)>r + [ r (*) i+ .(«)J*. (.7) For the specific heats at constant pressure and constant volume the two equations lead to the equations Ur) p ~ Cp ' (f)^--(fr)/ (18) The specific heats at constant pressure are seen to be equivalent while the specific heat at constant volume is greater than the specific heat defined from equation (1). The specific heat along the saturation line becomes dH _ r dT ~ Cp *&. \dT (19) c-HSM'fflMZ),] dv T jdT If the relation pv = RT is applied to (16) and (17) there results for the former dH = C P dT while (17) becomes dH = (C v + R) dT = C Pa dT. The difference in the saturation specific heats is / s^ l~sv ^- r »),-(^)J + r ^ Taking account of the equation for C Pl — C P2 in equation (5) and L one obtains the relation The equation C„ — C S2 = -7= — — provides a further relation which dl 1 assists in comprehending the difference between the definition of heat contained in equations (1) and (2). Writing AC Sn for this equation and Ay s , 2 for (21) it follows that L = r(A 7si2 -AC Sl2 ). (22) The equations for the Joule-Thomson experiment are at once deducible from equations (16) and (17) ; assuming that H is constant one obtains: dT dp dT dv T {ff)- V (23) (24) FUNDAMENTAL THERMODYNAMIC RELATIONS 7 The above relations serve as a general basis for using the quantity defined by either (1) or (2). The present tables are based on equation (1), which represents the heat added to a fluid within an envelope, while (2) evidently represents the quantity of heat supplied when a fluid is forced to flow from one p, v, T condition to another p, v, T condition. General Formulae Deducible from Equation (1) Independent Variables p, T. Independent Variables v, T. dQ= C,dT - T {~)d P . dQ- C.dT + r(J£) *. (*±\ = c* ( \dTJ p T \ dT) v T' 'dp\ >T \dT/ v \dp) T \dT) p \dv)r \c /§Cp\ = _ T (&v\ /a£,\ _ T (Pp\ \ap) T \dT*J \av) T Vary." For Q Constant For Q Constant T fdv\ zap) (dT\ = \dT) p tdT\ = _ la 77. \dp) Q C p \dv) Q C v *L) (d_p) ^ . (§1\ \dT/ p ~ \dv) T ' \dp/v THE THERMODYNAMIC PROPERTIES OF AMMONIA General Formulae Deducible from Equation (2) Independent Variables p, T. dH=C P dT-\Tt - v\ 'dv_ \dT. dp. (-" V dT, \dT T\dTj p \dTJ T' (dT\ T [dT) v I \dp/ H C p — p- = -c dH- Independent Variables v, T. c H%u dT+ A%)Am dv. C v +v dp + (#)„="-(f!" I (dH\ /d* rfflM%),]fr + V_fdp\ T\dTJ v \dT) v ' T\dTj v dT\ \dv/ B pH- (§E\ = T (d£) \dvj y Sl - 7s 2 dL dT Hi — H* = U\ — U 2 + piVi — piV-2. 2. FUNCTIONAL EXPRESSIONS FOR THE CHANGE OF VAPOR- PRESSURE WITH THE TEMPERATURE A knowledge of the relation between the pressure and the temperature along the saturation line is of first importance in constructing a table of thermodynamic quantities. From this relation maybe obtained: (i) the specific volumes of the saturated vapor through the equation of state of the dp vapor phase; (2) values of -rfp, for use in calculating the heat of evapora- tion by the Clapeyron Equation. The problem of obtaining accurate dp values of —^ depends evidently upon the accuracy with which it is possible to relate p to T by means of a suitable equation. Considerable attention has in the past been devoted to this subject, but most of the methods of * Since ( — S, J =%=,= - from pv = RT it follows that for a perfect gas where Cj refers to the specific heat at constant pressure as the pressure approaches zero. It may be further observed that on applying the same pressure volume relation to \ T ( — =1 — v the specific heat y, becomes equivalent to C p . C 8l on the other hand reduces to C„. = C v , — R tt^~ ' a log T FUNCTIONAL EXPRESSIONS 9 attacking the problem have their starting point in certain integrations dp of the Clapeyron equation L = T -p^ (pi — v 2 ), which may also be written: dp — t^-, 7 dT. It is easily seen, for example, that the latter T (vi - v 2 ) equation, L being represented by L + a{T + a 2 T 2 + ■ ■ ■ + a n T n , Vi by , and neglecting v 2 , leads to the expression P log P = J Lo + a 1 T + a i T i + ■ ■ • + a n T" Jrn , ^ dT + m. = - k^ + a, log T + at'T+ ■ ■ ■ + a/T"-' + m, (25) where L ' — ~ and c/, a 2 ' have an obvious significance, m being a constant K of integration calculable from a single value of p at a definite temperature. In practice the constants of formula (25) are evaluated from several smoothed data suitably spaced with reference to the temperature. Con- sideration reveals at once, however, that a method of evaluating the con- stants is to be preferred whereby the inevitable inconsistencies of the experimental data will be disclosed and eliminated. The following method of procedure was accepted in the case of ammonia as a means of accomplishing this object. Van der Waals inferred from certain considerations relative to his equation of state that l0g t = a (f- J ) (26) should be valid where a is a constant. It is well known, however, that a is not constant, but varies with T* If, however, it is possible to repre- sent a accurately as a function of T the correct relation between p and T will result. Writing (26) as T ( -f L \ = a it is possible to calculate values of a throughout the extent of the vapor-pressure data available. For a number of substances a lies on a curve resembling a parabola. It is a matter of experience that it is impossible to draw a representa- tive curve through experimental data where a minimum occurs, but to avoid this difficulty it is only necessary to plot the a's with (T c — T) as an ordinate and by extrapolation obtain the value of a indefinitely near the critical temperature. This section of the curve is fortunately very nearly linear. Assuming that a may be represented as a + a, (T t - T) + a, (T c - T) 2 + • • • + a n (T c - T)», * See H. Happel, Ann. d. Physik, 13, 340 (1904); also Marks, Jour. Am. Soc. Mech. Eng., 33, 563 (1911). io THE THERMODYNAMIC PROPERTIES OF AMMONIA a would be the value of a indefinitely near the critical temperature. If now the variable is changed to Z = ^^ = 0l + • • • + a n (T c - TY'\ the difficulty of being obliged to draw a smooth curve through a minimum will be avoided.* Rewriting (26), taking account of the Z function, there results Z(T C - T) 2 + a T c . ,, . , , log p = - — y — y + (log p c + ao) ; writing a T c = co and (log p c + Co) = m, \ogp = - Z(T °- T T)2 + w + m. (27) This equation in practice is most convenient for calculations since Z (T c — T) 2 may be obtained with sufficient accuracy with a 20-inch slide rule; there remaining only the division of w + Z (T e — T) 2 by T to be carried out by logarithms. If desired, the critical constants may be absorbed in the constants of the equation logp=-j,+ C + dT+eT 2 + ■ ■ ■ ■ (28) 3. THE VAPOR-PRESSURE DATA FOR AMMONIA The most reliable and systematic data in connection with the vapor- pressure of ammonia are due to Regnault.t Other measurements have been made at isolated sections of the vapor-pressure temperature curve by Faraday,J Blumcke,§ Brill, || and Davies.^f The data due to all these observers have been admirably treated by Goodenough and Mosher** and also recently by Holst.ft In the Hoist treatment of the data a few new measurements carried out by Hoist were included. These additions consist of three measurements between — 32 and —44° C. and also one each at 19. 58 and 45. 05 C. The Hoist treatment, however, does not lead to values which differ materially from the Mosher values although Hoist perceived that the Regnault pressures above zero were too low. The vapor-pressure values used in the present tables depend entirely on the data obtained at the Research Laboratory of Physical Chemistry of the Massachusetts Institute of Technology. Measurements of pres- sure were made by equilibrating the pressure exerted by the ammonia * Sometimes, owing to inaccurate data, the value of ao at the critical temperature is difficult to determine. For several substances, however, it has been found that no appreciable error is made by assuming 3.00 as the value of a - t Mem. de Vlnst. de France, 26, 598 (1847). f Proc. Roy. Soc, 78-A, 41 (1906). % Phil. Trans., 135, 170 (1845). || Ann. der Physik, 21, 170 (1906). § Wiedemann's Annalen, 34, 10 (1888). ** Univ. of Illinois Bull., 18 (1913). ft Les prop, therm, de I'ammoniaque et du chlorure de methyle, Leiden (1914). THE VAPOR-PRESSURE DATA FOR AMMONIA ii Fig. i. against a piston by means of weights, and the final temperature measure- ments were made with a platinum resistance thermometer. The cali- bration of the pressure piston was accomplished by direct comparison with a column of mercury 12.8 meters in length. The device used for determining the equilibrium of the piston is illustrated in Fig. 1. 12 THE THERMODYNAMIC PROPERTIES OF AMMONIA The mercury-in-glass column is indicated at H and communicates with the mercury in the steel cylinder at M. Leading from the cover of the steel cylinder are two steel tubes, one of which passes to the Cailletet pump which serves to elevate the mercury in the column M, while the other leads from the mercury to the steel device A . From A the oil tube connects with the pressure-measuring piston E, which has attached a motor-driven device at R for reciprocating the piston through an angle regularly. The adjusting of the oil on the piston side of A is accomplished by the screw-pump D. The temperature of the mercury column was read by means of thermometers placed at intervals along the column. The average temperature was then obtained by graphically determining the area on a rectangular diagram between the curve drawn through the temperature readings and the axis of column length. Division of the area by the column length thus gives the true average temperature. It has always been customary to consider the piston in equilibrium when the piston appeared to neither rise nor fall. Since the correct cali- bration of the piston was a matter of primary importance considerable study was devoted to the problem of investigating the sources of error that attend detecting the true equilibrium of the piston. The method finally adopted consisted in observing the motion of the mercury at its junction with the oil at N in the steel capillary A by means of a telephone receiver connected in series with the secondary of a small induction coil adjusted to the proper frequency. The connections of the circuit are evi- dent from the drawing. An insulating joint is provided at / through which passes the pointed platinum wire (p). When the weights on the scale pan 5 are insufficient the mercury will rise in the capillary at N and excite the telephone receiver. If it is desired to confirm the observation the circuit is broken by the injection of a minute quantity of oil by means of the pump D. The weights are adjusted until the removal of o.i gram causes contact to be made and the addition of o.i gram permanently prevents contact. Since the diameter of the capillary was about 0.15 cm. while the diameter of the piston was about 0.476, a motion of 0.1 cm. of mercury in the capillary corresponds with only 0.01 cm. vertical motion of the measuring piston. The leak of oil at the piston, of course, would cause the mercury to make contact even if equilibrium had been attained. The diameter of the hole into which the piston was fitted, however, was only 0.01 mm. greater than the piston and observations on the rate of leak were made. The rate of leak under the calibrating pressures was 7 X io~ 4 c.c. per hour per atmosphere and thus the arrangement permitted readings being taken rapidly and accurately. The average of two sets of the gauge calibrations agreed to about one part in eight thousand. The telephone device was employed in all the final vapor-pressure measurements and an improved thermostatic arrangement, containing the ammonia under measurement, permitted a given temperature to be maintained constant to within 0.005 C. for long periods of time. The real difficulty in making THE VAPOR-PRESSURE DATA FOR AMMONIA 13 accurate measurements lies, however, in securing true equilibrium between the vapor and liquid. To aid in securing equilibrium, the ammonia in the container was agitated by shaking the container during the course of the measurements. The data of other observers in relation to the measurements carried out at the Research Laboratory of Physical Chemistry is illustrated in a Z plot, Fig. 2. It will be noted that the Z function serves well in making evident inconsistencies in the trend of the various observations. \ c A. w < , / ,''""° ^ / / / / A \\ Nv ■ I / / / 1 *\ \\ 8 \^ °^\ + - £ \\ • • • \ • ■ A \ \ \ • Hegnault • Brill X K-Onnes + Davies ■ Faraday ▲ Biumcke Goodenough-Mosher Keyes-Brownlee \" V .\ 10 CO 80 100 120 110 160 180 200 220 Fig. 2. The equations of the vapor pressure are as follows: , j, 1209.88 + z(r, - D 2 , N logio/> = 7.9"2l 2 ~" '-• (29) z = io- 4 [-u-9oi + i.ooi8-io- 2 (r c - r) + 3.2715 -io- 4 (r c - ry], or eliminating the critical constant T c , logio p = - I9 ^- 65 + 16.19785 - 0.0423858 T + 5.4131 - 10- 5 T 2 — 3.2715 • io~ 8 T 3 - (30) 14 THE THERMODYNAMIC PROPERTIES OF AMMONIA The critical constants are as follows: T c = 132.9 C. p c = 1 12.31 atmos. v c = 4.236 cc. per gram. The value given of the critical volume was derived from the vapor and liquid saturation specific volumes by means of the rule of the "rectilinear dp diameter."* The formula for —e, follows from the above vapor-pressure dl equation in its second form and reads: || = />[ 453 ^; 28 - 0.074571 + 2.49282 • io- 4 -r - 2.25987 - 10- 7 r 2 ]- (31) 4. THE SPECIFIC VOLUME OF THE LIQUID AMMONIA Before discussing the experimental data the question of the empirical equation which is to represent the specific volumes of the liquid may be considered. After modifying it somewhat the equation of Avenarius seemed to be the best suited for the purpose. The Avenarius equation reads : v = a + blog(T c - T), (32) where T c is the critical temperature. Any empirical equation must satisfy the terminal conditions of the curve at the critical temperature, and must yield a finite value for the specific volume at absolute zero, assuming that superfusing could, of course, take place to that extent. The equation does satisfy the latter condition, but gives an infinite value to the volume at the critical temperature. Granting its validity, if v is plotted with the logarithm of (T c — T) on a rectangular diagram a straight line should result. It is needless to state that such a condition could scarcely be expected to hold. Since, however, the Avenarius form of equation does rectify the v, T curve to a considerable extent, the pro- cedure adopted for the ammonia liquid volumes was to assume the equa- tion v = a — log (a — T), where a is a function of the temperature. To use the equation it is merely necessary to determine the constant a for some accurately known specific volume far below the critical tempera- ture, arbitrarily assuming a to have the same numerical value as the critical temperature. Values of a for all the remaining data can then be calculated and plotted with the temperature as a coordinate. The curve for ammonia resembles a parabola with a minimum at about 48 degrees. The total change in a is only a few per cent, and its representation as a function of the temperature is comparatively easy. The particular ad- vantage of the method lies in the fact that slight inconsistencies in the experimental data become at once evident. In Fig. 3 the a values corre- sponding to the experimental data of Dieterici and Lange are plotted on * Compt. rend. 102, 1202 (1886); Compt. rend. 104, 1563 (1887); Phil. Mag., 60, 291 (1900). THE SPECIFIC VOLUME OF THE LIQUID AMMONIA 15 the same scale as the Research Laboratory experimental data, the latter being represented by the curve. The dotted line represents the smoothed data as given by Mosher. It is evident that there is lack of agreement between the Lange data and the present work. It is also evident from the figure that the specific 138 136 132 130 128 126 Dieterici • Lange Goodenouj gh-Mosher vmlee > :> - h^— *-* ^-* ** • • • • • •• . »...*• • - * • • • • • • • • • -10 -20 20 40 Fig. 3. 60 S3 100 120 volume curve can be accurately obtained from about five exact measure- ments of the specific volume at suitably selected temperatures. This latter fact led Mr. Brownlee to measure accurately the volumes at the temperatures -33. 5 , o°, 35 , 68°, no°, 120 , 125 , and the full line in the figure is drawn through the volumes found at these temperatures. TABLE 1. SPECIFIC VOLUME OF LIQUID AMMONIA Temperature, C. a from R. L. of P. C. Data Dieterici Lange Brownlee -5° -3° —10 +20 40 60 80 100 120 133-22 132.61 132.06 131-83 I3I-42 131. 