Phase Equilibria in Hydrocarbon
Specific volumes, Joule-Thomson coefficients, and isochoric specific heats have been determined for ethane. From these and other primary data, values of heat content and entropy have been calculated for a series of temperatures from 70" to 250" F. and at pressures from atmospheric to 3500 pounds per square inch absolute. Several diagrams illustrate the thermodynamic behavior of this material.
Systems XVIII. Thermodynamic Properties of Ethane'
above and below the specific volume which corresponds to the critical point, throughout the temperature range from 60" to 140" F. Joule-Thomson measurements also were made a t pressures from atmospheric t o 600 pounds per square inch for five temperatures between 70" and 220" F. These data, with the results of the atmospheric specific heat work of Eucken, were used as the basis for the derived thermodynamic properties reported in this paper.
B. H. SAGE, D. C. WEBSTER, AND W. N. LACEY California Institute of Technology, Pasadena, Calif.
Materials
I
I n the investigation of the thermodynamic behavior of a material in the critical region, the purity of the sample is of paramount importance. For the present work a sample of impure ethane (approximately 95 mole per cent ethane) was obtained from the Carbide and Carbon Chemicals Corporation. This material was fractionated three successive times in a column packed with glass rings ( I S ) ; the middle portion from each fractionation was used as the feed in the next step of the purification process. The overhead material from each fractionation was condensed a t a pressure of approximately 1x inch of mercury in order to remove small traces of noncondensable gases. The material thus purified was then used for a series of P-V-T measurements. It was subsequently mixed with a larger quantity of ethane which had been similarly purified and was subjected to two additional fractionations and partial condensations. The product from this latter purification was used for a second series of determinations in the critical region. The two samples were found to be identical in behavior within the experimental accuracy attained. For this reason it is believed that the samples of ethane employed were of such purity that no measurable errors were introduced into the experimental values as a result of the impurities present in the samples. The samples exhibited less than 0.2 pound per square inch change in vapor pressure from dew to bubble point3 a t 70" F. Except close to the bubble point and the dew point, the change in vapor pressure with volume was not detectable by the pressure-measuring equipment employed, which had a sensitivity of approximately 0.05 pound per square inch in this range.
N STUDYING the thermodynamic properties of sim-
ple and complex hydrocarbon mixtures, it is desirable to have available the thermodynamic behavior of the pure constituents in the same range of temperatures and pressures through which the mixtures are to be investigated, Such experimental data for ethane, one of the important constituents of industrial hydrocarbon gases, is scattered and incomplete. Beattie and co-workers ( 2 ) published satisfactory experimental information upon the specific volume of gaseous ethane a t volumes greater than 0.13 cubic foot per pound. This work extends from room temperature to approximately 480" F. Porter ( 1 8 ) determined the vapor pressure and the density of the saturated gas with reasonable precision from -180" to approximately 60" F. Loomis and Walters (IO) determined the vapor pressure in the vicinity of the atmospheric boiling point of ethane. Maass and McIntosh ( 1 1 ) measured directly the density of liquid ethane a t low temperatures. Haninlen (7) and Kuenen (8, 9) determined the vapor pressure of ethane from low temperatures through the critical region, but this work was done many years ago when such experimental technic was not as well developed as a t the present time, and the samples of ethane employed were of questionable purity. For this reason the data of Haninlen and Kuenen have not been considered in connection with the present work. Eucken and Parts (6) reported data upon the specific heat of gaseous ethane a t atmospheric pressure a t temperatures from 70" to 220' F. The lack of satisfactory pressure-volume-temperature information a t specific volumes less than 0.15 cubic foot per pound has made desirable a rather extended experimental investigation of the thermodynamic properties of this material. The experimental work reported in this paper consists of P-V-T determinations from atmospheric pressure to 3800 pounds per square inch2 a t twelve systematically chosen temperatures between 70" and 250" F., together with specific heat determinations made a t several constant volumes both 1 2
Pressure-Volume-Temperature Measurements The general methods employed in the determination of the pressure-volume-temperature relations of this material 8 Bubble point is that condition of the sample a t which i t is entirely liquid except for a n infinitesimal amount of gas phase. For a pure substance this corresponds t o "saturated liquid" while dew point corresponds t o "saturated gas."