21 131-225 131.40 131-775 132-49 I-5656 1.6342 1.7227 1.8250 1-9595 2-1525 1-4375 1.4895 1.5480 1-5795 1-6503 -7383 1.8487 1.9982 1.4227 1-4745 1-5332 I-S657 1.6387 1.7256 1-8331 1-9747 2.1836 2.5891 16 THE THERMODYNAMIC PROPERTIES OF AMMONIA Table i gives a survey of the agreement between the Lange* and Dieterici values and the values based on the Research Laboratory meas- urements. Attention may be directed to the agreement in the value obtained by Dieterici at o° C. The deviations in the Dieterici measure- ments and the recent measurements lie in the direction of the difference between the hydrogen scale and the mercury scale. The two latter scales, of course, agree at the freezing point and the boiling point of water. Without knowing the kind of glass from which the mercury thermometer was constructed it would be difficult to correct the Dieterici data. The maximum difference between the two thermometer scales occurs at about 40 C. and would likely not exceed 0.12 C.f A greater error than the thermometric error, however, would result from the temperature expan- sion of the glass container used and its dilation due to pressure. The latter cannot be calculated but must be determined experimentally, and even then the glass used must be carefully annealed after having been blown. The temperature expansion of German soda glass is about 3.0 X io~ 6 , which gives 0.0021 as the correction due to temperature ex- pansion. The thermometric error amounts to 0.0006 c.c, thus giving a total of 0.0027 c.c. as the amount by which the Dieterici value is too small. Dieterici f gives 1.7227 as the result of smoothing his experimental data. The value arrived at in the recent work is 1.7255 c.c. Correcting the Dieterici value leads to the value 1.7254 c.c. The attempt to correct the Dieterici work at higher temperatures is difficult owing to the un- known stretch of the glass due to the increasing pressure. It will be noticed from the a figure that the Dieterici experimental values become increasingly small as the temperature increases, which would be predicted in fact owing to the pressure and temperature dilation effect. 5. EQUATIONS OF STATE IN GENERAL The state of any substance in either of its three phases may be repre- sented as some function of the variables p, v, and T, but for practical requirements in connection with ammonia refrigeration machines it is the vapor phase which is required to be accurately represented by such a function. The number of formulae§ proposed are very numerous, but * The volumes inserted in the table were calculated from Fig. 3 by drawing a representative line through the Lange values. t See Guillaume: "Traite Pratique de la thermometrie de precision." | Winkelmann, Handbuch der Physik, 3, 965. § Starting with the general equation of the Joule-Thomson experiment (23) the Callendar equation may be derived by assuming n to depend on the temperature; as ■=; , and independent of the pressure. For example: r \ar/p~" _ dT _ ^a_ C p dp ~ M ~ T" ' x , „ , . , . , . T dv — v dT „ a , If C p be assumed constant the equation may be written — ■ — = = C p _ n+2 • Integrating EQUATIONS OF STATE IN GENERAL 17 equations of the general form suggested by Callendar * seem to have re- ceived the preference. It seems not unlikely that this preference may be attributed to the fact that formulae of the Callendar type give the volume explicitly, and such an equation is most convenient in preparing tables of "properties " since volumes at constant pressure are desired. The mat- ter of primary importance would appear, however, to concern the general consistency of the deductions and inferences which follow from the pro- posed equation rather than the saving of labor to the calculator in pre- paring tables of "properties." The history of the subject of equations of state may be considered as included in the much broader attempt to increase our understanding concerning the continuity of matter from the point of view of an explana- tion of the phenomena in terms of the motion of the discreet particles of which the substances are assumed to be composed. Van der Waals,f considerations led him to a rational equation which represented the continuity of the vapor and liquid phases in its general aspects. The equation of van der Waals, however, while leading to many generaliza- tions fails to represent accurately the p, v,~ T relations, even in the vapor phase, with sufficient accuracy. Many of the numerous formulae, for the most part wholly empirical, which have appeared since van der Waals' Avork was published, may accordingly be regarded as an attempt to pro- vide an equation which would represent with sufficient accuracy the p, v, T relations of substances required in technical work. The vapor phase of water for example has received much attention on account of its tech- nical importance, and an empirical equation due to Knoblauch, Linde, and KlebeJ has been accepted as representing the vapor phase accurately within the range required in engineering" practice. The equation reads: BT i) = — P - (i + ap) r c(f^) 3 W0>" Cp a + I T n + l D this equation there results When the temperature is high and the volume large pv = RT may be assumed to represent the behavior of the gas. This identifies /(£) with — ■ P The complete Callendar equation may then be written _ RT a 1 V ~ ~p~~ "n + i T n ' * Proc. Roy. Soc, 67, 266 (1900). f J. D. van der Waals, Kontinuitat, 1872. See also the Yan't Hoff lectures. Note. — The van der Waals equation reads RT a p = r ; , where a and b are constants. v — b v l % Verein deutscher Ingenieure, Heft, 21 (1905). Berlin. Also see Winkelmann, Handbuch der Physik, Vol. Ill, 1 121. 18 THE THERMODYNAMIC PROPERTIES OF AMMONIA This equation represents the somewhat restricted range of the measure- ments made by Knoblauch, Linde, and Klebe, but begins to fail as small volumes are approached.* If ~^ is formed from the equation above it turns out to be a function of p and T. Examination of the Linde data just mentioned shows on the other hand that the pressure is a linear dp 2 function of the temperature which would make — ~ 2 equal to zero. The d 2 t> consequence of — ^ being equal to zero or a function of the temperature is of considerable significance because of its relation to the general equation : (dC\ _ T (&£) \ dv ) T \dTVv -pf~ 2 ) is a function of the volume, [C V ] T must be a function of the vol- ume; but if the second derivative of the pressure is zero, C v is a function of the temperature solely. Unfortunately it is not easy to measure Cf and therefore C p is measured. The general relation C v = C p — T\— ^) •(— ) permits on the other hand the computation of C v only when T[-~\ ■ (— — ) \dl/ v \dl/p is accurately known. The strongest proof of the independence of C v from the volume is therefore at present furnished by the linear increase of the pressure when the vapor is heated at constant volume. * Mr. R. D. Mailey, at the Research Laboratory, has made a very careful study of the proper- ties of water, liquid, and vapor phase, and over a range of temperature exceeding the critical temperature and to pressures above 500 atmospheres. One of the writers has had the privilege of examining the data in the vapor phase and finds the equation used in these tables to apply. This would indicate that equations of the type of the Linde Equation are defective in form. t J. Joly. Proc. Roy. Soc, 41, 352 (1886), (1887); Chem. News, 58, 271 (1888); Proc. Roy. Soc, 45, 218 (1890); Phil. Trans., 182a, 73 (1892), 185a, 943 (1894); Proc. Roy. Soc, 55, 390 (1894). Joly employing his steam calorimeter measured the specific heat at constant volume of air, carbon dioxide, and hydrogen. The measurements of the latter substance were not carried to completion. A. Winkelmann (Winkelmann, Handbuch der Physik, Vol. Ill, 228) discusses the air data and points out that Joly's values are too large from a comparison of the ratio C p /C v . This latter quantity has been measured by a number of observers and the ratio is close to 1.405. The Joly values of C v on the other hand lead to 1.390. The values obtained by Joly moreover seem to indicate that C v is a function of the volume. Consideration shows, however, that Joly's C„ is in reality C v + T\ —\ ~pp+ A.ff, where dv is the sum of combined thermal expansion and pressure expansion of the copper sphere which was used to contain the gas under measurements. The term AH represents a quantity of heat absorbed by the copper sphere containing the gas, which results from the altered heat capacity of copper under tension and also the absorption of heat due to the stretching of the copper sphere when the pressure increases from the pressure at ordinary temperature to the pressure at the final temperature of the steam. The latter quantity is small, but becomes significant at the higher pressures employed by Joly. A note discussing and recalcu- lating Joly's experiments is in course of preparation. EQUATIONS OF STATE IN GENERAL 19 The Joule-Thomson measurements* have been frequently regarded as furnishing a crucial test of the correctness of form or the accuracy with which the constants may have been determined in an accepted equation of state. The Joule-Thomson numbers indeed do furnish a sound basis for testing equations of state, but the measurements are unfortunately most difficult to make and experimenters who have occupied themselves with the problem have not always arranged to carry out the measure- ments in such a way as to yield numbers readily interpreted in connection with the Joule-Thomson thermodynamic equation of the porous plug experiment. For example, while the equation requires the difference in temperature of the gas before and after the plug for a small difference in pressure very often what has been measured is the difference in tempera- ture corresponding to a large difference in pressure. f The Joule-Thomson measurements in the case of ammonia are due to Wobsa.J Wobsa's measurements exhibit the anomaly of making the coefficient n diminish with increasing pressure at constant temperature which would lead to the inference that ammonia vapor compressed at constant temperature approaches more nearly the ideal gas state.§ From measurements of the boiling point of liquid ammonia supplied in wrought iron cylinders it is possible to compute the per cent of water present by means of the Van't Hoff formula. The per cent of water appears to be of the order of 0.5 to 0.7 per cent. The presence of water accordingly in the commercial ammonia employed by Wbbsa may possibly account in part for the apparently anomalous trend in the measurements.^ The Wobsa measurements have been admirably discussed by Goodenough and Mosher and nothing can be added to their treatment until further measurements have been made. * A lucid discussion of this quantity is given in Noyes and Sherrill's General Principles of Chemistry. t W. P. Bradley and C. F. Hale, Phys. Rev., 29, 258 (1909). t Zettschr.f. d. ges. Kalte Industrie, 61 (1907). § An ideal gas is one following the equation pv = RT for which m would be zero. If In a mixture of two gases the constants of the equation (33) for any given constant composi- tion would be a function of the constants of the components. For example, assume that (a) of the cohesive pressure term may be written, where x is the fraction of the first component: a z = ai(x) 2 + 2 a i2 (x) (1 — x) + a 2 (1 — x) 2 , 012 being the cohesive pressure constant for the unlike molecules. If the attraction were large between unlike molecules, as is the case for ammonia and water, an would be many times larger than either a, or a?. The equation (33) used in connection with the Joule-Thomson equation (23) gives for moderate pressures: — -P dT = RT p dp C Po 2d. Now -jt=, is the principal term of the numerator, and in a mixture, a and /3 would be replaced by a-x, fix. From the comment above it is easily seen that a x might be larger for a mixture than it would be for either pure substance alone since ammonia and water have considerable mutual affinity. 20 THE THERMODYNAMIC PROPERTIES OF AMMONIA 6. THE EQUATION OF STATE FOR AMMONIA VAPOR The equation of state used in the computation of the pres- ent tables has already been briefly discussed in connection with a number of other sub- stances.* The equation reads : s a a u & o m £ o Q o t£ 7? r (* - /) 2 (33) The constants of this equa- tion for ammonia vapor have been derived from the measure- ments made at the Research Laboratory of Physical Chem- istry of the Massachusetts In- stitute of Technology. The values of these constants are: logi 5 = 0.98130 R = 4-8i77; 3-Q8 v a = 34610.1; and I = — 1.173. Small volumes and high pres- sures are best suited for the purpose of determining the con- stants since the deviations from the relation pv = RT are great- est at small volumes. In the present case volumes less than 15 c.c. were not used in evalu- ating the constants of the equa- tion above. A number of meas- urements were made at large volumes, but great difficulty was experienced in obtaining accurate data owing appar- ently to the adsorption phe- nomena due to the steel walls of the container. The comparison of the work of other observers may be most * Frederick G. Keyes, A. Journal, Vol. 1, 9 (i9H)- 5. R. E. THE EQUATION OF STATE FOR AMMONIA VAPOR 21 easily compared with equation (33) by substituting the measured volumes and temperatures in the equation and comparing the pressures. It is per- haps better in the present instance, however, to compute the volumes for the measured pressures and temperatures. The result of such a comparison is given in Fig. 4, where the per cent volume difference is given at the calculated volumes. The Onnes* groups of data are substantially at constant temperature while the Perman and Davies measurements are at one atmosphere pressure. Hoist states that the isotherm in the Onnes data at 45 degrees is in error. The magnitude or the nature of the error is not stated however. It is well known that ammonia is adsorbed on glass surfaces to a more marked extent than any other gas, consequently there exists the possibility that the somewhat erratic trend of the Onnes measurements may be due to this disturbing effect. If this were true it may be stated that as the temperature falls, increased adsorption would cause the volume to grow small too rapidly at constant pressure, while heating the glass bulb loaded at room temperature would cause ammonia to be given up and hence give too large a volume. Perman and Davies f * H. Kamerlingh Onnes' "Report of the Third International Congress of Refrigeration," Sept. 15 to Oct. I, 1913. f Perman and Davies, to satisfy themselves that there was no adsorption, measured the density in two glass globes of different capacities. One bulb had a volume of about 0.5 liter, surface 3.22 dm 2 , and the other 1.77 liters, surface 7.10 dm 2 . The ratio of surfaces, accordingly, of the larger globe to the smaller is 2.2 times. Langmuir has measured the total quantity of water vapor evolved in a good vacuum from a glass surface, in passing to 360 C. The globe was a 40- watt tungsten lamp, which has a surface of approximately 1.61 dm 2 , and the quantity of water vapor evolved amounted to 0.3 c.c. o°/76o or about 2.41 X io -4 grams. The weight of water is accordingly 1.5 X io - * grams per dm 2 . If it is assumed that ammonia dissolves in the water film in the same manner as in liquid water, there would be 1.35 X io -4 grams of ammonia adsorbed per dm 2 . If p is the true density of the ammonia, v the volume of the globe in which it is pro- posed to measure the density of the ammonia, u the weight of ammonia adsorbed per square dm. of surface, and s the surface of the globe, we may write: W S Total weight of ammonia in the globe is pV + as = W or p = ^ — u — • Let the subscript 1 denote a globe of radius r\, and subscript 2 denote a second sphere of larger size and radius r 2 , then —^ , the apparent density obtained in the first bulb, is equal to p + w tt W 2 . S 2 T 2 =p + "v 2 - If A is the difference in the measured densities, and, similarly, -rz- = p + - . V 2 VI W, W 2 I 5,\ / , 5 2 \ IS, S 2 \ (1 i\ (a) The value of the density calculated by the equation of state is 0.76994, while the density found by Perman and Davies is 0.77085, the difference being 0.00091 gram. From the equation above, =(f-")s =aoo ° 9i (9- 2 V 1 Now for a liter sphere r = 0.621 dm . Since -= = -r or 0.207, w = 0.000188 gram per dm 2 . ■J 3 The number obtained above by means of the Langmuir datum is of the same order of magnitude 22 THE THERMODYNAMIC PROPERTIES OF AMMONIA work was carried out with the greatest care and the average of two series of duplicate measurements at zero degrees and one atmosphere are in good agreement. Measurements have been made by Dieterici* of the specific volumes of the vapor along the saturation curve. The measurements were made in, 100 150 200 Volume in C.C's. Per Gram Fig. 5. glass f and depend on the accuracy with which the liquid volumes are known. Hoist has also computed by means of the Onnes virial equation (0.000135). Applying the values to the two spheres used by Perman and Davies there results: Ap.D. = 3 "p.d. I' '' rr * j = + 0-000327- (^) = + °- 000235 - u L = 0.000135. w PD . = O.OOOI88. ri = 0.4925 dm 2 . r 2 = 0.7510 dm 2 . = 3«L The difference in the apparent densities therefore would amount to only about a quarter of a milli- gram. In view of the difficulties attending the accurate weighing of large globes it would appear that the detection of adsorption by varying the surface is not very sensitive at one atmosphere pressure and zero degrees. * Dieterici, Zeit. fur die Desam. Kalte Industrie, 21 (1904). f Young, Trans. Chem. Soc, 59, 37, 126, 929 (1891). THE HEAT OF VAPORIZATION OF LIQUID AMMONIA 23 the specific volumes of the saturated vapor,* the constants of the equa- tion being based on the measurements of the vapor phase isotherms ob- tained at the Leiden Laboratory. The saturated specific volumes used in the present tables were computed by means of the equation of state (33). This computation requires the saturation pressures which were determined from the vapor-pressure equation (31). In Fig. 5 the full line is drawn through the computed saturation specific volumes while the experimental values of Dieterici are entered as indicated together with the values com- puted by Hoist. The full line is a representative line through the Dieterici and Hoist values up to about 70 degrees, when the Dieterici data assumes a distinctly different trend. The specific volumes of the liquid obtained by Dieterici on the other hand show a trend in the opposite direction. 7. THE HEAT OF VAPORIZATION OF LIQUID AMMONIA Measurements involving the heat of vaporization of ammonia were made by Regnault, and of these measurements twelve f survived the reign of the Commune and were later published. A careful consideration of Regnault's data involving the heat of vaporization of liquid ammonia has been given by Jacobus and Denton.f Franklin and Kraus§ measured the quantity at the boiling point of liquid ammonia ( — 33.2), their value differing considerably from the value obtained by Estreicher and Schuerr.|| The original communication containing the Estreicher and Schuerr measurements is not available and hence a critical examination of the method used or a review of the data used in making necessary corrections is precluded. The method pursued by Franklin and Kraus consisted in vaporizing a definite volume of liquid ammonia at atmospheric pressure by supplying heat electrically. The calculation of the heat of vaporiza- tion requires the electrical energy, the density of liquid ammonia at — 33. 2° C, and the value of the calorimetric equivalent of the joule at 15 degrees. The value of the electrochemical equivalent of copper used by Franklin and Kraus was retained in the recalculation. The recom- puted mean of the Franklin and Kraus measurements using the latest density data and the 15 degree cal. employed in the present tables accord- ingly is 336.58 Cal. at —33.2 degrees. A confirmation of the general correctness of this value may be obtained from the data concerning the elevation of the boiling point of liquid ammonia. The data in this connection is also due to Franklin and Kraus.H The mean value of * The Onnes equation reads: p,-RT + * + %+ ■ f Ann. de Chim. et de Physique (4) 24, 375 (1871). } Jacobus, Trans. Am. Soc. Mech. Eng., 12, 307 (1891). § Jour. Phys. Chem., 2, 555 (1907). || Acad. Soc. Cracovie, Bull., 7 A, 345 (1910). H Am. Chem. Jour., 20, 841 (i£ 24 THE THERMODYNAMIC PROPERTIES OF AMMONIA k in Van't Hoff's formula I L = — — *-— J , taken from the elevation of the boiling point where water and alcohol were used as solutes, is 3.398. The Van't Hoff formula leads to the value 336.8 Cal. as the heat of vapor- ization at —33.2 degrees. The value obtained by means of the Clapeyron- dp Clausius relation, T -jL (vi — v 2 ) = L, where the quantities on the left of dl the equation are obtained from the vapor-pressure equation (30), the equation of state (33) , and the equation of the liquid volume, leads to the value 336.5 at —33.2 degrees. The equation relating the heat of vaporization of liquid ammonia to the temperature depends on the heats of vaporization calculated by means of the Clapeyron-Clausius equation from the data obtained at the Re- search Laboratory. The value of L was computed at 8o°, 40 , o°, and at — 70 C. The value of L at —70 degrees, on account of the uncertainty of the vapor-pressure equation at the lowest temperatures, cannot be con- sidered to possess the same relative accuracy as the values of the heat of vaporization computed for the higher temperatures. The values cal- culated, however, at the temperatures mentioned were related to the temperature by means of a modified formula due to Thiesen. The Thiesen formula connecting the heat of vaporization with the tempera- ture is L = C (T c — T) n , where c and n are constants and T c the critical temperature. The equation satisfies the current ideas concerning the ter- minal conditions of the curve (L, 7") — namely, it yields a finite value of the heat of vaporization at the absolute zero and a zero value at the criti- cal temperature. Taking logarithms of both sides of the equation there results log L = log C + n log (T c ~ T), consequently the logarithm of L is a linear function of the logarithm of log (T c — T) and ,, - = n. d log 1 The equation was not found to hold strictly for liquid ammonia although it does satisfy the values very nearly. To modify the equation it was as- sumed that the differential could be expressed as , — = a + b (T c — T). d log T The resulting equation was then integrated, yielding the equation log 10 L = 1. 568 1 7 - 2.822 • io" 5 (r. - T) + 0.43387 log 10 (T.-T). (34) The values of L calculated by the latter equation together with the Regnault- Jacobus and Kraus values are given in Table 2. Gilles Hoist,* in a recent publication concerning the properties of ammonia, computed the heats of vaporization of liquid ammonia from Regnault's data, using the more accurate Dieterici specific heat values now available in computing the corrections. The average temperature of Regnault's twelve measurements is 11. 68° C, and the rate of change of the heat of vaporization with temperature may be taken from equation * Gilles Hoist, Les proprietes thermiques de Vammoniaque et du Chlorure de methyle, Leiden (1914). THE HEAT OF VAPORIZATION OF LIQUID AMMONIA 25 (34) to reduce each of Reghault's measurements to the average tempera- ture. The result of this averaging is 295.7 Cal., whereas equation (34) leads to the value 294.3 Cal. at 11.68 degrees. The average Regnault value is accordingly 0.5 per cent higher than the value derived from the equation. TABLE 2. VALUES OF HEAT OF VAPORIZATION L Temperature Calculated by equation (34) Observed Percentage difference Observer -33-4 336-7 321-3 -4.58 Estreicher and Schuerr -33-2 336-5 336.6 +0.03 _1_ Q S Franklin and Kraus measured Franklin and Kraus from ebul- -33-2 336.5 336.8 + 0.08 lioscopic constant — 23.71 328.I 316. 1 -3-6 ( -19-55 324.5 335-t +3-2 Regnault — Jacobus — Denton - 9.72 316.0 3I7-0 +0.3 I 7.80 298.4 293.0 -1.8 9-52 296.7 295.0 -0.6 10.15 296.0 292.4 — 1.2 to. 73 295-4 288.1 -2.5 10.90 295-3 287.0 -2.8 10.99 295-1 293-3 -0.6 11.00 295-1 291.3 -i-3 1 1 .04 295-t 292.5 — 0.9 Regnault — Jacobus 11.90 294.8 285.8 -2.9 12.60 293-5 291.6 -0.6 12.94 293-1 283. 8 -3-1 15-53 290.4 285.2 -1.8 16.00 289.9 294.0 + 1-4 17.00 288.9 296.8 + 2.7 19-53 2S6.0 296.5 +3-7 ' 28.18 276.4 292.0 + 5-8 f 29.22 275-4 291.8 + 5-3 Regnault — Jacobus — Denton 30.92 273-4 285.0 +4-2 { Hoist in his summing up of the properties of ammonia has computed the heats of vaporization by means of the Clapeyron equation, using the specific volumes of the saturated vapor based on the Onnes "virial " dp equation of state and using values of — ^ derived from a careful study of Regnault's vapor-pressure measurements. Table 3 contains the Hoist values compared with the values computed by means of equation (34). TABLE 3 Temperature Computed by Hoist Computed by equation (34) Percentage difference -40 328.5 34L98 -3-9 -3° 322.5 333-62 ~i-$ — 20 316.0 324-86 -2.4 — 10 309.0 315-74 — 2.1 301.4 306.01 -i-5 + 10 293.2 296.OI -0.9 + 20 284.4 285.49 -0.4 + 3° 274.8 274-43 +0.14 + 40 264.2 262.67 +0.67 26 THE THERMODYNAMIC PROPERTIES OF AMMONIA Regnault's values of the vapor-pressure were perceived to be low by Hoist, and it is now known that the corrections applied by Regnault to his mercury thermometer below zero were in error. This circumstance would make uncertain values of -= resulting from the vapor-pressure curve dl and also the values of L calculated by means of the Clapeyron equation. A glance at the Z diagram makes evident at once the erratic trend of the Regnault data. Accurate experimental values of the heat of vaporization of liquid ammonia are necessary in the temperature interval between o degrees and 20 degrees; however, the Franklin-Kraus value at the boiling point and the mean Regnault value at n.68 would indicate that equation (34) represents the heat of vaporization with substantial accuracy. 8. THE SPECIFIC HEAT-CAPACITY OF AMMONIA VAPOR The measurements of the specific heat-capacity of ammonia have been reviewed by Nernst* and the results summarized in the equation: C„, 1 atm. = 8.62 + 0.002 t + 7-2 • IO~ 7 P. (35) The equation gives the heat-capacity for one formula weight or 17.034 grams. The equation of state (33) applied in connection with the equation C v = C p — T( — 7j\ ( — j leads to the equation for C v as follows: C v = 0.35116 + 1.055 • icr 4 T + 6.05 • 10- 8 T\ (36) Accordingly, the specific heat at constant pressure is given by the equation c P = 0.351 16 + 1.055 • icr 4 r+6.05 • 10- 8 r 2 + 7 * . — - 2 , (37) 1 "" vV ~ RT (v - iy v — S I 1 \ since (fr). = (^h) and (if. T / aS\ 2 a (v - S) 2 \ \V v 9 -) RT{v-lf! The quantity / C p dT or the integral heat along a constant pressure curve must be obtained by integrating graphically the term RdT / _ aS\ 20, (V - 6) 2 ' V vV RT(v-l)> Fig. 6 gives a picture of the C p field. At high temperatures and low pressures the equation (37) tends to resolve into C p = C v + R as in fact the diagram illustrates. * Zeitschr. f, Electrochemie, 16, 96 (1910). THE ENTROPY OF AMMONIA VAPOR 27 0.8 0.7 0.6 0.5 400 Lbs J SF ECIFIC h EAT OF AMMONIA- GAS PHA SE 50° i\ \100°F 150° P. 200 Lbs. '^SOTF 2°° F ;3oo^ f. 1( 50L OLbsyC^^ 3Sy/^ j/ y y '/^ ^^OLbs. -100 100 300 400 500 Temperature Fig. 6. 000 700 800 300 9. THE ENTROPY OF AMMONIA VAPOR Equation (14) gives for the entropy $ = J -jr- + R J J^ZT^) + * ' The main difficulty that arises in the use of this equation is the integra- which contains the transcendental 5. Up to the present tion of dv time no integral has been found for this expression in terms of ordinary functions. One method, however, of integrating the function is as follows: . assume I = log (v *~ 8) + afi I — • 7 J v - 8 s J v 2 (v - (38) •j_ e "dv 8 ° ■ J v 2 ' {v - 5) The problem now is reduced to the integration of the second term of the right-hand member, and since d- = dp = - -dv it follows that It can be easily shown that the series part of (38) converges for all values of the variable p. 28 THE THERMODYNAMIC PROPERTIES OF AMMONIA Let e"* = z, whence rpp , flog z , J^ dp = « 2 J* dz ' and integrating this equation in z there results r(logz) n , _ _ ri /log z\" i / log z V" 1 i: w - i / logz) \"~ 2 £ J z n+1 """' \_n\ z ) n\ z I z n 2 \ z ) z 2 , (»- i) (w - 2) /logzy~ 3 i , , , , . + i y v. — S — y ? + ' ' ' ° {n + } terms - (4o) Applying (40) to each member of the series, collecting and rearranging, leads to the expression 4J>+ ■]-H'-U. (n-i)l + (k+~k 2 + \ 2-2 p(-k + —k? + - ■ ■+ r J ^-k") \2 3-3 (n+i)" / V3 2 4.4 k 2 + («+i)! T 2 !(« + 2)»- K ) / I & + -1) m) n Vm + 1 (n + m ! (rc + kA , p logz , /? I where p = - ■ — 6 - , & = a Z Table 4 represents the values of these series terms for various values of the density p of ammonia. In spite of the somewhat formidable appear- ance of the series portion of the integral it is seen that the series converge with such rapidity that the labor of calculating is not excessive. The computation of the series at 25 c.c, 50 c'.c, 100 c.c, and 500 c.c. is suffi- cient, since beyond 500 c.c. the series gives a constant. In practice a plot of 2/(p) is most convenient. The complete expression for the entropy may be written as follows: $ = 0.80859 logio T + 1.055 T ■ io -4 + 3.025 T 2 ■ io -8 + 0.2688 log.o (»-«)+ RZJ(p) + $0. (41) For volumes greater than 200 c.c. per gram RHf(p) may with sufficient accuracy be assured constant. THE SPECIFIC HEAT-CAPACITY OF LIQUID AMMONIA 29 TABLE 4 p=o.o5 p = 0.02 p = O.OI p = 0.002 p = O.OOI p = 0.OOO2 Series Equation Above 1. 26177 0.27012 0.07114 0.02026 1.7069O 0.02732 O.OO4O7 O.OO063 O.OOOIO 1.9020 0.00935 0.00077 0.00006 2.0802 O.OOO42 O.OOOOI 2.1057 0. OOOI I 2.1241 k series p series p 2 series p 3 series p' series p* series p 6 series p 1 series '«(-£) 0.00608 0.00055 0.00016 0.40939 O.I9587 O.18182 O.I 2 140 O.OQ344 0.02904 0.01909 0.01465 0.00956 0.00297 0.00192 2.04122 2.II67I 2.12702 2.12876 2.12902 S/(p) 10. THE SPECIFIC HEAT-CAPACITY OF LIQUID AMMONIA In carrying out accurate heat-capacity measurements by the method of mixtures, it is necessary to have a large difference of temperature be- tween the thermostat and the calorimeter, in order that the resulting temperature-change may be sufficiently large to permit the necessary percentage accuracy. There is considerable difficulty involved in obtain- ing the precise value for the water-equivalent of the calorimeter, and also in obtaining the value of the specific heat of the steel container or other receptacle containing the ammonia to be experimented on. The following method of measuring heat-capacities was suggested by Dr. Charles A. Kraus of the Research Laboratory. A steel bomb con- taining liquid ammonia under the pressure of its saturated vapor is brought to a constant temperature in a thermostat above the calorimeter; it is then dropped into a calorimeter containing a definite weight of water, and the temperature-change of the calorimeter is observed. Another steel bomb identical with the first, but containing water under the pressure of its saturated vapor, is placed in the thermostat and dropped into the calorimeter. The weight of water in the water bomb is adjusted by repeated experiments until it gives practically the same temperature- change as the ammonia bomb. Omitting corrections, the specific heat- capacity of the ammonia would vary as the ratio of the weight of water to the weight of ammonia multiplied by the heat-capacity of the water. This method does away with many of the objections to the method of mixtures. It is, of course, dependent for operation on a large tempera- ture-difference between the thermostat and the calorimeter, but the errors are the same or nearly the same for both the ammonia and the water experiments and consequently compensate. Mr. Henry A. Babcock after having completed the measurements of the specific heat-capacity by the method already outlined undertook the development of a method which would permit the measurement of the heat-capacity over very small temperature intervals and at various tem- peratures approaching the critical temperature. The method consisted 30 THE THERMODYNAMIC PROPERTIES OF AMMONIA essentially in rotating a steel ammonia container submerged in oil in a silvered Dewar tube. Measured amounts of electrical energy were intro- duced by means of a combined platinum resistance heater and thermome- ter. The amount of energy necessary to heat the oil and container was determined at a number of intervals between 20 and 120 degrees. The electrical energy necessary to raise the apparatus through one degree with the ammonia present was then obtained. The heat capacity of the 1.35 p 1.30 /- SPECIFIC HEAT OF L IQUID ANU IONIA KEYES AND BABCOCK D. DATA DUE TO DIETERIC1 AND DREWES ^1.25 '3 OS a O +-» von S. VON STROMBECK VON S. • W 3 0, to 1.20 D. / D / f D. D. 1.15 D. 4- /-fD. ^D 4-D. -fo- be a .