Previous articles in this series appeared during 1934, 1935, and 1936. All pressures given are absolut,e.
658
INDUSTRIAL AND ENGINEERING CHEMISTRY
JUNE, 1937
have already been described (16, 17). However, numerous improvements have recently been made in the existing apparatus which have increased considerably the absolute accuracy of the experimental work. Work of this type involves the measurement of four fundamental quantities-pressure, temperature, mass, and volume. A brief description of the methods employed for the evaluation of each of these quantities will permit a better estimation of the accuracy of the experimental data. Figure 1 is a schematic sketch of the equilibrium apparatus: The steel pressure cell, A , had an inside diameter of approximately 2 inches and an effective length of 11 inches, and was used to hold the sample. The effective volume of the cell could be varied by the addition or withdrawal of mercury through valve B. The volume of the cell above the mercury surface was determined from the height of the mercury within the chamber. The position of the mercury surface was ascertained by means of an electrical contact mounted upon the end of the hollow rod, C, which entered the bottom of the cell beneath the mercury surface through a packing gland, D. The connection to the contact, E , was brought out of the apparatus through the hollow rod and was connected to an appropriate relay system for the actuation of a signal device. The position of rod C was varied by means of the threaded lower portion which engaged nut F . This nut was mounted between preloaded ball bearings and was driven by means of worm G. The rod was carefully threaded and lapped so that the maximum error from linear movement was approximately 0.0002 inch in a distance of 12 inches. A counter connected t o worm G recorded directly the position of the contact. By this means the position of the mercury surface could be determined within 0.0005 inch throughout the range of pressures and temperatures after making suitable pressure and temperature corrections which were established by direct calibration. The cell was bored and lapped to a true cylinder whose diameter varied by less than 0.0002 inch throughout its length. This per-
HIL.
OIL LEVEL
CONTKT
LEAD
u FIGURE 1. PRESSURE-VOLUME-TEMPERATURE APPARATUS
659
mitted a linear calibration curve to be employed for most purposes. To avoid changes in the effective volume of the system when the position of the contact was moved, plunger H was mounted on the lower end of the contact rod. This second plunger had the same diameter as hollow rod C; and since the cylinder was filled with mercury and connected to the mercury space of cell A, the change in volume due to the withdrawal of the contact was exactly compensated by the displacement of an equal volume of mercury from the lower cylinder. The use of this compensator reduced the pressure correction for the instrument to less than 0.03 per cent at 4000 pounds per square inch. By suitable calibration it was possible to determine the total volume of the cell at any temperature or pressure, within 0.0005 cubic inch, in a total volume varying from approximately 2 to 30 cubic inches. For these reasons it is believed that the total volume of the sample was determined to 0.1 per cent throughout the temperature and pressure range reported in this paper. The temperature of cell A was maintained a t any predetermined value by means of the thermally insulated oil bath, J. This bath was equipped with an exterior heater, M , of such capacity that, unaided, it maintained the bath temperature at approximately 2" F. below the desired value. A small immersion heater, N , of low thermal capacity supplied the additional heat necessary to maintain the bath a t the desired value. This heater was controlled by a photoelectric relay circuit which was actuated by the light reflected from a high-sensitivity galvanometer. One junction of a thermocouple was placed a t the outlet of the oil bath agitator tube; the other was immersed in an agitated ice bath, the circuit being completed through a potentiometer t o the galvanometer. This arrangement permitted the rapid attainment of the desired temperature and its precise maintenance with a minimum of effort. Another thermocouple located within the bath adjacent to cell A was used actually to measure the temperature of the oil. In order to determine the temperature within the cell, a thermocouple was located within hollow rod C. This thermocouple