£.... Ludeking & Starr A 2^ . . Drewes 2>.6>. . . . Drewes 1. 0.4\ . . . von Strombeck I J 3 ... . Drewes I %'h. . . . Drewes Ir^Q . . . PART II TABLES OF THE THERMODYNAMIC CONSTANTS OF AMMONIA DESCRIPTION OF THE TABLES Table I gives the thermodynamic properties of saturated ammonia with the temperature as the argument, while Table II gives the properties with the pressure as the argument. The lower limit of the temperature table is — ioo°F. ; the values being tabulated for each degree to 150 and to 200 for each five degrees. The pressure table (Table II) is complete for every pound pressure from five to two hundred pounds pressure, from two hundred pounds for every two pounds to three hundred pounds pressure, for every ten pounds to five hundred pounds pressure, and for every twenty-five pounds to seven hundred pounds pressure. The superheat table (Table III) gives the temperature, the total heat of the liquid, the vapor volume of liquid and vapor, and the entropies of the liquid and vapor corresponding from the saturation pressure to four hundred pounds. The total heat, the volume of the vapor and the entropy of the vapor is extended into the superheat three hundred de- grees, every ten degrees of superheat being tabulated to two hundred degrees and every fifty degrees from two hundred degrees to three hun- dred degrees superheat. In calculating the various quantities appearing in the tables large graphs were constructed from the values calculated from the equations already discussed. The vapor pressures were calculated corresponding to each 18 F. interval using equation (30). A check on the values tabulated from the graphs was subsequently obtained by calculating the pressure at temperatures nine degrees from the pressures which served to construct the graph. The heat of the liquid was obtained by calculating the values needed for the graph from equation (43). This equation is obtained by inte- grating equation (42) with respect to the temperature. The values of entropy of the liquid are given by the equation which results from the integration of (42), after first dividing by the temperature. A general check on the values obtained by the method outlined was subsequently obtained by calculating the rates of change of the quantities from the corresponding equations which result by differentiation with respect to the temperature and comparing these calculated rates of change with the successive differences of the tabulated quantities. The volumes at constant superheat (Table III) were calculated at suitable intervals from equation (33) and their reciprocal, or the density plotted against the saturation pressure. The resulting graph is nearly 34 DESCRIPTION OF THE TABLES 35 a straight line which greatly facilitated the reading of the densities. The densities were afterward converted into volumes by means of a table of reciprocals. ~~The total heat was obtained by graphically integrating the graph of the specific heat-capacity of the vapor plotted against the temperature and adding the quantities so found to the total heat of the saturated vapor. The graph of the entropy of the vapor was calculated from equation (41). The consistence of the superheat table was checked by applying the -~\ = -£ in the following manner: Values of C v were calcu- dl/p 1 lated for the vapor and compared with the differences in the total heat quantities at constant pressure. These values divided by the average absolute temperature were then compared with the differences in the tabulated entropy at constant pressure. The Mollier Chart. — The solution of many refrigeration problems is greatly facilitated by the use of the usual heat content-entropy or Mollier diagram. The diagram accompanying the tables, I, II, and III, has curves at constant pressure, curves at constant quality, and constant temperature. The ordinates are heat contents and the abscissae are entropies. To bring the diagram into convenient compass oblique coordinates have been used. The horizontal lines are lines of constant heat content. The oblique lines are inclined at an angle of thirty degrees to the hori- zontal axis. Attention is directed to the fact that twice the vertical distances are equal to distances along the oblique lines. 36 THE THERMODYNAMIC PROPERTIES OF AMMONIA M M CN *& IflO r-»co o « H-'O O M IOCO H ^"O0 (>.•* HOO i^ c* OO ^w CO v)« ON "?*•-* O^O CO mmmOO O^OnO^CN *COWNN £•£* "£"£*£ hJ|H Tf O f- *+ O oo oo £>• r-* t-* LO tN >0 rf hcOvO O O O O O O Oco oo 00 co r* t>. £-~o >OvDO wio dOtCNMM MMMMM MHMMM H M H M M ;;::; \ \ '. '. \ d d " d d' : : : : : : : : : : Mill Mill I l I I I I I I I I iOCO O w -t \0000OCO O N t O CO O O) ■<+ co to -^- •**• -"i- -j- tJ- io *o to to loo o o O o r-* r^ r~- OOOOOOOOOO COCOGOCOGO OOOOOOOOCO OOOOOOOOCO ^j- -^- -^ rj- -tf- «i- "* -=*• ■* **■ ^ ■* rt- Tj- ^ ^■'ti-i-^ Nfoa-t O" -rf- O tJ- o to cow OO O h n n c^i 1 tJ- too O r- coco OO H NfNCO I*) O ^j" O LO M \Q io«ti"^ O m O OCO N<0 ini" W) ci >-i O O O (nmmOO o O OCOM r— j>- c— r-* r-- t— t-- r— o O .'O'OO'OO o O O O lo o o o o o i^i^iri ioin inioioioio iooN O m co 'd'O r— O m CO r-O "* N w o Oco r- \o incoN h O O Ooo 00 COoooooooo coco nnn c-» r- r-~ r-* r-~ i i I i i I I I I I i I I i i i i i i i <\> go O r^ t^ Q -i io m O h lOfONn too r-* O *h fO -^J- c-o (n n O O i-< « O M C>Q M IN Tf <0 ^- ^" •=!• ** OOOOO -t-^ COO too O to m oo lo to M^t^-Mio h MOfOto >ONO N lo COOtOOO 0)00 (O-O O ^ MMMtNoI toro-^j* LOO C^. t^-00 COCO CO O0^00\ OOOwih mcJcJco<0 fr- ill I I I I I I I I I I I I I I I I I Mill I I I II TABLE I 37 1 a W -& M TtOO H m o o o o CI CI CM Cl CM r-* co O r-. ^ CO NO T|- M O- On On On OnOO M W M M M CCj > JIH 'O to O- to ^h q\ n-co co w O Os t> tJ- ^f **■ CO <0 CO h On r^NO co con w r-» O0 CO £>. t^-NO CO CO co to CO IO Tj- CO CNt M CI I-- CI t^. CI ■o to to Tf -5f co co CO CO co CI CI CN CI ct t>. ci t^ cn r-- co co ci ci w CO co co co co co toNO i>-00 .ci (-* ci r^ ct •h O O On On co co co ci ci m co to r-» CO cooo coco oow n r^.NO Cl Cl Cl o cn On rf- co co co oi H M W H M CI NO H to On 1^- rh ci O'NO CS CI CI M M M M M M M ^+- On fOOO Ci tJ- m OnnO tJ- H H O O H M H W H !>. coco cooo M OnnO -*■ w O Cn On On On w O O coco coOO co ONNO rf M On oo co co oo r-- O o 1 1 1 1 1 o M M 1 o M M 1 M M 1 o M M 1 6 M M 1 3 c CD C o a > D •O 00 O W "-vO to rt- IO to to to to co Csi m O On tJ- Tt ^- -^- co io to to to to oo r^ j>-no to co co co co co IO to to to to tJ- CO Ol M co co co co co io to to to to a - 3 M 6 O (OO On ci i^- r^. o c^ to 00 O ci toco co toco O CO to t^- CN to r-. «n ^h i w Pi H W W H r-- r — i: — r-~oo CO fO co CO CO TO to to to U") CO 00 O On On co co co co co io to to to to On O O O CO Tfr- ^t Tf ^J- io to to to to M l-l H M CN t "*■ Tt- Tf Tt io to to to to Cl Cl Cl CO CO •>*■ -SJ- ^ Tf T|- io to to to to CO co '*' ■* Tj" ■^ ■<*■ "* "*■ Tf lO to to to to j iono 00 O w C* CO tONO t*- ao h n no [MM ■<*• CO *■ M M 1 r-^NO tO HJ- CO rj- ^ ^- 4- rf M M 1 ci ih OnOO r- ■*" "^ co co co M M 1 c si 5- m| > onoo o oo co ci *-* m r-^ M co "^T'O t~^ lO io to to >o O O O O O tJ- OO cn O NCO fO0 ^ I/TO NO NO 'O O O o o CO O f* t^NO CO M CO NO Tf N c> O ^ it ^O O i^ r^ t~* O o 00 On CO O NO OO O CI Tt t^ f^OO OO CO O O O O O *+ O On On Cl CO to to f-* NO CO CN) H^ CO CO On On On o o o o o On -3-no to NO\H Hf-O On ON O O O O O M M M O o O o °£ ^ u O 4» > P. ail CO > t^ t-*o0 co 00 to co - ■«*■ H OnOO CO On m f^ tt m CO O ci to on "^r nO co O f*. to CO O CO no co OnCO 00 r» r- H M H M M NO NO nO to tO M H M M M Tt ^t ^- co co M M M M M CO CI CI Cl M H M M M M M M IH O H IH M H M O On On On M IH a* m JH P. CO CO "3"nO On 00 Cl o O ■*■ M conO O ^ O "1 « H ON'COOO COCO Tt00 M O O ci tt o- COCO COCO co IN to W On M NO CO M IH ON ^ NO CN O Cl CO Cl IH Cl io On to OO ■"*■ no co ^ - OO CO On On O O H N « ,VN CN Cl CI CI CI co -d" to ionO Cl Cl Cl Cl Cl t^ t^-OO On On O Cl Cl Cl Cl P. El S 1 Ih - OvOO r->o CO N N « W 1 1 II 1 lO"t COW H N CN C( N CN 1 1 1 1 1 O-CO t-^o M M M M M 1 1 1 1 1 IO ^ CO CN H M M IH IH IH 1 1 1 II O OnOO r-^NO 1 1 1 1 1 tO ^ CO Cl H 1 1 II 1 38 THE THERMODYNAMIC PROPERTIES OF AMMONIA s a O > •& i. 1872 1.1850 1. 1828 1. 1807 1. 1785 ro hi ox f- to r-~ r-* t^o O H HI H HI HI rj- cxi O OxOO to co m CO xO xO O xO to to HI M M HI HI I"- r^o ^ co tJ- CN CO O to h)IH O tOO ■*** nj - OX ft O *0 ^ n « w 01 t-~ O ft t^» hi O xO H XO CN ft CO CO CX| CN (N CN CN CN CXI -o ta-t r^ coco co ox M ,M O OX 01 • CN 00 co Ox ft r-^O O lo to to hi r-. ft M O O h r^ co to ft *t CO co HI HI HI HI HI 3 '3 a* 4^ 00 coco o r^ r-- r-o q 1 1 1 I 1 ft Ox to O O ■tH ©N't xO xO to to to q 6 Mill . bo Cu a t? NOlO « ^ n w row) wj On Ox Ox Ox Ox ■<*■ "*• "t Tf ft toxo 00 O cn CO co CO ft ft Ox Q\ Ox Ox Ox Tf ft ft ft ft co rf-xo r-^CO ■* tj- rj- -*■ to to to to to to Oi O O^ O^ Ov TT^-ti-'t O f- Ox O H to to too O Ox Ox Ox Ox Ox ft ft ft ft ft CN CO tOO t~~ ^O <^ ^ O m M n co ft M O- r-* r^-xo xo to to to 10 to CN CN CO CO CO r-O to Tf co ^ ^O ^ ^O '\0 to to to to to rt to tOO l~* CN HI OxOO O O O to to to to LO to to 00 CO CO CO Ox r^O to ft co to to to to to to to to to to c S'3 8.2 a to -0 LO co <0 CO CO ^O 1 1 1 1 1 O OxOO l^xO r r r t r to ^t CN HI O ? T M 1 Oxoo r— ^t Mill co C-l m O Ox M II 1 00 xO to ft co 1 1 1 1 1 w i> ox to Ox to CN CO H CI \Q Ov O M M M M CN ^NQ CO CN Ol CN CO CO M CN COO O Ox CN IOCO CO CO ^ -Sf •* O Ox CN O O H i-C/D H IO to to too O to hi r~- co 00 cn to Ox co r-~ r-- r^co CO to ft 00 CN CO Ox Ox Ox O O O O O 0) > ft ft±i > co r- r-00 Ox m ox r^ to co cn CO O to 'O Ox COCO co CO hi CO I>- -tO O Ox HI Ox to cn 00 O to Tt CO H. O rt M HI O CO co hi ox r^-O OxOO O to -t cn to ox r-»o to ft co co co CO cn hi Ox OxcO 00 00 co COCO NNN r-. i>* r--o 00000 to to to to to to to to to ft K ft & N W) O J>-0 10 co 00 O ft M hi 5 CO co h -4- Ox t^-O O to "sj- r- too -0 H co LO O CO « Tf OMO tN Tf NO OVH cj o Tl- IN -+ « oooo On t— lo CO "N O0 O ^ co tS fN HI M M w M 1-1 o o o o o o o o M H M M l-H M H M M M M M M M M HH " HH «„H H l-H H as 1/1 CO NO LO VO Th Th 00 -+ O O M t^ fo a> "t O O NQO Tt On lO M c— to On to ON KlIH CN C| nO OO ci Tf- r-- On ci -1- I-- On IN ^t "*• CI IS ^t r- On hi n)0 lo n On Ci H roiT cr -& 8 8 8 8 8 8 Q M M H O O O M CN CI o o o CN CN o o in ro o o ro fO to o ■3* Tf «* "t lO o o o o o to o lO lO O J o n o 1 I + On On hi co co LOO \0 00 O hi w cn co t(- loo NCO H Ci co t)- lo *0 «00 CO CO O no t*« f"- f*- On On On On On ^1- "* Tj- Tj- -Tj- N N l>- NCO CO 00 OO CO 00 OnOiOnOnOn ONO'OnOnQn «* -*■ rj- tj- r)- Tt-Tj-Tjrrj-"^ OOOOOOCOOn OnOnOnOnOn Ov On On On On OnOnOnOnOi O 1 On On On On On On On O On tJ- Tf Tf Tf Tt- CI HI HI CI OnOO ^- -t-- r — o o *o to lo Th co co co ci H On O-CO OnOO NO lO On On On On On Tt" Tl- Th **• ■* tJ- co cn m O CO no >o t|- OnOnOnOnOn OO OQQO OO CO rj- -^ 'H- rf rf "1-rtTl-rJ-T^ co ci m On 00 CO CO CO n ■* *fr Tf Tf ■*- oo no to tI- n n n n n Tl* -* Tj* Tf Tj- CO N OnOO n n r-vo no rj- tJ- ** Th ^ c I 8 - i o <5 wiNOO ci CO «OnO 00 On M co loo r~- CO O m ci co io r— co On O M (N CO Tf LO o O O w m VO LO lO *0 LO LO -no lo *d* co CO "i CO Ct CS (NINC1CICI LOLOLOLOLO LOLOLOLOLO co ci i CI M o > I I + Th lono co O CO ^ LOO CO Ct co lonO t— On O On m Ci co ^nO i co lO -00 c5n r— go h co Th lo r- On HI CI CI C4 tM C| m r~- ci co lo 0O « NHVO ci co co ^ ''t CI CI CI CI CI COcoOOnOn incOnC loo rOTj-LOLz-jO COCnmcolo CO N^O iCt COCICNMO IHMM fO IO O CI N, N N't H O MClTfOON j^^m omo>ni^ coco itO ^ cicO'tOO TO O r-» f--co goonOn OOhicici cocotJ-lolo iciCici cictcicici cococococo cococococo CA-t OCO0C OnciOciOn CO CTh ^N h N -t W pi r- co loco i-i loco ci lo cn coco no m lo lo O On OnOO l^-O OLo-^-rl-co CICIMMO 0On OnOO 00 Tj" Tj* Tt- -+ tj- •t'tt^'t cococococo cocococ cococococo CociCiCitN (bo MMcot^Tt coloOnloco -t Nroo O co OnOO O lo O LO O LO hi 1^- CO OnO CO O f- LO CO Hi On t^O O LO ■4- lo r~-c6 6 r-- r— r~- t^-co Tf tT Tf -*■ -* 4 o THE THERMODYNAMIC PROPERTIES OF AMMONIA >. o c o ft a) > ■& CO H TfNO CO Moron O MD ^O 'O O O O O fOO On Ol IO O CO NO iO ro NO to to -1IH Ol 01 CO rf tO iO m t-» co O Q On O- 00 O O On On On NO r-co On O to m i>- ro O COCO NNN On On On On On m M ro *nO NO On CO cn rj-NO NO co On IO w ■^ ^ co (O co On On On O- On CO o "^ -st-o NtOO Cf CJ tN Cl M M On On On On On "" O O O '3 2* -fr NO On H CO tO CO LO00 . t^.00 CO O O O NOlH WN-t to l"*. O *N * coco aao O O O O no CO O oi -3- nO CO m co to On On O O M HH M tO r- On m co N Oh tJ-n£) O M H M + o o J3 CQ bo C « c u P r^.NO to *■ -tf- ro <0 ri h OnCO J^\0 to rt CO h O On CO f^NO to rt- S S? 1>.nO to Ti* co NO NO NO NO NO t t "* t -t CN H O OnCO nO no no to to Tf * tJ- rj- ^f NO to tJ- ro cm LO to IO to LO ■* T(- * * * m O OnCO nO * * 4" * * to "d- ro oi m ■+ 4 ■* * 4 4" Tf 4- * * c 4) c o o 5 > 5 6 NO t^-OO On On O M w r-i ro Tf tf IO tONO NO r-cO On On H H N fO 1 H < W 0< S w "*• •* "<*■ * -+ lO to 0 LO to to "O U-) IO to IO 'O to LO to to to IO LO LO IO LO IO LO to to to LO IO to LO to to to to IO to to LO to to to to LO to to to to NO NO NO NO NO to to to to to to to to to to _1 j u 5 tA *^fOW« m O'CO t— NO to * ro OnO CO co CO tO CO + ro ro tj- -<3- ^h rO -^-nO I^-CO * ^ ■* ■* * On O M CO * tj- to to to to tONO t-^oo O to to IO tONO 3 u mj £• COCO tJ- w Q rO OnnO to O NO NO r^OO On co co co to to CO t^CO On PI NO (O O t^ to Q. Q M |_ cv ro * * * * NHCO t M ci t^ to ro CO *+ Tf lonO * * 4- * * O oi to to O M QiMO* r- I>-CO On O ■st- * 4 "^ to COCO tJ- 00 CN O ONN m oi ci ro "^t" LO to to to to O O o 3 i 3 > 3. > oi ^- t-» "st" ioO "iw'O r* C-»nO no to oi i-» ro On to to **■ r}- ro ro M ct fONO On h-1 1^ CO On to ro oq o M m ro r- ci co tJ- oi 00 to m co w O O On 01 O On On On to 01 CO to Ol On OnCO CO CO N M CI a IN M (N W W N - c^. r^ w CN CO * CO CO co CO co TABLE I 4i >> p. s c w R a) > ■& CM VO LO O N UTt N (H N N N N OOOOO f)NH WIN On t^-O ■•* CM M M M M M 00000 OIII 0095 0079 0064 0049 COCO COCO CO CO h °0 f— O O On On O On On co cm r^ h no IO -^ CM M 0\ On On On OnOO On On On On On d > ►JIH 00 roo o> CO lOH NfO O O O O On On OnOO CO CM tOCO On CI no CM CO to OnOO 00 nn 00 CO CO 00 00 lOCO H to On m Nt)-OnO 1>.nO no no »0 CO CO CO 00 00 CO OnnO cm CO tO ■<*• itf- ^|- CO 00 00 CO CO 00 wjnh wa lOHCO ^0 CO CO CM CM CM CO CO CO 00 CO O '3 ■& -^-vo ts ao 00 O « -tN h-l CM CM CM CM m cm ro -rt- to O^H fO>ON CM CO CO CO f> NO r^OO On O On m ro toCO CO *t- tJ- rj- rf O h w ret cm *frNO CO to to to to to tO IO NO NO *"- O CM ThNO CO NO NO NO NO NO O m c 1) c 0) a p. 5 D i->oio \no no O f*» t-» *-*■ CO CO CO 00 CO CO CO CO 00 00 00 co co 00 r^ OOOOO V) 1/1 10 I/) 10 00000 to to to to 10 00000 to to to to to 00000 to to to 10 to to to to to to P CM M Q\ £*-VZ> to co cm O CO t-^NO *ej- CM M OnCO NO ■«*■ CM M On (^ to CO a O On r^O to ■3- ^ ■* <*■ ■* ■^- (O CI H On co <~o co co cj -^ rf Tt -*■ -* CO J^nO to ■"*■ CM CI CM CI CM •^- Tj- -3- *fr •+ CM H O OnOO CM CM CM M M ■* "d- Tj" Tf Tj- r^ to t}- co CM ^■M-Tj-Tl-'t a 3 O rt > rt'o a CO "!J- **■ to 10 to to tONO NO NO NO NO NO tO 10 to to to 10 Tt "^ CO CO CM 1 w » < w H H no NO nO >0 no IO tO IO LO *0 IO 10 lO to 10 NO NO *0 NO NO 10 o to to to to to to NO NO NO NO NO to to to to to to 10 to >o to NO nO no NO NO to to to to to to to to to to NO NO NO NO NO to to to to to to to to to to ►J ij n co r^ to "tNO ©N to •* cm 00 nO to fO m On r^ to cm 00 IT) vf- CN M O O Oi O O O ■^- ^4- -^- -^ ^J- O>00 N^4, CO CO CO CO 00 -d- rj- -*■ f-NO to *t CM r^ f— 1^. r-~ r^ ■+ ■* ■* t ■* M O OnOO no r-* r-->0 NO no tJ- tJ- •* rt •*■ g' 3 ffl 6 CM TfvO CO O h f^mso> M CM Tj-NO I>- On O CM tJ-nO t^- On M CO "^J" m CM co tJ-no \0 O O O O r-CO On O M >C\OnO NN CO ^t »OnO t^- t-^. r^ i>. t^ t^ CO O M CM CO r^co 00 00 00 rf to r^co On 00 co co CO 00 Q " ~\> miCT rots tOMD l>.CO O IO IO LO *0 to 00 rh co to c- W N IN M N H CI fO "^t" nO no no no *o t-^NO On to On CM ro CO "^" to tONO l^-CO On NO NO NO O NO r^co O m cm O M CO *+ 10 r- r-- t- t^ l^. CONO t-^ On CM no r^co i-< r^. r^ r- r*.co O 3 . °.£ ai > P. d±; GO > O O CM ^ *~* 0\N^ H0O r^ 1^ r-~ r-\o O fONHVO no to 00 to nO no no to to NCO 't H N ro 00 nO CO to to ^- ■>*■ tJ- rf C4 O O h 0>MOfO ■^h ro CO co co O O O l-» CM m On r^ to co CO CM CM CM CM 4s go- Eg 2 ai J- ft Oh p. CO to ro N w O O M CM rJ-NO On W - O CONO O no I s * **- r-~ ^ CM lOCO H -^- 00 CO CO On On r^- cono O On O O w M CM CM CM CM CONO conO M M CM CM CM CM CM CM CM CM O co N t-t rf co co co ■* ^ CM CM CM CM CM d EC - too t--co 00 CO 00 00 CO O m cm ro -3- On On On On On 10 no r^oo On On On On On On Q H CM CO tj- OOOOO H M M M H iono r»co On OOOOO 42 THE THERMODYNAMIC PROPERTIES OF AMMONIA ■o n to 00 CO 00 CO oo on i^ r- r- r^. 1^. (^-O no oooo VO tr V On On On On On O o o o> O a- on a o- O o> on on o* o> On On On On On o O t>. to r- to r^ m r- m to O tJ-00 cm r^- > r^ CM On m CM 50 ^t r^- ■*■ ' PO OvO i^^irji- t xf cO co CO 00 00 CO CO r^ r-. r-. f"s r- !>. 1-*. r-~ r-» f- r-* f-* r-. t— r— r^ r- *"- 6 O O O CO o CM -+ to y; wco 00 C> O O co tJ" LO to to o •N i^ lo r^- c* cO vo r^ On t)-nO CO O o* •©- I-- r- co co X) CO CO o. cr> as <-> <-tn f) n o {) M M M w H HI M M M H M M HI M H( P r^r^ NOO NO NO lO to co N n IN W H HI O On On OnCO t~-NO NO o o o o o to to vo to to O O LO to »o O O lO to O O O O O vo to to to to o to o to O O O lO to to Q O O O Q 5 O O O O to to vo to to d a) > P M O CO LO CO M OnnO ■* M CO "0 tJ- CM On <*■ cm O-nO ■t H O0 V)N m o co j^no M M O -* ■* t}- tJ- tJ- O o •^ Tt Tt 38 CO tr^^O to co 0> On On On On f-O co ro CO co CN On CO ON O00 N OnOO CO CO co CO ■O lO CO CM M OO CO CO OO CO co co co fO CO O\0 LoLOtotOLO ^Tt-^-^^J- Tf r- O -^no m rtOO conO 0 to rf CM Hi OnCO t-^MD ■^- OnOnOnOnOn COCOCOOOOO ID it > o, rj- hi OnOO O- 'O'O'OO N O-hco VOOO cn -o to m r-^ -tJ- * OOCMLOOnco P^MLOOnCO -^- to to vonO no i^. r^ r— O0 D N IN W CI (N N CI PI N O H fl rot N PI vO o i - 00 On On O O CM CM CM PO CO On COOO N N HI O HI LO O O-HIMPICN ,n-. ro ^- Tj" LO COcocococo cocOcococo TABLE I 43 O c w o o. > -& in ■«* Th -tf- "■*• o^ o> o> o^ o^ O no cm ***■ cm co h O oo r-. Tt ri- tj- co co On On On On On co co co co o On On On On On CM CM O CO NO CO M ^nO On CM CN M On On On On OnOO ^- CM H M W M cm moo h 'tc- Onoo i>» r-.NO in 00 CO CO oo CO CO o O o d > ►JIH MM NCI N Nrt-Q ^^ N N M H M n N N N N cm r— cm r- cm O co OnnO HlO O On On n n nno O Nfl NN N CM On in « 00 OnGO coco N NO NO NO NO NO MOi 1 N o NO NO NO NO NO cm inNO to cm no n o>h ^ iono CO mD >n co M On io >n in in in tJ- o o 13 a- -£ no n r-- ncO n ^-doo O N N N N fO N W N « N CO O o o cm tJ- n on h co co co co ^f O W N (S Ot o o o CO lO I s - On m CM CM CS CI CM O in On CO f"^ CO co co ■<*■ , ^- inNO l>.CO On CM CM CM CM CM CM N l/TO On in in in^O n.00 H CM CO 5*"NO CO co co co co co o O O O o 3 n bo u V a 1 p. & lO Tj- CO CM M OnOO nno lO ■"*■ CO "N M O w co in i>. On m co inoo m 88888 ^ . lO ^) 1^ io io Q On On On On o aa^a On On On On O On On On 0> On <*■ ■* ■* ■* -=t Onco r-^NO in On On On On On "*• ■<*■ "^ ■* **■ Tt Tt" CO O M M On On On O 1 On On > (3 OnO co O n "tHOO IflH t^- "^ O i>- CO O w CO tj- On co Tt" co On CM ^3 to 1 OnCO NnO **■ r-» c-» n n i>- co co co co co co cm O O-OO n N nno no co co co co co no in 'd - W <5 CO co CO co CO LO to in in in U-) lO to IT) lO COM3 i-N O N (N « N N in io in in to lO l/)tOi/HO 00 no tJ- cm O to io io in in io in in in in co in cm oo co O OOO no in in -sj- M* ^* , ^- u-N io in in in r- O **■ r- m rj- co cm oo f— io Tf -ej- *^" co co co to in in in in io ■a* "S > "H ° ►J 1-1 M N co Ov^O o«3 ^O 0 N M « N W NO t>- 0> M IN W (N CO CO CM Tf" IONO f~- co co co co co On in m r* t^- co r}- in inNO t*- ^ CM O c- N t^-OO On On O m] £ Q\M C] IOC M CM CM CM M t^. r^-O no no 00 O N -^-no W co co co co \OnOnOnO n CO O "N TJ-NO co ^ ■"*■ 'ch -^f OO l>- CM CO no cq Oh pon -3- in noo On OnOO f*» r^ co *^- H O CM On On On m CM i" ION On 3 - da > CO - r- i^nO no cm no tJ- -^-no r^- cm co -d- O no no in in in CM M CM lOOO '^t - N "t h oo in co "^ *T ■"* CO CO co o O O O 4.s to i-> ^ o. ft in -o r^co On Tj- -t tt Tf -- r^co co 0000 O M M M 1-1 M CM CM CM CM CM co co co co CO CO CO O O o^ o^ o> ft tt't^t ft t -t -t ft ft ft ft ft ft ft ft ft ft ft 10 O CO cm I--.CO CO CO cocO t~- to CM CM CO ft tOCO M ft 00 COCO ft O O CM O CO O ft CM M O r— vO ft CO CM O CO CO NN [-». vO^OO to 10 10 to to ft ft ft ft ft CO CO CO co co co co 10 to to 10 10 to to 10 to tO 'O to to tO LO tO IT) IO to to 10 £f*o* 10 O co ftO CO CO CO to co MOO to ^NCHO COO O CM 10 r-*. O M CM CO ft toO r-co CO O O O H M IH CM CM CO ro co co ft ft CM CO co CO CO co co co co CO co ft ft ft ft ft ft rt ft ft ft ft ft ft 10 o io to to to to to 10 CO ft CM M CO 000 CO M M M CM ftO O ftcO ft O CM O *- ft CO OO co O r^ ft HI O r- »o _ 0>MO ft CM O OCO IO ft CM l-l CO CM CM CM CM HI M M O O i) (i O O OCO CO CO 30 CO CO CO 00000 OOO O O O to to to to to >o to to to to to -o O O to 10 10 10 ft -t ■* ft ft ft co co 1 l Mil 1 1 l l l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 CO co O CO O loco CM CO 10 O OcO co H O O ft co OO O ft O IO IH to O "" O CM CO M to O co J>- M ftCO M to O CM O O coO O CO O O co f- O CM CM CO co co ft ft ft 10 to too O •n t-s r-^co co co O O OOO 00000 OOO OOOO O O M O ftOO^M CO «0 0 co W O I I I I I I I I I I I II I I I I I I I I I I I I I I I ih . O M roO O r-^co O t(- O to (n ooo OO M ^O^^N O hi CN ro v: M O^mN O fO h cO O IO (v HOO^O ^t =1 r^. f-*-0 o o ro ro ^ o> O^ O^ O^ O 1 ^ Tj- ^ -^- to to o o o o o Tj- Tfr ^ ^f Tf- \j-j i_o to to »o 0> tt o> o> 0\ "* Tt- Tf ** 0^0^0^0^ Ov Ci 0\ Qi O^ rJ-Tj-Tj-^Tl- Tf ^ Tj- Tf ■<*• Ol/1 't w w H w P4 w w ft ft c s ° 6 CO hi -rto O roin N 0\Q CS wJ-O CO O M PI fO>ON ON HI N CO Tj-iOiOtoto 0000 W ^ Tf t "* ^f- ^J" ^ ^ "+ "+ ioioto>oto lototototo t^. r^ E-- r-^.oo •^- -* •*■ M* t io to to to to CO OO 00 CO On Tt *J* ^ Tf Tf io to to to to oaaaa onoooo ^ "^ «4* tJ- rj- Thtototoio lototototo lototototo en hi ooo r-. 6 <> r^.'O to co r^- t^ t^ r^ IO tj-) lO io to t^-O O 'O o O O f- r^co co O h M ro rh to r^ C\ -t con M O r- r- t-» r-~ f-^ \n to to to to Ooo J^^-O to \0 O O) ^o *o IO to to to to -rf- CO CO ■ roO COOro IO N O 't t^ OOn'noOn c-)ioO>ctio NN0OO0O0 OOOOO HIMMMHI N H H CN fl hoo h ci ^ o r^-co tN r^ O O ■"* co r^o t-~ o m O MflfOO OOO^CNM t-i I^-O *^o O^ 1 ^ co too to O "<*■ O O ro hi 000 t-^ o i>.o to co n h ooo r-- l~^OHlO•^■ io O *d" hi hi r-~0 r- i>-oo O O « "^"O OtOThcocj hmO Oco OOO ooooco r^r>-i>-i>.i>. OOOOO ootou-jto tototototo ioioio"t^ (2° OMCo^fto 00000m + ci ro-t tOO M (N CO Tj- IO _ O 1^-00 O O rococororo corococo'^- o r^-co o o m « to ^h to ■^■■^-TfTj-io iotototo»o o r-oo o O to io to too 4 6 THE THERMODYNAMIC PROPERTIES OF AMMONIA a c m O ft •& r-- hi o hi o ci m O\00 O CN IN M H H H N CO OnO lo co cm O On H M H H H M H M M tOO N't M co r^ lo 'd- co O O O O M M M M M O co no ^ CM CM Q OnCO !>■ O O- On On m m o O H OnCO !>■ \0 LO TJ" Cl M On On ON On On O O O O o io -^ co co O OnCO NO OnCO CO CO CO O o o o a. i tJIH h n ■*d- ci Cl Cl HI M M CO NO NO LO Tf OnO CO O 00 O O O O On M H H M I--CO On CM 0> O-cO 00 CO O o o o -d" !>. O COO O r*» lo tN CO NNNN O O O o M O hO cm r^ tJ- in on i-- NO O NO LO LO O O o N co On lo ci "d* ci On NO lo lo ■>d- ■* •"* O O O O M W H H M H H H M H H M H M H M H M M M M H M M M M M I-I HI M •a '3 a J -& CO M O Cl CO O Q Q O O O O O LO IN On lo m LO I^-CO O *N O Q O w m o o o r^ CO On LO O co lono 00 o O O O O LO O LO LO M CO ^O l^. IN CN CI CI IN O O On co C— i-i lo CO O i-i co tJ- iN co <0 co co O O On Cl LOCO hi lo r-~co On hi CO CO CO CO -"d" o o o o o O ! 1 + o O o o o to a c o Q. > P NCO On ih ci cO "d- lonO i>-c0 ao h ci co co "d- tJ- LO LOO O t-*- CO CO O hi O O O N n o> o> o> o^ o> t ** rf ** f r-^ r-- r- r^ r- On On On On On *<*■ "d" ■*■ **■ 'd" i^ i^- r-00 00 On On On On On ■* ^ -* •<*• " On 0> On On <* «t 'd- -dr Tf 00 CO co co 00 On On On On On -d- 3- ^" " P CM O ^ "t •O On in LOCO H TfNO fO NO On On *d- t CO On OnCO CO CO ■* -t Tt" TJ" Tt r-NO no lo -d* co co co co co ^d- 'd- Tt tJ- ^t ^- CO CM CN M CO CO CO CO CO O O On OnCO COM N. N t- ■d- ^d- Tf 0 LO LO LO co co CO co co LO LO LO LO LO LO LO LO LO LO 8 -a cfl"o ►j H COnO On M LOCO H "d- t^- cOnO On m On On LO LO LO ^- "d" lO LO LO LO LO co n r-o >o Tj" Tt" Tf tJ- -d- LO LO LO LO LO lo "d- to Cl CM ^r -t ■* ■<*• ^f- LO LO LO LO LO m O O On On ■dt- rj- -d- co co LO LO LO LO LO co r- r-^o lo co co co co co LO LO LO LO LO lo *d- *dr co cm co co co co co LO LO LO LO LO G 8.2* 3*3 a r^-oo M O On jj>- lo (O m On I~^ lo co w On r— lo CM OnnO roO Ni- W On LO Cl N H O O H M 1 1 + Cl CO *d" LO LO NO r^OO On On O i-i (N W CO tJ* LO loO I s * NCO On O O 5 +» 1* «i> O co looo O OS a. ail CO . > -d" w O w v> CO H -d* X- O O oo c-no r^ ■^ r^ m lo On tJ* CO CO - COCO ■* On com n i-^o CO O CO N LO LO M O CN 00 O O LO LO «d* O N O lo ** O N CO O "df ^* co co CO n- ■* -d- -d- «* ■* ■*■ *t Tf ■* ■^r "^ 'dr CO co co co co to co CO co co co CO CO co co CO co pfe Do H - LO CO H CO NO NO w H OI CO M CO LO IN CO ■* Tt- NO OnnO co O *0 cm t-^ r-co 00 CO OnO Cl CO ^d- r* O H CM LO M CO rf o co co CN On N O CM CO CO On O M C] IN CO tO CO CO co CO ■^t* lo lono e*. co to to co to N-OO On O O CO CO (O -d" "*■ IH H CM CO CO -d- -* Td- rj- Td- ■>d- LO LOO N •d- -*■ ^- -H/ Tj- NCO CO On On . t^. t^ r* MD t^-00 ON O c» r» t^- r-oo M CN CO Td" LO CO 00 00 00 CO NO NOO On O 00 00 00 CO on TABLE II 47 B In o > co co co co co lOI 1 W)« H CO CO CO 00 CO 9 9 9 9 9 M H M HI HI CO ■**■ too t-- O OnOO r-^-O CO NNNN 9 9 9 9 9 M M 1H M H CO On O W CI IO tJ- -rj- CO . t^. r^ q q q q q H H M H M CO Tj- LOO I s * H ONCO f- 1-^. t>.o O NO 9 9 9 9 9 On On ci NO NO Tf -^f CO o o o o o o q q q q H H HI HI M 1.0624 I. 06l6 I.O608 I.O6OO I.0592 d £ h3iH 0\0 <0 M On tJ- tJ- co co co O O O O M M H W M CO Cl . 60 H (U C , 13 a h On On On On On On On t "=t ■«+■ -t "*• On Oi On On On o o> O* Oi o> O^ On On On On On On On On O Th ^ Tj" ^ •«*• O^ On On On On On On On On On xt Tf Tf Tj- tJ- On On Q Q Q On On O O Tj- rt IO LO LO OOOOO OOOOO to to to to to d „ r-. roo O to On PI NO M tJ- On -d-CO M t^ d Nh loON tJ-co co r- ci N W)C< tON -a ,s s | r- t-».\o o to t-^ r-*. r-* w t-» Tf -^- rf -^ rj- Tf tJ- co co ci r- t^- r-, r-». r^ ■* -^ -* ^ ■* M M O O On t-^. r-- t^ r— no r»- rj- Tj- Tf tJ- Onoo co r*NO NO no nO O O \0 LO LO Tj- Tf nO O no o o Tj" Th Tj- Tf -- r-*00 oo co On On On O H < ro co CO to <"5 IO LO IO VI to 10>0 T lO lo CO "* Tf -<*■ , ^- tn io »o io io io ^o >o io IO r(- rt Tf- Tf Tt- LO LO IO IO TO LO LO LO LO LO ^ Tf Tj- Tj- Tf LO to to to to to to to to to 't't't'tt LO to to to to IO LO LO IO LO Tj- Tj- IO LO LO LO to to to to IO IO to IO to H CO ■s. tr 2 3 woo w ioO ■^- f>. M i>. o « o i^o ^r On Tf-00 CI !>. CN| r- HI LO HI O M O tH NO Cl M W O O CO co co CO <0 OnOO CO nn (N CM CN IN " 3" K 3 3 5 rh OnO co On IO CO On "^ M O WOO 'tO O m o0 ■<*■ lOH N COCO c^OO Tf On lO m m Ci to co (N « N N N ■ONO t*- W M W « W 1^-00 CO On W CI Oi N CO O M HI CI CO CO co co co co rO Th tJ- LO LO CO co co co co O O t*- t-*CO CO co CO co co g Q 5 M i> CO LOO On M O O •-< M H co co co co co w)Nh conO CN IO On 3 * > i lO H OO ^J- no co OnO co Cl Cl HI H M - co Q 00 M O O O On ci i- n 't IOCI ON-t On OnOO CO 00 r— hi to O H< ONO ^t HI CO c-r* N N ci 0>0 tJ- ci OnO rf ci O nO O O O O OnCO I s * t^- OO LO CO Hi On LO IO LO IO Tj- CO co co co co CO co co co 0 co co -^h to io io to to to io CI CO CO Th M NO H NO H LO to IO to to io too O r-*- O H O H O CO On On O O lO to too o CO 00 On On On HI O H O HI H H CI Cl CO O O O O O H tJ- On Cl On O H LO O , ^- CO Tf Tj- 10 to O O O O O i p. M Cl CO -^" LO vO r^co On O On On On On O M C4 co tJ- to O o Hi M t-i M W O r-oo On O O O O m M .00 On H H M H H 4 8 THE THERMODYNAMIC PROPERTIES OF AMMONIA o < CO D, s W M O a, ■fr ion o ro>n GO i>- l>.vO iO O O O O O Tf CO CO i-3 IH CO O . **. t-« On on on on on On m CONO On oi m On I s - lo On On On On On - no md no lo lo On On On On On OCONO f* iO tI" (N m On LO LO LO LO , ^- 0> On On On On O0 M NN N r-NO Tf ro h Tf Tf- Tj- Tt" Tl- On On On On On N NN NN OM MO-t •^t- co co CO co On On On On On o O O O "2 *3 cr 13 ■& CO CO CO CO CO O i>-00 on o r-- i>. r- noo O O O CO 00 CO CO CO M CN to ■^ LO CO CO CO CO CO O O O O 00 00 r^NO lo no r^co On O CO CO CO CO On O O o ■•t CO .yD LO lonO X-~CO On On On On On On o o o o o ■H- CO CI O On O H D MfO O O O O M M M HI M o o o o 3 M a s c O o. D rO rorf «t in LONO NO NO 1"- c^ r^ r-^.00 co 00 CO 00 On On On On O O H M M 88888 !/■> IT) LO IO LO 88888 IO LO LO LO LO O Q O O O O O O O O LO LO LO LO LO O Q Q Q O O O LO LO LO IO LO O O M H M o o o o o IO LO IO LO LO o o o o o LO LO to LO io cc) > C3 COCO -^ O Tt" CO -3-co coco Tj- On LO M LO OO M N« NOICO ■* C> V0>0 H N H O O On On iO vO 'O lo lo ^" ■* ■* Tj- Tj- coco n r-^NO IO LO LO LO LO rt -3" •* *t **■ >0 LO LO LO Tj" LO LO LO LO IO «* «fr n- «fr ■«■ Tt" co co "N w J^ coco rt- On rt lo h r^ is a aj Q° H*r *-* O conO t-» CO f— co~0 O M M M *■ fCt NH ro •+ LOCO 0) LO LO LO LONO NO "t ■*■ "* •* ^* O Oh ion CO M LOCO M >0 NN t--00 t **• **" "* •* t** O Thoo ■^-CO M TtCO CO 0O On On On •* "t Tj- -qj" TH- o o O o O O aj > a >^£ 3 a > j>- r^ r-oo O t-~ lo co m O ^" ■* -^ ■■* ■* IN CO LO t"*. On CO nO Tj- ■ LO On CO f- CN| O O 1-1 M Cs] t-^ r* i>- t^. r^. NO •^'00 - r» r^. r». i>. r- >-t LO On co t}- LO lo lonO r^ r- t--. t^. r- Nh V)C> ro o nn r--oo c— r- r-. r— t-» 3 . Oh a m n co **■ lo CN 0* C4 C-l IN H H M M M NO t^OO On O N (N N N rO H W M M H t-t CN CO Th LO CO CO fO CO co Ht M 1H M W nO t--00 On O co co co co -3- M CI CO ** LO •* •* M- 4 -* nO t^QO On O Tf ■qj" Tt ^H- LO M t-t M M M TABLE II 49 TfNH LOQO N so ThQO CM vO 8 "+00 wjnh wa co P"- •3 r-\o o m Tt- •t ro to w M O ON CO oo r^ r-MO lo in Th CN CM H O -©■ fO flfO^ f) CM CM CN CM H ONOO MD LO CO CM W On 00 sO LO tJ- cm H OnOO f-sO ■*■ co sx O* O* Qi On On On On O^ ON On On ON ON On On On Oi On On On ON OnQO CO CO oo co CO O O X) oo^o "oi-w O CO SO -4- cm CO so -d- CM 00 nO rj- m CO NO T* H On Mflr^O N -st- loo t^.00 On On O h CM co co ^t" lonO t-- t^OO On O O H CM CO CO Tf lonO r-. r** O O O O O CM CM CM CM CM CM CM CM CM CM Ht M M HI W HI HI HI M M M M h< M H HI HI M HI HI M M M M M H M M i-h H o o o O D O. cO > £3 tH M CM CM CM CM co CO co co co " & coco -to >fl m r-*. 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SOLO'Tj-COCM M0 ONOO t-- ooooooooco ooco t^ t^- n r^r^r^r^t^. nn^ € O **- H ^-00 « ^OOcOI^H i*o OvfJt^O ^-OO M -^-00 C^ lo O^ w O Q\ COO co 50 THE THERMODYNAMIC PROPERTIES OF AMMONIA D. o c O _ > CO r^NN N O OnOO 00 t-» O o o M VO H tO f-*\0 no to ^- O O O COCO co *"- fNj Tf CO CO M CM o o o o o on 7 Oil 2 0107 0102 0097 i>. t->. r^-oo 00 00 j^no to -3- Q Q 00000 H M H M M H H H M H HI H M H M M M M HI HI (. M H M H H »-H O co r^^o on aoo CO CO GO CO CO CO CO V5IOPI M CO CO CO CO 00 co co co co co OMOPOH CO IT-NO to ^f r-- r-^ r^. r^. r^. CO CO CO CO CO OnOO nO tJ" tO CM HI O OCO r-*. r-*. j>-no no CO go 00 00 co OnO co hi On to co w OnnO NO nO nO to to 00 00 CO 00 00 o o O '3 « a 1 -e- 3 ■*■ M CO to CI CO O On O H M N N PI H) M M M M H W) r^ ro W) PO *4- hi oo ■tr w lonO no JS.CO PO ro PO PO f) O0 ** M 00 "*■ CO On O O HI CO co tJ- tj- Th CO H >t N O PI ^f tONO J>- t)- Tt- rj- rj- + o O be u *d C t-. 0) d o o. - CD & > no no no no o r» r-~ r- r*. r-» r~- r-* r-^ r-. r*. !>. 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OO S o O CO « no 09. °0 "f CO 00 fN VO S ^ ^ on »0 nw 10 oo m "^T ON CM "* O On "CJ" M NO CO CM CO w coin | CM 1 CM VO j CN co | CM CM ro m i co CN 1 co t 1 coo 1 CM t ' CM q h ro O m q q ^ '3 NO O 8° " in d 0* NO CM O a d no d o* ON On CO GO N tN 13 M 1 1 r i 1 1 1 I 1 I 1 1 1 1 1 1 d d, d d d d d d B - B « B ~ a ^ s ^ S d s -s B _■ d> o O QJ -e HO?>-e- na>-& ha>-o. Ha>-e- hc»>-9- HO»>-s- na>^ in NO t>- 00 On M M CN M 56 THE THERMODYNAMIC PROPERTIES OF AMMONIA CO CO On CO lO On CO ^ N CO r-^ LO o o O ION to rors *t LOO CO LO LO M HI LO On lo rh 1^. N Tt O OO co ©h toto Tt O NO CO 00 M 1-1 co m COCO co ro W N co co r^o co co co C"» co CO OnCO co n n lo h O 00 CO M CN On Cs' M LO On H t-s On hi On O CO M M M l>. M co w O M O CO CS (--.CO CS N00 CH t>.00 CN N Oh CO On hi + w, + « + « + u , + « + « + m + UO o H CO co LO On i^- o N CO t^ LO O LO O loo lO NO ■^- C) LO co lo -rh HI CS -7}- On CO CO r^. co co O CN o aooo ro Tf On m co O0 NrO m CN tJ" co co m ro co COO cn co CO cs CO co COCO lo CO n cs "4- h cn ro M CS tj" M M LO «*" O H mooh On loco hi HI 0> t^- M coO O hi lOCO CS NO CO CN ■O CO cs O CO CN O CO hi O CO hi J-^.00 M NCO HI + m + « + " 1 + 1 " + u, + 1 " + « + 1 " ^ On o M CN O -t CN o On CO t-». LO o lO LO C io »0 M -3" rt- oo -t CO ■<*■ co M -^J" CO On N « t^. LO CS O "* M o 00 On On co fO tJ- On N co CO On CN CO M M O CO co O 0> co CO LO On CO co m O co fONCS CO no ■"*■ m O N CS HI CS CO W M LO On M NOM h OO N H H H NH CO HI O M Tf NW Lo N CN LO r~" cs LO 1^ CN LOCO M LOCO M O CO hi O CO hi + « + ^ + ^ + LO + « + L o + « + « CN CN On -+ O O On On O On CN o o LO On CO ■* n -+ lO LO co + >o + « + UO + 10 + « + l O + « lo NO CN t-^ On CO CN CS >o CO CN LO On ** On H Td- O N co LO CO CN Tl- H CN co co h hi f^ O On O O N O On O O On o nO 0\CO CO rO ■^-cO n co CO CO -tf CO M CN CO ro On hi ro co ^J" CS co co On co CN CO LOO cs NO co m O 1** M M CS CO O M LO On On M i^ OnOO m On O i>- hi HI O O HI CO M LO HI CN o + LO + « + ■" + *" + LO + LO o O n •* On M LO ■* ■^- +-> ■* N ■* ON CO 00 t^ co O CO CS LO CO M ^ CO M CO CN O M On On On co On J>- M CO NOO co o in On NCO <0 Tf N CO CO OO N O- ro Hi OnCO CO coco r- c-i co COCO CS COCO O CN CO ^f CS CN M f-- M CN M O CN M M cn co On M LO COCO M r-* tJ- t-* m On LOO hi HI LOO HI COnO lo hi o 5 MOM CN NO CN CN O HI cs O hi CN O HI CN O M (OO M COO m + '" + « + tn + LO + 1 " + 1 " + "> + « n CO i-O o CN O LO LO < — 1 o On n ro CO Tf nco co CO t^- lo CO m On tj- cs co r*. -^- cs CO CN Th CN co NO cs co cs On cs z; NO N m O N o H cn CO On M LOCO CO H r^ On I s - hi On O O H M O LO HI CO M Tf HI o a lo cn M LO CN M LO M HI LO HI HI LO M MOM CN O HI CS O HI + « + "" + 10 + *° + v, + 10 + v, + « M cn On lO r- CN M cs < CS LO CO cs O o CN M O CO lo m On tJ- COCO CO H CO M N N ON M f*. N -. CS COO On CS CO H co cs Oh CS O M M Q\ K On H I>.CO CO 1-1 ■^■co r^- m CN OnO hi O O LO HI M O ^H co hi -tj- HI M Tf CS -* HI ■<*• M ^ HI ■* hi LO M LO HI LO HI 1 ^ 1 ^ 1 "* 1 W 1 ■" 1 w + 10 + « CO M ON -+ o M 1-1 CS On CN LO On co CO CO LOCO o N LO M N O CO o r* On LO On LO LO M CO '*■ CO t ■<*■ CO co o M O On cn LO LO Tf CN H LO CS CI CO N M N ■O O CN CS O m co cn O O O CN N H 0> N N M H CN On M r~- coco m *Sf CO C- HI CN rfO M O LO LO M CO LO Tf HI 0> O co M CN tJ" CS M Tj- M M Tj- M M rf m m tJ- h HI Tf HI ^ HI Tj" M 1 "> 1 •" 1 ^ 1 ^ i ^ 1 *° 1 "> 1 ^ N On ^ CO o CN O On CO r-~ LOO o o NO CN LO CO lo CO ■* LO Tj" M CO O co O CN o. O ■* cn LO CS LOCO cs r^. r-*. cn LOCO CS q q cs LO co CS O CN !> NO O M N OM-I CO NH CO O H On lo hi O LO M d 4 m HI CO M CO CN CO M ro M ro H ro m rj- M "t M Tf M LO LO LO LO LO LO LO LO LO o **> o% M CO O M LO H CO o O o N CN c* J"^ 4 cs 6 CO o «*) o W LO M H CS vo CN M « o M HI M o I Th CN ! T|- ro 1 LOCO j LO On 1 O co 1 O On i NCO i NOO *S 1 CO On 1 ro cs 1 co lo 1 CO On 1 co ■^• 1 COCO 1 CO co COCO CN LO CN LO CS •* CN co CS ro CN cs CN CN CN HI M O M CN O M LO O HI q o m tJ- q w H. O HI On O H N O HI J CO 6 d d t^ 6 LO cs d d N LO n i i n i i NO 1 1 O 1 I O 1 1 o 1 1 LO 1 1 LO 1 1 d d d d d d d d B -s B ~ S -s S 7^ S TS a ^ a ~ a -• D o o OJ o CD O OJ -0 OJ o (D O ho>-$. ha>^ na>^ na>^ Ha>-& ha>^ Ha>-e- Ha>-e- co Tf LO o t-^. CO On o M M M HI M cs TABLE III 57 o o *5 in 00 O M Tt o>oo cm in N QiiOH NO OO co CN vO in o ^ ■*t Onoo in O O CN M I s - On CO CM NO + Tf On CO co O no in • CM* CM* M* !>- O- CO CM NO + CO NO M COCO in cm co" r-. On CM CM NO + 00 CM in NO M M Tj" CM co co cm in r^. co t>i m N 0\CS CM NO + On in On f-- M CO On t-» in On co in m I-- On CM CM NO + in O CO M co in 4 m H 4 4 M CO O CM CM NO + C-] in On O CO hi cm in (ONO co hi CO On CM CM NO _1_ w cm in O ■* H onco I s - in CO CO in w O ^■co in in I s - NO -*** t» o co On in tJ- CO NO M CM CO On re *+ M no CO CO M CO ■* OO On O O- co f-- O Tl- CO I s - O I s - CO ^"00 ■* I s - O invo NNIIN H M NO CO CN NO + O Tf H CN no CO CN NO + cm inco m CN vO CM CM NO + U-JNO NO CM NO CM CM vO + r^ cm in m CM NO CM CM NO + On I s ". ^- M CM NO CM CM NO + M 00 CN t-l COnO cm CM NO + CO On M M covO CM CM NO + o p* I s . On O i--nO On M CM tJ- r>. CN in cm vo Tt" M CM Tj- CM NO -tj- t*- in CO cn -3- ■-rr co r-* M ^co in o in CO M On , ^- CO to ■<*■ ■* CO I s . On CO CO CO On CM t^- NO CM I s - CM CO roiOH -t CO I s - O 00 CM co H M t)- NOO M * no co co H no + O OnCO M. t-. CO CM H NO + CM O NO M I s - ^- CM H NO + in O tJ- t-. ^- CM M NO + M t^ M CO >-l r^- ^t* cm M NO + O- M CM M N't CN M NO + M CM M M CO ** . T± M CO CM -^ ^t On VO On O COCO in tJ- nnOnh Tj- CN CN M NO + OM Nh in CN CN M vO CM On in M in CM CN M NO + io0 1- in co cm M vO + J>- H CM M in co cm M NO + On M W M lO CO CM M NO + M CN M NO CO CM M NO + CO CM On HI vO CO M M vO + -a a .« a 1 NO in to OnO co ■<*■ I s - r^oo m CM M CN M NO + i>- in On cm ■^■nO co tJ- O CO NO M CO H CM M NO + On ^t" -<*• CN 00NO N't CM On 4 M CO l-l CM M NO + CO co M Q\ CM in On CO CO >-< CM M NO + CO M M ■3- OO H NO O COCO On i* r^. hi m CO CM CM M NO + NO CM On M CO ^OO •<*■ OH 6 H CO CM CM M NO + I>. I s - NO On to On !>• to M M On HI Tf CM M M NO + CN On CM CM On to inco to CO CM CO M t inco ^t CM CO in com •sj- m On •"*■ CO M Tf MM oo in co ■<+■ CO CO M CO CO CN in O t CO On H i>- O On co ionO co NO to O NO On CO co ^ co CO OO I s - cooo COCO tJ- CO CM CO O00 CO -3- **■ to O CM N« NH M M CM M NO + O co *n h CM M CM M NO CM Tf Tf M CM M CM M NO + in Tt- cm CM M CM M NO + M f-. M M M CM O CM M + OnNO M CM M CM M NO + M \0 On M CO W M M NO + co C--CO hi CO M M +° in O < °o in vO O CN M On ^ CO ■ t 3* On in r- o "*■ "t **■ ■* o CM "fr CO O CO *d-co ■■*• co *"*- to -o On CO O M CM On COnO CM CO NO On OnCO co CO O to On !>. 00 N co I s - O co CO o *- O I s - I s - co to hi co w I s - i-~ m O O CN M NO + co in m M O CM M NO + CM On co H M O CM in On CM M CM M NO + M r- O H H M M CM M \0 - + On H O Ht M M CM M NO + M M On HI CM M M M NO + CO CM 00 M CM M M M vO + z: o < o CO NO O CN O o toco "+ CO C\ lO M CJv •& co O co CO ^ in On CO to **■ to CO NO co t-^CO m no O to On o W TfOO to inco CO in On co !>. co m X s - co On ON I s - -=hNO COnO I s - CO o ■* O invo co CM 00 to t-. CN NO M Oi O CM NO -f O to m m O O CM M NO + CM Tf CO M O CM + *° lO tj- CM O O CM M NO + M r^ in O m O O CM M vO OnnO O w O M M NO CO HI MOM M VO + co I s - I s - HI M O M M VO + Q w H < o o O CO On On co co co o in in On tJ- cm in co I s - CO CO co O co CO t"- M IONO CM co M M NO I>» CO tt "t co I s - in On I>-no CO O CO to in o r-- m vo co in rj- co On in cn in CO HI io co r-"- I^nO m CO ON CN in + O 00 tJ- m On O CM in + CM On CO M O O CN m + lO On W On On CM in + r- o O h On O CM NO On O O H NO + M M CO M O O M M \0 + CO CM I>. M O M M VO + CO o O -*co On CM 00 to in Onco "■*■ H O co CO Tf CO N CO CM lO CO co no M -^- CM NO CO M CO NO co co O co CO in On m in COCO O CO VO o I s - I s - lO co tJ- O CO On in o o t CO CM CO r- Q\ cn O tO-tH CO O CM + 10 CM rj- CM M 00 O CM + 1 " in -^- M CO O CM + 1 " M i>- in m CO On CM + "> On in On hi CO On HI + •" H VO CO M On On M CONN h On On hi + "> u o ct > 13 NO no NO "* CN NO 6 M co cm in o CN CO o 1 CO On cn in M O l-l CO 6 I s - 1 1 d -9- On O cn in in O cm I s - On M CO M to in in On CN lo ) Th co 1 CO CM cm in N O H 6 o" r-. i i d CD CO co in inco cm OO NH CO M in NO CM H i inco 1 co in CM -tf- I^O H r-^ O NO 1 1 d 0) o EHa>-e- to CO rj- r-. r-^ cm CO* v6 M CO H in CO CM ^Q j in On 1 co O CM CO q w in 6 NO 1 1 d QJ O NO in -4- inco cm On >n M CO M in ON- o CM CM ,_, | no co 1 CO tJ- CM CO -* q m CM 6 NO ' 1 d 0) o M u->NO M CO q q cm O* in h Tt" HI in M NO 6 1 no On 1 COCO CM CM M H 6' 6 NO 1 1 d CD M O co in co cm ■* M in co vO CO HI M 1 NCO 1 co co CM CM On M I s *. o" in 1 1 d CD O CM vO NO CM O NO CM M CO M •• M NO CO i-i ■* CM O M ON O m co h co OnnO Tf co nO cm CO co CO t^. CN CO ON M NO CO ■■=*• 'sj" Ht co Onco i>- co tJ- CM CM CO w IOHC H NO CM LO M CO CO 4 M d 1*3 4 h M tJ" CO M co "4" co M 4 4« H O ION M flO O^H co o>h OQ On m On On H OCAH ON ON M ON ON M + « + 10 + u, + " + "> + "> + « + 10 on co 00 On CO NO On r- o OnnO M CM co r-. CM "^t- CM O CM NO M NO ON no o N CO CM H *t CI M H co CM WO no co O . 00 OO H -d- ^ o\ o LONO co w CO t^. co co co O CM NO M CM O ON M co fOO rj- co O M NO ON CM lO ON NO CO o •^- ^J-cO ih COCO o M M ^- CO On tJ-00 co NO W CO CO -^"NO >N Q\ On m cm "3" CM NO CM ONNO CM CM Tf ONCO CM CO ion ioh >0 W -t H CO fTt H O CO CO m m co CO M CO *<*• CM M 4" 4 .CO M lr-*CO ih t^CO l-l I>-CO w t^OQ M + "• + "> + m + « + « + 1 " + v, + LO CO r*. (N CO CO CO M ^f H O M LO LO CI CM t» co co rf On H NO On (n NO O- O CO "* ON tJ- lo On M OnOO CM ONCO nO c*n N "*■ O i^- h On r^ o M O H CO OiW)lfl«N no GO On ci CO CO CO CM ON t^-CO CM w- q ^t- cm on -rt- q • i-i VO Nm + « + u, + ■" + "> + .o + v, + u, + w NO M NO r— CO M T^ r^ CM On NO LO Ol M W NO CM CNI LO ON O lo t^- M NO OO CO co -^t-co ■^t- r-co M N N cm roN NO 00 NO "^ NO NO M NO NO o no H Onco cm On cm cm * co to r-~ -3" CO N M ionO cm r-~. i : — i NO ON IH IH COM3 M conO m conO i-i TfsO M tj-NO M TfVJD M T)-lO IH TfO IH O + -> + "> + LO + w + v, + « + 1 * + <" y> On LO Q CO t-* M ^h vo «"- LO co LO O LO to r- Tt- r^ ? CM O < no r^O CO lonO **- no M 1>. LO CM H LO NO CO ■ rt " H O ^f o H NO in W On OnnO Cm NO to M Cs co On lo OH J.H NO H CO M OO M CO H O CM CI H l-l CO CM M CO CO M M ^J" ^{- M H NO ^t O H CM NO h CM nO m IN NO 1-1 CONO M conO m CONO M conO M + m + "" + u, + LO + "> + 1 " + "° + « ^ CM OO M NO CO IN < lOO On cm O 00 t-* ^f -1-NO LO CM ON ON NO VO LO CO LO LO Tj- M * M O rl- CM lO '*■ no co co rj- CO co M NO CM o m NO On cm On On co CM NO "^-CO CN| COCO CO CM On COCO CM -3-no ^h CM ON O O CM Tj- COnO CM Q <*> VONO ro M NO NO CO H co r— + LO + LO + "> + « < ffl NO r- 00 rt. °* ** r^ ■*• ID CO M NO !"•» lO CM -°^CO Tj- LO CO M nO CO NO ■"*<*■ co no tJ- rh co co M co co CM W o NO CO CM Th ON CM IH CO M o (M M VONO CM OnCO CM NO ^f LO CI COCO O cm On CM ^ CM Tf- LO H CM Onoo r^ CM tJ- M tJ- cm U-) M CO H NO M CO M OO + 1 " + m + « + ^ + « + « + w, JT-* co On M CO CO l-l LO vo co r^ on M LO CO M t^ r^ CO co M conO tJ" co co {-» no IN NO LO 1 ^ 1 ^ + 10 + w, + ^ + ■" + «o t-. CO On CO CO o u. LO M t- vo CO O ON LO lO CM M CO OO On Tf o CM CM NO M On O NO CO O O On NO ON •A tj- q M CO M m cm h « H H CM H M CO M H CO O M CO O M CO ON M "t M Tf H - CO NO to CO H t-, H ^ V o t On CO t^. o 1 CO M 1 co no 1 On CO ON H 1 ON 1 O CM O LO 1 M ON TJ 1 co ^f 1 co ON 1 CO ^f 1 co M 1 co r^ ■*■ co 1 Th on ' ■■*• LO CM M IN O IN Cm o cm On CM ON CM OO CM 00 g* vo q w no q m NO O M r- O w on q q cm q q lo q o co q q j CO M o ON r^- 6 LO o 4 6 CM d d I I r i 1 1 1 1 1 1 1 1 1 1 1 1 d d a. d d d d d S "S £ -: 6 -S S ^ 6 ^ S ^ 6 - e - CD O CD O CD O 0) o CD O cu o ^. na> -©. ha>^ ha>^ ha>^ HO>-©- ea>-©. HO»>^. cm (O ^t LO NO r>- CO CM CM O) CM CM CM CM CM TABLE III 59 3" ^O co O H NN m LO lO CN M CO On CN + 00 On CN CN O + CO \Q O M OO ON IN ND O n i>m On On M cn no On t^-00 -*■ H WCO H cn o + "1" °! 1 1" COCO CO M + -3-co t>. M ao>H CN NQ + o NO 0\NO M Ot SO + t^ CN O SO CO CO O »D On OnCO tJ- On -4- Tj" CO ID CMO^'t H SO On tJ- ^ OnCO "* l>- CO w ^- CO Tj- t^. t^ Tt to On O COVO CN IN VO NO On On M COO H CN O + + Oho -J- r- » + + co i-i no CN NO + + NO CN ID H CN NO CN NO CO CM M \0 M ^J- NO •<*■ "* On w t— On co m CO tJ- co »o CN CMOcD-st i-. Tj" M On On co m co ID CO On H CO T}- M M NO + + + + + •t^-NO lo H On *t" H i-i o + NO nO tJ- i-i On •* H M NO o On «D no ID NO CO no On t-*> I s - "3- CO no Tf co Qn NO CN CO CO ^" NO NO 00 tJ-nO i-i co LO O Th coco On O nO co CO Tf co H co ID COCO no co w M NO + NO co t"- M NO CO M + + + W ID ID M ^ CO M + CO ID >D ► NfOH M NO + M NO + NO NO Tt" i>. CO m M NO + Tf CN M M 'O + NO co M T}" CN M H NO + o ID Th On nO ^J-nO m CO co co ION Nh CM M M M NO + t— ID co OnnO On M ID CO NO conO m CN M M M NO + CO M Tf * CO M CO M M M NO + On M M H •* NO ID CO M CO H M M NO + o M NO O NO conO H t— co ■^- ID CO O ID On O co co On CO M ■^- co >D NO NO NO CO On CN nO M HTj- co m O co On CO CN CN Tfr "St" On CN ID CN VD "*■ CO tJ- co NO CO M M CO CO rj-NO On CO ION N H MOM M NO + NO CO NO M M O W M NO 00 CO ID M M O M M NO + O O ID M CN M +"° M On "^" M CN M + ° co O co M CN M M^NO t|- CN M w o + CO M M NO N M CN M M M NO + OnCO O co no *4- co co CO f- M tJ- co co On t— co Tf I>-nO co On M CN CO t— CN M lO W ■^ ^ IS. CO >D CN NO M O O M M NO + + + M O M H NO + + + NO ID CN M O M M NO On t— I— co ID ci Tf CO co no co O co COCO ^ co On * HCO* na>* hO>* na>-& a 0) O a S «• o 6o THE THERMODYNAMIC PROPERTIES OF AMMONIA CM cm "+ M o w o o M "O On O ■* TT r^. on CM rfr CO On M Tj- CO On CM M 0> CO ^O On cO coco CO Qn !>. rh n N Tt CO SO C0 OnsO « ^WlO °_ w O"o W CO nO CO CM ^ H « Ci CO OnO cm M CO CM CM coco r~» cm Tf "* CO CM tO On O CM O Q\ lO H M H SO O M Tt f> O M so f* On m OnCO On IH m CO CO M CO ONCO HI to OnCO kh O 0> H O On m O On m O On O On M On m O ID M LO M LO M LO M LO M LO M LO M IO + + + + + + + + sO Tj- sO to NO O NO CM -<+ CO LO On On 4 co 0> CO co lo CO On so r- tf CM CO CO COCO CO tJ- l^. CO M NO ■* -^O COsO nO m ■^- CM CM CM io r^co cm o 0> (N N ~ h On O >-t w M M M Th M O M so cm On t-i On co On m O On O On On OO On m On On H O- On M ON On On On M IO m to t-t to + « + •" + « + ^ + " 1 + + + <0 CO o> Tj- to t^. LO CO CO vO CO O ■* CO On SO Tf CO On so ^t CO Cn CM CO N CO fON CO LOO> co co lo ^- r- to •"*• lo -f CO i^ *■*■ so cm co o 00 -GO M m CO 00 w co OnCO m lOONH r^co m CO CO M CO CO CO CO CO CO OnCO OnCO ONCO + ^ + "> + 1 " + 10 + « + 10 + u, + 10 o o co M CM -3" CO LO M ^O o o NO -* CM 0> CO ■* CO ON t^- ^f t^- On CM t^-O 00 rovO CO LO LO co to -^|- •* o -t Tt" On CO 00 m co NO f— CM o CM TTOO 0* O0 H CN IN 'tCi'O c< 00 *<*■ H CM M CO O- CM CO CO CM CM ■*J-CO C- CM lo co to CM *■* o\ d d h WHOM 4h Oh sO cm On M On CM* OO W M COCO M co co t^ ch IO -t J> H O CO M t^CO M r^co r^.CO I--CO CO CO CO CO CO CO + ■" + ^ + w + « + « + 1 " + -° + 1 " CO LO i^. to to CO r- co lo MD On LO CO ON GO On CO NO CO On co SO On h OnO OO H M 00 CO M coco r— m LO QN C^ M l^NH NO 1>- H NO f- so r~- so •>- r~- r- r— r-» t-* r— ,_^ + "> + w + « + to + « + 1 " + ^ + w LO r- o d w M O On H 4h 6>h SO cm CO M On CM CO M M cm r-. M ro co r^ m lOfONH rj- r-- m LO C-. to r-^ lo r^. IO £-. no r- so r- O r- en O + LO + 1 " + to + ^ + 10 + 10 + «o + « 5 M Tt CJ to CO CO •CM ' CO **■ co co CO CM Th t-- CM t^ r— CM M CO < cm m co CO M CM CO x^ o CO OH Tjr co m ^f On O CO -+ o NO cm On o It cm O CM CM co no NO cm Th CM o CM CO CO SO CM M CM M CM cn r-^ x~^ cm Tj- CM *t CM LO f^ M M S On to O H m Lo On M •rt\6 On H SO njD CO H On i>-d6 w m r* i>- m coco r-» m LOCO I>- M COO m tJ-vO n-NO rJ-O rfso LOO lOnO LOO o 5 + "° + « + 10 + « + 1 " + « + < o + u , On On CO CM to CO CO M CM COO LO M M SO LO M ■^-nO H oo t-~ CM CM CO MM CO CO h co cm O *+ O rj- CM On CO CO On SO so CO o w ao ^ CO V)-t (N ■t OW « co r- -^- cm M M O CM co rl-sO m ■^- On CM m tO tO On M Q w H **' 6>do h M O On m •^- M CO M SO M CO M On CM CO M M CM !>. M co CM f>- M tO conO m CM lO M CO NO coo co sO COsO -*o ■^-sO TtsO + 1 " + "° + « + "° + « + 10 + ,o + « < 00 M >o •+ sO O to ON NO H O CO lo o LOsO CO M -d-so CM GO M CO O O CO On CO "*■ On Tfr- co On tJ- LOCO CO M CO so m r-^ o IM NC^ N GO CO CM CM rt- OnO cm CO -d- CM m M CO CO M CO ^ Tt" M ■^- On m m IO COCO M Ol 't Ol H M io On m •^f LOCO M SO O CO i-t OnsO t*- M m r^ x-- m r^NN h tOCO SO M m m CM IO + "> + ^ + « + u, + « + io + « M- r^ CM to On to ■^-CO CO CM ci r*. CM co r— r-^- cm. r^.ac Tj* co a TtCO On CO O t- r--. i>- r^NO M SO On lO O to io m m r- m NO CO M WCO H so -*■ m_ O M M iONh On LO M ■4 On m LOCO M LOCO M SO t^ H O r^ h f^- t^- M r^-sd hi NO H <*■ •d- ^J- ■^f T^ Tf ^t- ■^- to VO to to LO to LO CO CO CO CO -* -i- CO so r - CO -r CO H ro "t- to M 4 so On M* co to CO ^ M 00 to M M r-^. H CO 4- so co ■>d-co x> 1 M On ' Tj-CQ -L CM CM 1 Tf CM J- CO On 1 ^r lo _L ro CN 1 ■«*■ ON 4- ^ ^ 1 "3- On 4- toco 1 -<*■ co cm r-. CM so CM LO CM Tj- CM Tj* CM CO co q q C7 no q q no q o r- q o On o q co O O NO O cm q o 3 co 1 1 4 o" CO 1 1 m d CO 1 1 CO d r 1 SO 6 1 1 co d CM 1 1 m d CM 1 1 00 r i ,. d d d d d. s ~ s -A £ ^ B - S ^ E -; 6 ™ s « QJ O -©. HO?>-0 ha> -0- HO> -e- ha>-& Ha> ■«. na>-& HO»>-e- o CM ^ so O0 o CM <^}- ro CO ro CO CO •t ■* ^- TABLE III 61 n» to ON to CM CO to *3- i-*. M to CO to "!j- ON M tf o o M WO NCQOO i" CO oo »o OO O 00 •■*• PC M* to co -"t 00 CI CO tj- Tj- CO 5 •^J- co CO co ^ q ^J- CO ON CM O Q CM ion ■* ON ON IO M W 6 Tj- M 4 H 't M O* CO co M ON CM CM M H CO CM* H ro4 H M LO "3" H M «1 OlOlH O O M H O M O M M O M M H M O •-• CM O co r* co t^ coO co r* co r-. CO !>■ co *>- + + + + + + + + n. O ON r-*. o o r- co O co "$■ ^o ct co oo -d- + + + + + + + + CM ON ON ■* co o o n r» co O CO tt- ■*f ON co *Sf CO ON co tOCO im r-oo OO O CO co -^ r-* CO (NO Tt coO Tj- M LO CO to to O co "+• o ■N lOO co CO CN OO CO ■^- ON M CO CO r>- to co M CM CO CO COCO -*■ co ■^ --^ ON co to *o co ON »» ("O M M O0 CM M , ■^00 vN M O On m H ON O H M O O M co M ON H iO cm 0> m ON "St H ■«" H *<$• M *t M »o M M IO M LO M O CM SO IN SO CM O CM O CM O CM O CM SO + + -h + + + + + o "* ■* o CO ITS. CO CO O On On CO cm r-~ co cm CM O ■* M o o M M cm Tt-O OO toO co O to co O to "*■ ON H" Tf On Tf CO ■<*■ co so ■* co o CN m cm CO CO OO Tf co rj- io r-~ co CO CO H CO m 00 to co CO ^ CO ■st O co iOO CM co CO ChNfOM M J>- CM M ■4-ad m m so ON M M ddo h M 6 M CO M ON M IO M ON M 1"- CO M 00 CO M OO co M 00 co m CO CO M ON *t M ON ■* On ■*!- M so M SO w O M O M o M O M O M O + + + + + + + + _ -8 Th co CM On o -a O cm CO to M Tt m On ON ■*■ O CO O tJ- CM M IO oo to ^- co CO tJ- co co Tf to CM rf O CM CO co M O -* H o so cm r^oo co oo lo "0 t1- CMj co co CO ONCO co M -+ CM CO CO OnsO co ■^-sO co co LO M ON CO OO CM M M N CM CO TfOO M M O CO O M On ON H M On On m co O ON m to M 00 M •^i IO CM M O CM M O CM M O CM M SO CM M N CM t— co r^ co K M O M O M O M O M O M O M O + + + + + + + + CO H M r»* to o CM CO 1 CO N to O so iO m- M O 1 M CM M _ Cj _ M t1- CO M M O co O m On Tf- O M M ^- on M co to On m to LOOO M Tj- -t« M lo cm m to CM M LO CM M SO CM O CM O CM M SO hi so M O M O M O M O M O O + + + + + + + + sO to O CM CM CM ON o cO to Tf CO OO ON ON CM co t*- GO H co r- CN] OO CO OO **■ CM CO CJ H ** M Th -"t" CO m so cm On ffi cm tJ- co co oo coo co ■^J-CO On co oo to rt co m O On co CO to -^ co "3" CM O CO lo N*0 CM o 2 OO cm M m r-. m h -^t- N O M O co w ON ON ON M m On On m co O On m to O OO M CO M M Tf t-< H ^" M M ^- M M Tf M to M to CM M SO M O H O M O M O M O M SO < + + + + + + + + o o M t-» to to CO to 5 On to O ON CO co On r^ r*» cm O r- CM CM LO N cm so cm CO CO ON M H 4 6>H co tOCO m LO LOCO M M H M CO H M CO M M co M M CO M ^ w -+ w ■* M s < M O M O M O M O M O M O + + + + + + + + n- r^ o to "* CM LO CO LO Th on !>. tJ- ON CO O co O OO to co O CO CM LO M CO tJ-O ^O M CO to ON "vt- O On Tt M OO CO OO CO SO N N o n h a^ CO On IN co rj- too co CO CM O CM h MOM CO CM M CM TtOO O CM LO CO CO CM H ©NO M M M O M M ■- M O r^ m r-^ r- m t— O M r--o w -©. HO>* ha>^- HO> -e- HO*>-e- HO»-«. na>^ o ct ■.SO M t-^ COCO CM M CM to ON to -rt CO no -t On On CO On NlO H COCO LO HI N On lo m O a^-H o on O ON M On m On CM On CN O^ CO On 1-. LO M LO M LO lo M LO M LO l-( LO hi lo + + + + + + 4 + n- CM ,_, sO CO LO O CM to LO *4- r^ O r- >* M O t"- O CM TfO cm CO On sO O CO o 00 loai 1 IN "t «N H W CN CO CO CN r^^o w M »^* -t t^ CS| O co co cm cm CO On m SO LOO hi n On n i-i O>0 Nh M so M io H O H On CN lo h CO CO IO M N CO -st M O <* -t Hi On GO ON ON On o On O On m On H On cn On io LO M LO lo i-i io M LO 1H LO hi «0 + + + + + + + + CN n M SO CO o M CM O LO O O t-^ On (^ O CO LO O O co ONO On N CM CO On cm On CO o ■* o SO so On cm Tt On CM ONCO O N N o LOO CM "1 't hi O cm n so i> CI r^ rt M CN C- HH o M O cm l-l CM O O0 M O CM LO Hi N Tf N M On LOO h i-i iosO H LOsO SO M ONIOH COCO LO I-I NCO "t M O On Tj- hi 00 GO CO CO ONCO C^oo ONCO O CO O CO HI OO LO LO LO LO LO M LO M LO HI LO + + + + + + + + n SO SO H CO CM CO M LO "3- M O J>.sO CO N CO co H O CM CM NO On cm CO lo t-t O ON O . On >0 M O CO M M CN W)NH O On ^t m N ON N H On OnO h H O so M LO HO H ON M LO M CO CM LO H N CO "t M O co -st M n n n n CO CO co co CO CO ONCO ONCO O CO to LO LO LO LO LO LO HI LO ^ + + + + + + + + o ■ so On q^ O CO O TON CM PON Ci OO SO ON LO *o o Vi to CN On CI *t N N CN CI W 't H ON ON M NO "t M O to O i-i ci O hi NO O CO HI * n -to H On t^-sO w M LOsO H LO LO LO H OsO lo m (ONIOM N-C0 tJ- hi O CO Tt HI O N SO N t-*. »>~ t^- r^ r- r-. CO N CO N ON N O + •" + 1 " + u, + to + u, + ^ + ^ + LO Z a- sO 1^. LO On CO so o ct CO ON CO COO cm r-- CM On O CM CO N < ON co On co noo ON CM 00 o CO »>- O CM O CM CO LO CM On LO o o -t o ■a- lo o CO 1-1 t LO LO M (N co H !>. )>~ t>. H O- co co m O CM ON I-I CM N lO H. O CO co m s N OO hi On OnsO m m O so H LO O ^O M ON M LO M CO CN *^- l-H N CI rt m O co rt hi too LOO so r^ SO O o- jt- r^- N N CO N o + 1 " + ' n + « + to + 1 " + *" + 1 " + "> On n CO O CN CM o -t < CM CO CO -1- On lo oo r^ so On CO CM O l o On CO CO CO N N On On t-^ o loo O O to CM CM »t CM On •* so h. co o LOCO so M ^t*5^M in nh M r-- -tO H N H CM M O OnCO i-i CM Tt -t W O O CM HI □ N coo M On 'tO H h tJ-sO M io LO LO H OnO to i-i COO -t M N N ^t HI O CO -t hi -tO tJ-nO iosO LOsO lOO sO'O O O NO + "> + w + « + LO + >o + LO + 1 " + 1 " < "<*■ CO LO ■* O o 00 n cm NCO ^f -st lO LO co 1>- O On CO M O lo On co CO CO sO On lonO o CO lo o o -t CM CM CO CM On co O M CM 05 o LOO <0 M Tj" O CN M cn lo M X-- N LO M NCO O M SO N N H CM CM CO HI O N l-l H NCO so w On OnsO H m OnsO I-i LO LO M On to m CO M -Ct I-I N CN ->t HI CM -t HI co to CO LO Tf LO ■<^-sO to LOO LOO o o CO + "> + LO + « + to + "° + 10 + "° + >o CO ^ CO J>- CO o LO CO CM SO sO - co CN M CN CN On CM O CM M o tO -^- CO ^ -3-O0 H M _|_LO + « + LO + LO + 1 " + ^ + 1 " *t *t SO O o o On O CO TO sC' -t CN H 4 LOO N On r— co CM O H On HI CO -st On -=t N -t CO co O CM O *H On to CM CM ^ so an O t^- M 1-. CM M COCO M M LO M O M M CO s6 i-i CO LO M ON LO M On LO M d 4 h M 4 M M 4 HI CM CO M > ■*t *t ^~ -st LO to LO LO LO lO to LO LO LO LO On CO On o O CM CM o 10 t cn !>. N o CN o n o M 'O a. CO N n T3 '3 M CO + ^ CM NO o co M "* _t_ n lo ' "■ CM d h d to d 6s d ij 1 r i 1 1 1 1 1 + + + + + + d d d d d d d d S ~ (U O S ~ £ 7^ e -A B rJ, e ^ 6 ~ S ~ O CD ■e- HO>-fr ha> -©- ha> -e- ha> -e- ha> -e- hO»> ■&. SO CO o LO o to o N LO ■st t LO LO o o TABLE III 63 *>. CM CO IH ■* 00 H Cm r-. ov M lO ^ CO Q O 00 O Tj- H CM CO CO lo ON co hi CO CM M ON CO M O ON ON CM 00 CM on r— O Tf ^O O O »0 M UTt Tj-I- M ■* CM CO f- ""*■ t^- 1000 , ^- MflH W) O r-^vo co CM lO O CO O * O CO N>00 h O lO O M M vO ON M 10 r^co m ONOQ CO H co on r^. n r^ f* m O HvQ H m M O M M O M (N O CM CM O co O CO M •t r-« CO I s - co i-» co I>- co r^ to r^ co f- to t>> to + + + + + + + + t*- \n M O CM ro <0 co cm co tJ- to •■=*■ r- t+- ON LO On r^ r- on On coco CO ON N loo no -tin o' r^ rj- CM HI CO NO ON CM 10 10 l>-00 to r-^od on m ■■*■ co <*£■ r^ Ov ON oN *? CM ON M CO r^ on ch co r-* onvo to O O O to CM ONO CO O t". HI CO W ON ON M LO CO w ON M t"- M CO co t** H r^ coo hi O ^-O i- 1 \0 r- r- m t-^ r* t>.QQ r^co CO CO 00 CO ONOO CN O cm cm \0 CM O CM O c-t CM vO CM vO + + + + + + + + CM ^f M CO ON ON VO r- ^j- on (N VO O LO LO LO CM O LOCO vO M ON M . t(- co O LO LO CO CM CO M CM O r- cm Nn a h Ov M CO H H COCO H lO -^t- f- H on lo r-^ m COO O M x^- r^o hi O 00 LO HI m vo M lO tN lO CM lO CM 10 to lo CO LO ^f- vo CM NO CM O CM VO CM vO CM vO CM \0 CM O CM O + + + + + + + + r^. CO CO LO CO 00 ■* CO NO O CM IOCO co r^ ■^J-CO O ON LO ^~ O -* cm CO m CM ON CO m M3 vo r^ ON CM TtCO CM TtCO \0 r— °o 10O00 ^ ^ ly-) LO to W O H W) f- O ■* co r-- ovco , M 4 ON ThNO M COO O M l^-O LO M O ^ LO HI O ■* on tj- ■* ■* M tJ- M -^J- CM Tl- M NO IN vO CM vO CM O CM vO CM O CM O + + + + + + + + **■ CM ON CO LO OO 00 r^ "g On ON CM 10 r- CO O CM M M CM r- ^t- ■*■ »>- ON IO O 00 fO O ON WO CM ON vO LOCO CM l«*, N cm rfO O CO LO a O NO IO IO IO 0O ■t w w) CM lO ON CO f^ lO CM CM t-- T^-vO CM ^O LO M CM CM CM I"- CM VO ON CO CM s t^. M CO M ON CM CO M M CM r^. M 10 to r^ m ON -^"VO (H CO LOO H t^O LO HI O O LO M r~- co £-*■ ro CO co CO co CO CO ON CO On co O co « M O H vO M VO M VO M vO M O CM O 5 + + + + + + + + 1 CO ** h-1 CO M •3- CM 1 t— 1-1 O f- CM CO CM CM O co O ^t ONO CO ON ON M O CO Ov ON CO ON CO vo -* r^ CM OO CM Tl- LO NO ON tJ- * — - O 10 co tJ- CO TtCO O CM w ro N cn r^ co m cm Nh ION O CM O CM CM ONO CM O O CM CM 10 in J>.<0 CO M OvO CO M M t-» !>. M LOCO t^» H ON ONVO H CO O VH NO ^H O HI lO HI O ci VO CN r-^ cm r-*. cm r^ cm CO co CO co ON fO M VO M VO H vO M O H O HI O + + + + + + + + 10 M M CO T O CO 10 CM ^00 CM ^h 10 T^ H Tf O O LOCO lO M c/> O *-• ON 00 1000 ON IOCO O CO N vO COO CM O LO CM LO Tj- O O Th VO HI CN CM •^f vO ON Cs| CM M vO CM nh aw J>. ON tf CM O ON ON CM CM O LO CM O CO CM CM £ ^> N H00 H OiH NH H N NH LO CONO M ON COO M CO rf LO M t^- LO VO M O O VO H lO CM lO - CM CO CM H O M \0 M vO M vO H vo HI vO < + + + + + + + + 5 CM CO O CO NO ^ LO CO CM co t^OO CM -tf- r^ ■* CO LO On C— CM ON l>. CM o> toco CO H f^ ON (N N NO vO VO CM LO CM LO Tf CM O CO O W CO s «5 IO ON H CM Tf ^t-CO (N CM ON lO CM r-co co cm t^-vO CO CM VO O CO CM CM CO ^t CM O M CM t-» IOCO M ONvO *^ H M MD t** M LO r^.\o M OnoO no m CO ON LO M r^ lo hi 6 H IOH s -* M rh m lO M LO M VO IH NO M VO CM I>- CM M NO M O 1-1 vO H --O M O M O H O HI vo < + + + + + + + + CM CO L ^O CO CO Tj- O O O ■* H ON M lO ON LO COO SO CO f* O CO CO O 00 N CO OO VO ON OvvO Tf LO O M ^J" CM LO CO CM NO CO VO CM CM H °0 iONO*« 'J'HiO N CM vO CO CM f*.vO !>■ CM r-~ > CM CM O tt" *> CM CM O CO CM O I>- CM r^. t^ h OlH NH M M f^ W LO CM NO M ON COO i-l CO Tj- LO HI NLOLOH LO LO H CO M CO H "*■ M "t >H Ti- M LO M LO M HI O M O M O H O M O M VO ffi + + + + + + + + tf *f IN Ov M H O ON J>. w O ^1- CO O lO t(- r- O CO CM O ON co hh O "tf-O CO ^t\0 ON O lO O to , ^- NO O co CM LO CM CM J>. CM NO CO Hi "o IO >OCO - co u O to *t Ov -a- t- Tf CO co O CM O HI ON O CM O CM CM HI »0 Oi M *■•* *-* r» cm m COOO m H IOH O Ht HI HI ON M rt CO O m DO IOH ON lO M Ov LO H 6 4 H H 4 H M 4 M CM CO H ^* ** ^f "*■ ^h to LO LO LO 10 VJ lO LO LO LO LO LO O 00 ON O CM CM O LO ^J- 0) O QJ O QJ O HO>-& Ha>-e- fHa>-e- HO>^ hO>^ HO»-e- Ha>-& Ha>-e- ca LO LO LO "3- ■* LO LO NO *^» t>. 6 4 THE THERMODYNAMIC PROPERTIES OF AMMONIA o I ON M LO TO ■* to to O On CN O M CN M ■^-oo O H COO CO O J>- IO O O lo CO O CN M On N CO 00 co l>-00 CO OO N rj- oi n r- o nO o CO CO IO M q 'Itoh On On M CO -^00 M LOCO NO Ht hi CN to hi O t— co hi o ro lo t}- m cs-o ^- h OnnO "4" M N NW)H to r^. co h CO 00 CO ft O CO CO ft co On CO hh ■*■ o Tf *fr to O to o LO o o o o o M O M 'O HI NO M NO M VO H O HI O + + + + + + + + M C| co CO r-. 00 ON O Os O co f^ t-* CO NO Tf M CN O "d" CN 00 CO CO CN CQCO i^ o r-» co O t^- CO M NO tJ- loo is. o »o o CO O ff w 00 W 00 M LO ^O HI HI 00 ^ M O co co hi HI O M HI o OS f)Q t1-h co cs. m -3- M On m tJ- m CN CS CO HI IO CN CO HI CO CN CO HI co co hi CO CO CO HI co O co Tf o ■* o tj- LO O LO M O H O M NO HI O H. SO HI O H. O + + + + + + + + r-~ cs. OO CO CO Tt" LO o to Ox co m r— CO O) On r-» OO CN oo r- 00 Q\ r— CN V)N !>. CONO co conO O0 ■«*■ lo T^ OO LO ts co Tj- o- O -st o CO N tOH O CO M H On CO On m COCO i> h LO- W LO HI HI ^j- CO f> NO On cs m M CN ft HI o 00 WHOtJ-H t- LO »+ M OnnO co M CN NO CO HI to r^ co hi 00 NfOH I s - CO Hi COCO co h. CN 0* CN On OnOO ft CO "*NO M LO N rj- m HI HI CO HI O tO M HI M CO O HI tOOii-H ^ O t w ao tOH N H N)H tO Hf CO ft CO CN CO HI O CM CO M CO . HI CN On OO cn N3 OO O CN HI O H O H CO HI LO HI LO ^f ••*■ HI M NN M O HI HI HI M tJ- On hi <0 ■"* "<*• m ts. LO CO H ON LO CO M CN O CO HI lonO co m CO O CO HI O cs co m CO Cs CN hi O CO O CO O OO H. CO M CO HI OO CN O0 CN CO M LO l-l LO HI LO HI LO HI LO HI LO H. LO ^ + + + + + + H- + \r, H o «* N Tf o oo CN c-~ o NO ^t" O CO CI CO On CO r- co toco CO -si" oo po lo CN O *3* r- co CO f co CO CO c— On r— OnOO O co O CO O oo ft 0O ft CO CO LO LO M LO M LO HI tO M IO M LO c/3 + + 4- + + + + + o CO O co Tf o On CN O CO LO (N On OO co 00 On On ^f- ON O to GO lo ^t CN C4 CO i^ oi c-j co co oi 00 NO M •^ MM i>- CO o On to O 00 O O M O rJ-CQ M On 0>nO ft CO T ** m LOO CN HI H Oh h O c^ On hi M O CO M .nO CO r- CO t"» co r^ On Cs- On Cs + "> + LO + w + w + LO + to + « + "> < o "* ON CO Tf rs. M Th On O co IO t~-» N CN toco CO co On CO O -st" CO r^ M cn lo m r- no O co CO O OO CN On rj- CO ON Cs tJ-OO On cooO o 00 COO0 w O NO M On + ■" + -° o o > CN CO M co co M co co M co co HI -^- -e- HOO-e- Ha>-e- HO>-& HO-6- HO-G- Ha>-©- ha>^ LO o to 8 to »o oo CO ON On 1-1 H. M M TABLE III 65 ■fl r^ 00 ■* CO O <0 CO co co - co qvco 10 co co tn co co to q to HI t--O0 CO vq covq co M CO **■ CO O CO « O M NCOIOH 0> co 10 M « 1-lflH tO »0 IO M CO »Tt h vd -4 h COO ^t m Tj" M "* Ht -* M IO M tO HI IO HI VO H. VO M to r^- co r-» co r>. CO c*. co r-^ co f- co l^- co r- + + + -r + + + + ■*■ Ov 10 co t^- Cl r-^ Cl CO Cl M IO Th Ov co HI 1^ ci r-*vo t-- M 00 Cl Cl N H r-^. mo CO ty~, CO O Ov Tt" Ov Ov i^. r^oo Ov M CO O oqvooq re O co to CO O O N CO CO vO Ov to IOH N N m tj- ci VO CS Cl Cl h r-» m n w CO IO IO M KvO to H 0\^ V) M d r-^. rj- h tOCO ^f HI CO CO* Tj- M O Ov Tf- M ro O-t h « 000 000 OvCO O CO 00 CO M CO M CO CV1 O Cl vO N vo COO COO COO COO CO NO + + + + + + + + ■* Ov IO to CI r-^ to Cl O Tt- co r~- M 1-1 ^t- to 10 O Tf to o> CO ^t- 00 O CO ci t— r- -tN CO OwO CO vO vO tJ- vo 10 r^- r^ ■>*■ Ov ci tJ- °_ 00 O ^- A H Oi O "t H CI "t" W W1H 4h CO H ij-H O" Cl CO M CO Cl CO M w Tt- tO Tt IO *&\Q tovo 10 vO lOVO vO vo vO vO » r- Cl M (N tJ- cj 00 co 00 Ov Cl to r^ OO coo N ^J-O t~^ Ov »n co tj-j tf CO co ■«*■ ■o -00* 4" M OvCO ^ H n a 4 h tO Ov "^ M CO O CO H O O CO HI CO M CO M O CO O CO O co M CO HI CO M ^> Cl -tfr Cl Ti- + r- Ov vO co 00 O co 1 CO CO 't ci co K vn vn co co cn CO CI HI ■* Tl- M r^ co O Ov ci O m M 'taw O NN OMO 't w CO HI W Cl to to O ci Hi ONOO ci vo ^-O Cl M CO to Cl M O CO ci 4- M NtO^M Ov CO ^" H W t^M lOti-H CO Tt CO M O tO CO H CO to co M M O co ON CO o^ to O co O co to M CO M CO w vo M VO M vo Ol vo ci vo Cl vo Cl vo ci vO + + + + + + + + -f-> 5 Cl CN ■* Cl 00 r-- O COCO CO Cvl VO vO Ov H CO O r-- to 00 CO O CO OJ tN Cl r^. 00 - HI O Ov VO Ov O CO t-t CO Cl t-^O Cl Ov M co 01 CO 00 M CI IO Cl Ov Cl H VQ N N vo hi vO Cl H ^ ^-H f CO N 4 H t^ r-* -3- m OvCO ^ HI CI CO Tf HI IO Ov CO HI O0 Ov CO H O O CO HI co O co M CO Cl CO Cl CO Oi O- CI Ov Cl Ov Cl O co CO 2 HI O M vo H vo HI \Q M VO M vO ci vo Cl vO + + + + + + + + < 10 to CO vO to Cl Cl Cl 2 O to 10 Ov Ov co ** r-- tH Cl vo r^ to Cl i>- r-~ CO H N Cl ^J-H r^. m co Ov CO 00 ■- - Ov M O* *o Ov to tJ- tO Ov Ov Tf" vO Ov CO ■* O * co M CTt tOH IO H IO M IO HI VO HI VO M VO HI t-^ HI *"*. M CO M VO M \0 HI VO HI >0 HI VO M VO HI VC M vO + + + + + + + + - r- Ovvo O Cl CO M CO CO M CO co M CO CO hi 4 N H tJ- ci w tJ- ci m" 4 ci m > 10 10 to to to to to to 10 10 to to to to to to CO O) t^. CO CO ■* i^. Ov 00 q qv 00 to HI VO M CO !>. ci to CO 0" CO •* -_ "t t „ *o ^ _4- lr> VO ^° f* 1 *>■ T "fr to -J- lo 10 -f- vo M 1 "^ ' 1 ^ 1 N -f- OWO 1 H + OH Ov + 00 to t^. LO ■<*- IO M to r^. to CO vo On vo to '3 Cl Cl CN co CM tJ- ci ■* Cl to Cl to. Cl vO ci r— q q MOO j>- q °^ °. 9 HI O O 0OO OOO 00 q CO 6 r^. O d CO 0* ^ d d to d to d J H n Cl Cl CO CO to + + + + + + + + + + + + + + + d d d d d d d d £ - H « B - B ~ B ~ £ -s B - S ~ 0) O 0) O CU O -& f>Hv3>-©. hO>^ Ha>^ ha>-s- e-e- rHC*>-e- HO* 1 IO to to 10 1 CO CO Ov Ov O HI M HI t-t 66 THE THERMODYNAMIC PROPERTIES OF AMMONIA O o SO sO o> o >o CO CO M HI MO CO SO ON H r-. co r^. so ^h H ONCO Ht LO r^. ro sO "* to iO On r-. co CN *OsO M - M M NO o O co -+ ■*■ O M LO H ro w cn rf CO n M O M Ol sO cn cn cosO w CN r^. cn IN LO LO M SO CO CO M COCO "^- M CO sO LO O H co H tJ- m LOCO ~CO O SO M LO W LO 1-1 oo On r-- m CO M "t H CN lo CN Tf- LO M t-N co sO CN SO "^ M O so O CO o COCO co »h CO CO so O ON co hi co O o lONM H CN CO M IO r-N t-N (n h CN CO M LO + O 00 . CN M m r-N. M IO + so r- cs m M t^. IH LO + CO CO CN M M f~ H IO + o CO On CO On ^f -+VO co J>-sO HI f-OO CO so LO O - LO t"- M CN H On f- LO + O M CN M O r-- M IO + (N CN CN M r- H LO + ■* CN CN M O r*. M IO + SO CS! CN 1-1 O t- H T-O + CO CN CN l-l O r- H LO + o CN O On cn CO ■"t O O CO so w cn r— CO H LO CO ro cn CN t-- m co -^- LO CO CO COsO CN LO co O CO SO '*■ LOsO CN SO CN O SO M CO so co C- M O ■cf On CO O lo co O hi O "OsO cn m CO no JT—sO CN Hi CO sO O SO CN M ON NO + "•> »N sO CS m On sO + LO Tf\0 CN M OnsO so so CN IH OssO 03 NN H ONSO i-J o ro On On On LOnO SO On lo M LO-O SO H sO so H CO co O C-l CO co lo CN O CN O co «t O LO CN M CN O CO M CN LO CO CN M O ONCO io i ^- co 'vt O O to CN H t^. O CN M O O sN m CO sO CN M CN IH CO sO Tt M CN M CO sO SO M CN M CO so CO HI CN HI CO so o a, > '5 o* CN t>. on On lo lOM H LO LO ON »o *? CO -L M CO 1 SO LO cn r— lo q q co 6 + + a a - OJ o LO O lo O LO LO CN HI LO CO 1 *o o cn CO i o q 5-°' + + d S - CD o hC»> -©- tN. On m O LO co co O LO CN l-t LO LO M d + coco 1 so LO N CO on q q CO 6 + + d OJ o o b-co CN ^J- LO CN O LO CN M LO LO CN C-l -i- -rf LO 1 SO O cn On co q q so 6 + + d E ~ o M LO M TABLE III 67 H O CO M «t **■ cs co 00 00 O CO N- CO hi (N O H W ON CO O 00 ON CI CO N. N cs O ON cs coO cs 00 00 COCO CO N lO cs O m «* cs 00 co cs -^- es in N tJ- m CO N + n n tj- m \0 H co N + O 00 CO HI !>. HI co N + M O0 co hi co I"— + Tf ON CO HI CO N + O Os co m f— M co t- + CO O co M r— cs CO N O in CS SO O O Tf N n CO M h n OOOOO M On CO NO O so H O COO + N O co M COO + O HI CO M W On CO NO + CS M CO HI M ON COO + Tj- M CO HI CS ON COO + O CS CO HI cs On coO + CO cs co hi CS ON co so + O O cs CO On On O co *T COO Cs n M tsf hi co co CO O m cs . M COO ON cs 10 co co CS -o 01 + N CO CO M CS O + CO CO hi NSO CN O + CS tJ- CO HI NO cs O + N O CS O + O lO CO M l^so cs O + 00 in cs hi NO cs + O CO On co ON 'T n CS SO + a .a a CS H- n On co O rfrO Th CS IN CO M M 00 ON CO es 10 M OO On On H Ol m m cs 00 Tt- n On CS O O HI cs in O N ON CS ON ON HI NO O NCO co COCO hi ON CO cs CO CO COCO N hi IO H CO M es rj- Cs O + Nh rOH cs - tJ- CS CO w in N *=t h in on CO IO CS M - Tj- H CS HI O O O 00 -d- O H r^ in r^\o H NOH in CS M N\0 CS O OO HI in so t— r— in cs CO N hi in -3- 00 in COO O HI 00 On 10 CO O VO Hi W W CO in co h OO CS H O NO «1H 00 CN M O + O '3 & 3 CS N ON O to 1 "t °. IflN H in in ON <* in 00 4. MOO ~ so 10 in n in q 06 d CO + + d 0) O 10 O ^o lo « 1 Tt q in m in in k-H 00 1 C-) O so 00 M M O H ° * + + d a - 0) ON H O IO co co q in c-i m in 10 d -U CO00 1 no in IN OO on q q co d + + d a> O NOO cs -3- in cs in cs m in in cs N w 4- ■«*■ in ' 00 CS ON co q q no d + + d 0) O ON ^t H- ■* so h in cs m in m cs 4 4- to 1 O in cs on ^q q cd d + + d !p O HOi> -e- cs O HI N Th NOO in cs hi in in CO O r^ N _|_ in in 1 o\ Ci on HI O H in + + d 4) O 00 00 co on q q in oi m in in CO CO -4- O On cs O co d in + + d 6 _; OJ O cs M IN Ht CO M 10 co M in in M 68 THE THERMODYNAMIC PROPERTIES OF AMMONIA co O CN CN On CO LO LO CN o0 CN CN CO CN CO On ON 8? COCO On O t^- H ON M N t>- co ON O On LOCO hi o W CM H CO w w o + CN M CN M 00 H H O + Tj- CN CN HI CO M LO CN CN M CO M M NO ON CN CN M OO M M O + CN CO HI W M O + On m hi O + 00 r- O cn On co m O H M CN CO M LO CO Tf CO M O LO CO co cn CO O CN CO CN m CO LO On m a- M M CM O NO On NO tj- On OTfMO NO co On ON CO nO O O o NO 0O t^-CO co O On O O CN NCI00 O lo r*. CO r^ OnnO C^ O ^fl H io On m lo + CN LO CN M LO ON M LO + rj- LO CNl M LO ON M LO LO LO CN M LO ON M LO OnnO h m lo On M LO + CN O HI HI NO ON HI LO + LOO M H NO ON HI LO + o V© CO in co CO o> W n N O M ON O O ON H LO M O o O CO O CO M o NO <<*■ -*oO CO m o o LOCO co l>- co Tf On O On O CN co t-» r-o co O ^nO On On C^. O O On CN M ■^"CO M LO + CI Oi"N H Tf CO M LO + Tj- ON CN HI ■3- co M LO + LO O CN M t1- On M lo + On O i-* M "tf- ON M LO + CN O HI HI LO On M LO -f LO O HI HI LO ON HI LO + o V) CO Tt CO CO CN CO M O o CN HI CM CO w w O CO On t— lo r^ co ON CN Tt r^ co lo O O ^3- CN On ONNO cooO CO O ON LO co ON NO r-* O r~* O CO CO O lo On co N O O co CS M coco M LO + COCO M LO + tj- tJ- CNl M COCO M LO + LO T)- CN M cooO M LO + ON •<*■ W H COOO 1-1 LO + CN LO HI HI ■^-co HI LO + lO LO Ht HI TfOO HI LO + CO cn oi m o O M M -* O COCO M SO O t- O r— lo LO\D CO ON On o o LOO co m CO O LO ^J- LO LO NcONO CN O ON o ^r OnO ND O O CO CN HI cn n M LO + CN CO CN M cn r-~ M LO + Tj-00 CN H C-) N H LO + LOCO M 1-1 H LO + On On m hi W LO + ci Oh h co r— HI LO + lo On hi Hi co t"» M LO + o CO M ^ OnO N NO O CO CO H CM O m CO O OO CO OO NO LO o h ao ON CN LO CO co On !>• O O lo CO LOCO O ON H. Th NO !>• O O ON co co ONC0 nO CN CN HI HI N M LO CN CN CN HI M lO + tJ- CO M M H LO + LO CO M M M LO ON CO M t-t CN CO HI M M LO + LO CO HI Ht CN N HI LO + © o CO LO ■^f LO -l IN CO LO M CO On O On •H CX) CN *3" O LO On o r^NO NO tJ- 00 no co O LO ■*■ o o 'i- COOO t>- O o CO lo N co r- O>0 O On O ON On CN On m lo O Q N CM HI nO M LO + CN N M M O nO M LO + O no l-H LO + lO 1-. M M O NO ON t-- M M O no M LO + W Mi m M O HI LO + LOCO M M M O H. LO + o CO CO ■* cn O 0> O OO CO M CO Tf M NO>0 CO LOCO x^. co O Onoo o ON CN LO co O co M O CN CO CO CN l>- O ON HI Tj- CO CN !>. CN O O On LO HI On co lo O O M M H ono LO + CN M M M LO + **■ M M M ONO LO + IOCI H H OnO LO + ON CN M M OnnO LO + CN CN HI HI O no HI LO + LO CN HI M O NO H LO + o a. 00 Tt" co o o> o 00 lO HI CO co H GO O CO CO 00 CN CN COCO On NO LO r^ cn -*■ *-• r- O t^- CN LOO O On ON ■* CO HI LO LO O O On H O NO LO O > LO LO LO LO LO LO LO LO LO LO LO LO LO LO CN M o CO CO r-~ ON '5 O 00 w -1- NN 1 o CO cn o r-i CO oo -f- n oi 1 O cn CN M o0 O t-i CO to _|_ CO CN ' nO nD wow 'O CO CN + ONM ^^ NO O CN CN CN O M On CO lo + O r- CN CN CO O M -\- HI 00 * N* CN CO co O hi LO ?* CN + co -* 1 N HI CN 5*- HI O HI J LO o LO + + LO + + o NO + + CN NO + + o o NO + + o o N- + + *• + + d 0) o a 0) o d 0) o d cu o d a -; 0) o d CD O d 0) o LO LO M o o LO NO o CO o On 8 CN TABLE III 69 10 00 CO Os 1- Os CN o CN CO M Os co Cl M Cl CO CN M LO Tj- CN M 00 .eo 10 CO - OO NO Cl r» M >-> CO r^ M O OO SO •H 00 Cl LO i-i CO Os -* r» "t Cl H Os HI HI 1-1 00 O to CN H CN 10 CI HI •*■ LO CN l-H to so CN w OssO CN |_( c-l r-- Cl H to 00 CN rt sO 10 sO LO SO LO SO to so to r-« to I>- LO CN Cl O M ND Cl sO Cl NO CN O CN O + + + + + + + Cl CO LO CN '+ Tj" Cl *tt O OS LO CO Cl Cl Os W CO CV 1>- LO CN ;-..> O c- Cl t»* •+ r^ sO TfO Cl LO lO s O cn w r- M H tJ-sO M Os 10 CO Cl Tt" coco «- i>- CO Cl HI a- -1 HI _K *o 6 «* CM M CI 5 CN W ■* 3 Cl M LO to Cl M Os to Cl HI fN ■o CN HI 10 r^ Cl M •* rf *f ^t "t -"t -3- -<*■ LO -t to Tj- K 01 MO Cl sO CN sO w so Cl CN •O ci MD cS + + + + + + + 1 M CO to CN •& r~~ r-, 1 sO t^- r~- -+ M LO LO Os O -1- 10 r^ r-NO cosO LO OO ■* *t ^* (N sO M M Qs LO- O ■* LO 00 P* "*■ M co co co r^co M CMOO HI m O 00 Cl l-l Cl CO CN H Tj- OS Cl _ LO O l-H Os O CN HI CN O Cl H lO H CN H cO CO CO CO CO co CO co co "3- Tf «* Th ■* CN Cl sO CN Cl sO CN SO Cl sO ct so + + + + + + + 10 CN CO tJ- ^r r~- CO m 00 co co cr- M0 sO co r-. r— COSO O sO co LO to to CO LO sO r|- ^3" rt •+ CO Ci Cl -O H M LO 10 l-l os Th l-l CO "N CO M COCO Cl H r^ co *-* M O Os HI O ^ O (•0 CN M CN CO Cl M ■* CO CN M LO -+ Cl <~i Os ^J- Cl HI CN UO Cl H 10 to CN |_, CN co CN CO tN co Cl co CN CO CO co CO co £ Cl SO O tN SO Cl O CN \0 Cl sO C4 so + + + + + + + -i 00 CO Cl H co ci HI i-i r-^^o HI CTs « Os HI ft O <5 ci M CI r^- CN M "* r— CN M to r^ CN l-l OsCO Tl !_, CN X) Cl W to Os ,_, _ u> Ov Os Os Os OS M O O H O 1-1 O O hi CN O CJ CO + + + + + + + >} >0 x> Os ■+ Os C-* ■* ^*- LO 00 cr: O 1^. O Os ■* Os H -*■ ro -O co "i r^ W r^. C| X) 8 O. Os H -O q coco q Ti- r*- q lo-O q to LO q H M sd to LO LO to to LO LO to LO LO to to LO LO oi H CO CO r-. Os 6 Cl 4 to 6s Cl LO 00 i_l CO CO co >o CO CN CO 10 0. >0 Os Cl + r-- cn SO 00 + 1-* Cl CN + CO" Cl sO so + O O + O c~. + l-H X) + CO ■* 13 C) O Cl M CN Cl ' 1 co -* '3 t-^ 00 q M 1-1 M Cl t ~l co q M co HI cr LO !>. 6 6 CN sd 6 4- d 3 IO LO sO SO MD r~. r- + + + + + + + + + + + + + + d d d d d d d s s 6 E E - E S . aj O CD a> CD CD CD aj hO> •e- HO»>^ ^a> -G- ha> -0- na> ■o- HD> ■6- eo> ■9- LO O 10 O O 8 LO SO r^. CO O. w l-l l-H HI Cl 70 THE THERMODYNAMIC PROPERTIES OF AMMONIA ** o On M Tt ON o oo o 4 00 ON o o CN| COCO cOnO M On CO On LOCO On CO COCO 1^. *o hi tj- q o o q oq oq o O w t-» O O •^■yD o r-^ r^. »o o rj- r^ lo O m q Tt q 0> W3 M M M tJ- m m 4 4 M M i~- ■* M HI 4 HI H ro IO M M LO LO M H Os H M no + O M CN O + O M + O M CN O HI HI (N sO + ^1 O + CN nO + OO Tt CN CO nO CN f»- rj- Ov M0 LO LO M On r^ ON CO Tt O LOO I--CO On 00 oj CO LO !>■ Cn Tt r— CO nO o a O M r- O O Tto o On t-^vo O N c>^0 ■Tj- On Tt HI CJ Tt nO co CO O ONOO M M CN CO HI HI ^-00 M M l>.00 H M O CO HI HI CO 0> HI H LO ON HI M 00 On O On O On O O O O o o i-i o -. MD M -O ci no IN nO CI nO + + + + + + + o ■* NO ON Tt o 00 M M O C-! r^co CO Tt CO NO 00 COCO O r- o r^- NO NO nO NO LO LO 00 O Tt r- O O r-MD O On On ^n O t^» w LO O ^»- H -d- M ■* •* NO Tt CO O Oi cn M M CN CI M M Th - co M H O co M HI ro CO M HI LO CO HI HI r^ O CO O CO CO O On O O O ON O H O M NO H NO i-i o + + + + + + + CO 00 NO NO NO CN r- CN CN lo r-- oo CO ^ On NO LO CO CN t^oo fs. ci \0 lonO ON LO CO '-O CO LO CN Tt o O 00 r^ o O w O O On r-> LO O r- rt "t o ** co Tt M lo co NO no co O Ov\© M i-l CN t->- HI HI -t o. M M !>. I>. HI HI r- HI M co r-. i-i H U1NH H no o* 1^* On i>. On r- on CO ON CO On 00 On M U-) H IO M LO M LO HI LO M LO HI LO + + + + + + + ON NO "* *t NO NO NO m cn i-i oo Tl- -+ •rf^O CO ON CO On O sO On lo LO NO LO o -+ ON ro On co o O M o o o ■*■ *o O ai-^o r-^NO rf Tj" LO -^ HI !>. CN no X"^ CN On hi M M CN HI HI HI *t M H M r-* h M M O M HI HI CO M H HI IO H HI HI iy-1 o. NO ON NO On NO On I>. On r^ on r*. On M LO M LO M IO HI LO HI LO M LO HI LO o + + + + + + + 01 CO CO ON CO On Tt NO o CO CO LO 0> o "+ CO o ■N NO ro CO On 4J CN LO LO tJ- On "J" IN -it r- CO (N ^o no cn o o -*-o o O MoO On r^ Tf o r-co •* o «t t^. co HI Qn co O On cn O o lo M M CN LO HI M Tj- IO M M r- lo H )_| lo M H CO LO i_i HI LO LO M M c-1 TtCO H IO lOOO H IO LOCO M LO LOCO M LO NO CO HI LO NO OO M LO NO CO M LO o + + + + 4- + + £ CO o r^. o Tt r-^ M M Tf On O LO LO IO c r-~ On co CO o 0> -t >-< *+ LO co On CO CO cs CO CN co CN < o o no LO O On lo On CO M" O r- On CO -3-CO -o O M On CN o \0 On cn O O On ON M HI CN ON M M Tf ON H i-i r-* Qn HI M O ON M M CO On H l-l LO O- Hi hi £ co r~- ■sT *-- ■* N tj- t~. io r— LO 1^ LO 1^- H »0 M TJ-> M LO M LO M IO H LO H LO o S + + + + + + + OO CO On r^. O ON Tt § CO tJ- CO O O LO NO r^. ro f- lo rO CO co CN f") NO C-l o M LO O HI < o o oo lo o o tj- o ON 1- O t- co O ■* On co O HI On CN NO CO CN O O On co M M CN tJ- m m Tj" ■^- M M r- Ti- HI H O CN M M CO CO M ,_, LO CO HI HI Q cn r- ro f- CO 1>- ro r^ ■* Jr^ Tt r^ Tt W m in M LO M IO M io M LO HI LO HI LO w H < + + + + + + + CN CO LO CO Tt Tt LO U-) LO NO tJ-nO NO CI cOOO LO Tt NO O i-i CN Tf CI CO Cn| i>- o o- O o O H lo O + CN CN M H M NO l-l If) + Tt H IN LO o Tt r— CO <-o co On u co O f- o On LO ON O 00 LOCO m r-*. a V? ''T 9 IO co O *t co On co CN On o CN On On On Nh a > NO I-I I-I NO M M NO H 6 NO H d NO H LO H 6 LO M O LO IO LO LO LO LO LO IO IO O LO On LO LO LO LO NO O ■N 4 r^- CO LO & o o Tt 7" r - M ON HI M HI Tf HI NO HI (^ + tj- a> _L ^ M + NO vN o + 00 O f^-NO + On f-^ + o CO ^ 1 00 CN *d CI «*■ O) NO cn* NO M !>. IN t~*. '3 *"*• O H fN l-l NO O HI On O HI HI O HI >-e- HO>-& hO)> ■e- hO»> ■©■ ha> •s- ha> ■©■ HO>* o o o o o o o C4 CO ** LO NO W W «N <-< ri M ro O CI iO 0>H N Os >0 Os coco ^h ro CN O O r-i (N Os to 1-1 C| r^ h m ^- ^h Os M M O-OO m O "*t*00 HI 10 OS f^. . OS o CI O O VO to O 0>O H M O N O M O-MD o> H r^- m co m tJ- COCO Hi H CO *^- '- , so 0> W H . LO CO CO Os CO O ■* lo LO co ^^ t t to CO °o O to O hi Q-. H Os ^" O^ l-l r^ o^co m ■* " r^ M O 0- H" SO OsO hi 00 O*o0 w r^. 10 IN O Ci Os 00 vo cn + Tt OS 00 to IN SO + HI 00 to CN O + O O + w CO O ci + IO O HI HI OsO ci \0 + CO OO t to r^- Tt" CO *§ O M CI (N GO r- ■* O r-> HI tJ- .a "* CO ■* IT) CO r-* co CO •3- Cl O *-*■ CN H ts t-* >-l H TtCO M M r^-co m h. O CO ,_ 1-1 co O- M |_| VO OS M M 8 LO ^tf" sO ■* SO ^fr- sO ^t- r- -^i- r- -* f- t CN O ■n so ci sO ci so Cl sO ci (N O + + + + + + + 1 CO O o> O0 co Ov 1 ^fr O CO 10 CO sO so O -O CO O CO CO Os co CO ■* "N CO CI CN O hi ^O" O 00 o- O CO00 m O^ 1^-00 t^. m r-*. m "?h coo HI m r-^so H< O O tO HI !>. in Os M M M CN CN M H Th CI H M t^. CO M M O co ,_, M co co M |_| LO Tt" HI M <3- (N ^ *fr 10 -+ vo Th VO ^t" so "3- O ■*■ 4-1 (N O 0 CI d SO ci ci so + + + + + + + O ■* O Os Os O CO |>. O \r> r^ CI sO CO VO O HI 00 O CO so W OO CI h-t M VO as CO ' O O M Os M r--co m Os O I>- H 1^. -^- t-* H ■^J-sO so M M O >o HI so ci to M O Cr-O H. M cn O M M ■cf r- l-l H t^. r^ h m O r^ M IH COCO M hH lOCO HI M Z co co Tj- PO •"*■ co tf co vo co vo co to CO cj \0 IN SO CN SO ci so ci so (N sO IN O < + + + + + + + CO OO r-~- sO M r- vo s IO CO CI OQ VO Tf VO O t^ CO CI ro H IO CO M CI sO Os O s O O Os W O CO M Os *t r^ H r-*. t-^so m Th 00 w HI CI LO ^ O 't'tH rO Os H M Cn H M HI Tj- W H H i^. i-t m m M H HI CO ci M M IO . r^. h so m Tt" M LO O M VO IO >D NTfO < OS IO M M - HI -(J- ^ so Os Os Ci Os sO 0. O CO tJ-QO O Os "3- O O Tj-00 r-* r- O Os H sO O r^ Thso O ^f "* to O M t^ VO O OS O^ M M CN Os 1-1 M Th l-l hi t-^ O M M M t-l CO M hi VO O HI HI M M CI ci ci ci ci CI CI CO - a 10 Tj- q VO CO O ■*■ CO Os co (N Os q *1 Os Os HI On nh a > SO M H sd M M so H 6 *o m 6 SO M VO M 6 VO H-" 6 10 LO to 10 VO VO to IO q TO Os vo to **• vo M to 01 4 r^ CO to Os O O <* Tf 1-1 I~-- M O M CI M -+ HI •H !>. + s Os + 10 ►- + SO Cl -I- co 1 t^sO + Os 1^ + CO 0* 1 CO iN T3 - 0* 13 CO CO CO O^ Os Os -t- + + + + + + + + + + + + + d d d d d d d S ^ E e S - 6 s 6 ^ aj -e- ho>-g- na> -e- na>* ha> •o- ha> -e- na>^ (N CO Tf to t^. m - O) n Hi On In. in ro n c0 On CM co r-» CM r~*NO 00 O no HCO M o OnCO m o ■*co O O CO O o o On CO O O CO OO On O OO M M M CM M H M n h h M HI CM M M in m O HI On M o H NJH H N On CO On CO On On On O On On On O O 8 m lO M in h in HI in m in m in CM lO + + + + + + + O cm TT CO M 8 M nO NO m cm ^f o On CO ■>*■ NO NO o CO IN O- On oo O oo On IN. rJ-CO On s O CO On w M CM On HI Hi N00 HI M m On O in On O On 0> COCO O lO N NO IN. O r- N !>. I>. N r~- N 00 in- o M lO m in m in m in hi in m in m in § + + + + + + + s < n CO •*■ O r^. O CO NO O oo o CO CO CO CM Ci cOOO On co •O O CO o 0> in co O oo m N O c- D W N 1-1 o On in O On rt- co O On 00 CM o On On N O On co moo O f^CO OO On o OO ^H H CM CO M o NNNM H CM o in m O On HI O CO M O ■<*■ in. in N in n NO NO NO N NO IN- !>. r^ M in m in m in hi in m in m in m in < pq + + + + + + + ON M ^i- *fr On Tt- NO lOO oo O O CO N !>■ OO NO in h< CO On in On OOO CO l-~. r- N CM NO CO o M t^- M On On Tt* O On ■«*■ O On On CO CO o On On COCO On 00 OOO On N OI N On o CO Nm o n nm o f- !>. O M NO o in no On in O o co in w CO \D TtO *^-o ino ino in no O NO Oh M 1^ m in m in H in m in hi in hi in + + + + + + + w o o O in On CM M ■*NO CO On tj-no o m H O O OO CM N NO l>- O nO in no o' in no in □ M NO M On On CM On ■^t-00 On On oo in On On On OnOO On CO TfOO On NnO NO OO M M O CM M M o In. O O M o in On On On O roCO CM 0> CO'O COO ^-nO rj- in t}- io in in HI lO M in m in m in m in m in m in + + + + + + + n o ■* O O ■N NO CM >n 00 CO o m ■^■oo r^- CO NO N o o. N n OnnO COO r-- in m 6 in 6 4 6 4 6 CO . M >o O CO w CO CM M CM ^ CO ■tf- CO o CO 30 ■* CO 4- co 1 cm NO ' N OO m inyj I CO IN. 1 CM O M i>- + 00 On + On o X> NO + o CI m CM + CO nO O CM 4- On O 1 CM nj. m q CM T3 CM On 9 M ro N C! NO CI in O CM 3 CT d 6 io d M 6 o 6 M 6 ^6 d m d CJ CM CO J HI + + + + + + + + + + + -f + + d d d d d d d S 7* B ~ S -s 6 B S 6 ^ QJ QJ QJ O QJ o OJ o QJ o oj hO> •&■ HO> ■©■ ha> ■& hO)> -e- ho>a Ha> -©■ HO>* o CO 8 o CM o o & 8 CM co CO co CO CO * TABLE III 73 r* NO "t CO CO t^. H o r~ r^- . l-l r-- o t^ O On Cl O- VO ON o o M Tt o O* ** r- w t "* v -: CM 00 VO lO CM O M ^- cm 00 fO^t M r>. hi CO HI CO O" M M w o M M !>. t-4 M w M CM H H IT) fO h IH OS -t IH M co vo HI M ro M Cl - r-- O oo 00 O 00 ON O co t-* CO r^. co r- CO r- co r*. co r>- CO I s * + + + + + + + 00 H r-. vo o\ 1 CM CO vO o NO ^O CM O CO M to VO ■* ON CM co to ro ^t 5 Tf mO CO On co CM CO r-» CO o MCVO M C co vo M ^J- IH »H CO O cO M On LO CM M CO o CM i- 1 l>- !>• M M o CO CM w M Cl rO M l-t r^ *t M IH M to M M vo to w |H OnmD HI HI CO NO H HI HI 1^. cm r^ CM r^ CO r^ co f- co **>• Th r- coO . ON HI HI 00 CO M IH M cm M l-l !_) r- CM IH IH M CO M M vo co IH i_, On ■* l_l H CO Tf M HI OnO O O O -O NO IH NO M MO CM NO CM O cOO CO NO COO CO NO CO NO COO + + + + + + + ^3 Th LO CO r^ r^ t^- NO to Cl M r-^NO OO M COCO Tj- to CO CO CM O a co in fO M ■*■ r~- o o t o o O .K o M O LO l-l On to Tt M rh w CO <-< 00 CO CI On cm CO t- M t- o ■fcj *o CO O M M CI O H l-l i^- |H h4 M l_l M M l_t lO CM i_, IH On Cm M IH CO co IH IH e M r-~ vo CO io CO LO On LO On lo On lO O to <3 -1 CM o co O r^ -d- o -d- O 00 n- tj* O CM CM LO ON ■<* o l-l CM o LO 00 On CM ON O On 8 o M CO vo H On CO ■«*■ M •«*■ ^ PO M 00 o CM w ON Tl- IH o CO CO H o r*- m ID CO 5 H M CN ? l-l M t-* LO IH M H NO M IH tO O |H H On NO IH M co (>• IH HI o r-. r- "fr CO -*■ CO Tf CO ■<1- on «d- ci O -t vo co NO rO NO CO 1^ ■* t~- ■* r^ t CO Tl- CM o CN O CM NO c-i NO ri so CM NO Ci no < + + + + + + + CO i-^ w NO M O OO LO 5 ON CM W o On ON £_ O VO o> NO On r^-oo O CO COCO OO t^ CM r- o M t^ "fr o On M co o tJ-MD CM o CO IH CI O O- ^f" O 00 NO o Nao CO CO - w < CN On COCO toco CO r- IH r^ to r^ o o M o- **■ O On co co *frNO CM o CO M 1-1 O On -d" I-" O CO C-O O O. On o o CO O H M CN r^ M l-l r^- r^ M (-, <_, 00 •H M tooO w M On CO HI M coCO HI HI CO Cl ■* Cl ■* C-J LO CM to c^ lO CM NO -00 ON 00 o r-* r^ NO NO O- NO co nO 00 LO Cl, o H '-' co o On ^ CO IH l-l M N M M M x^. IH H M HI C-l M M iri o IH M O ci IH M CO CM o M CO CJ Cl ro cv co CM ^f M ■* n Tf Cl VO CH Cl o OJ O CM NO CM NO w vo CM NO CM O + + + + + + + r^ NO ■?»■ o ON CM o Cl to CO CO CM NO to -too r^- CO o r^ ft c» On NO CO NO r^. LO Cl •* r- ■* CO CO to o o^ q ON Ov to 0> On M CO ON ■NtOO <> 00 r-. ON q t>- On > to _ d io 6 4 6 4 d CO d cl d CM d to LO LO LO to LO LO lo LO LO LO to to to W o> ** 00 On CO tN- CO 00 oi M r- CO IH ■H- LO o On 00 CO oc M CM l O cs LOO CM r*. ON CO On o CO LO co to NO Tj- LO Tf" HI CO r-- M OO l^. IH co -o IH 00 no On "&■ o- On O :S + Cl CN o oO + o- o On + CM co O o CM + t*- CN CM +o CM o CM + « Cl CO Cl + M O CM '3 d d to 6 M o NC d M NO 6 IH d CM CM CO h3 M IH M + + + + + + + + + + + + + + d d d d d d d a E e B a E s ■©■ HO>> ■e- HO*> ■©- hC> ■e- Hcp»> ■©■ hO> ■e- hO»> -a- o CO 8 o CM §■ o c8 8 CNJ f*i CO CO CO CO 3-