permitted the measurement of the temperature a t various points within the equilibrium chamber. For all of these temperature measurements a specially designed potentiometer was employed. Temperature differences of less than O.O0lo F. could be measured. These thermocouples were calibrated a t the boiling point of water and a t a series of temperatures above and below this value, determined by means of a calibrated mercury-in-glass thermometer. It is believed that the temperature of the conterrts of the cell was determined within 0.02' F. throughout the temperature range investigated. A small continuous heater, R, mounted just below the oil bath was used to overcome any thermal gradient in the walls of the cell due t o heat leakage along its axis. Temperature measurements below the surface of the mercury near the bottom of the cell were utilized in the regulation of this heater in order to avoid thermal gradients. To ensure the attainment of equilibrium, a revolving cage of four vertical rods, K , was employed. This cage was driven by means of a pair of bevel gears through the thrust bearing, L. This bearing was far enough removed from the cell so that large differences in temperature in the packing were avoided. By use of this mechanical agitation, both thermal and phase equilibria were usually attained within a short time. The ethane was distilled into the apparatus which had been previously evacuated through valve P. It was added from a small weighing bomb having a capacity of approximately 6 cubic inches. The mass of ethane added was determined by the difference in weight of the bomb. To avoid loss of ethane in the connecting tubing, the remaining ethane was frozen in the bomb by means of liquid air. This reduced the quantity of ethane in the connecting tube to less than 0.1 mg. After making suitable corrections for air buoyancy and the normal balance and weight calibrations, it is believed that the mass of sample added was determined within 0.05 per cent of the quantity added. The mass of the sample within the apparatus mas checked by withdrawing the ethane into the weighing bomb, by use of liquid air, after the experimental work had been completed upon a given sample. The mercury-oil trap indicated in Figure 1 was connected to a specially designed fluid-pressure balance used t o determine the equilibrium pressure within the system. This fluid-pressure balance had two rotating plungers, one for use up to 5000 pounds and the other up t o a maximum range of 500 pounds per square inch. The force exerted by these plungers was transmitted through a series of precision knife edges t o a beam, a t the end of which could be suspended a series of weights. In the mounting and grinding of the knife edges, a technic similar to that used in the manufact,ure of analytical balances was employed. Care was exercised in the design of the balance beams to reduce the maximum deflection to less than 0.001 inch in a length of 14 inches. The balance was equipped with a lifting mechanism
INDUSTRIAL AND EXGINEERING CHEMISTRY
660 I.c
VOL. 29, NO. 6
This low a c c u r a c y
is caused by t h e rapid change in specific h e a t w i t h temperature throughout the critical region. It is believed t h a t the JouleThomson determinat i o n s m a y b e depended upon t o a t least 2 per cent. On account of the small changes in temperature e n c o u n t e r e d with t h e p r e s s u r e d r o p of a p p r o x i mately 1 pound per square inch normally employed, a n o t h e r set of measurements was made with a p r e s s u r e d r o p of over 15 pounds per square inch. It was found that these two
0.6
0.E
0.7
0.e
0.:
0.1
PRESSURE
LE. PER
SQ. IN.
FACTOR OF GASEOUS ETHANE FIGURE 2. COMPRESSIBILITY similar to that found in the better grades of analytical balances. The weights employed were calibrated against standard brass weights in air, and the necessary corrections for air buoyancy and the prevailing force of gravity were applied. The weights were mechanically added or removed, to avoid errors and to expedite the use of the balance. The point of balance was indicated by a light beam reflected from a straddle-mounted mirror which was tipped with any movement of the end of the balance beam. A movement of the plungers of less than 0.0001 inch could be detected by this method, thus permitting a rapid indication of small changes in pressure because no appreciable flow of fluid in the connecting tubing was required. The instrument was sensitive to pressure changes of 0.05 pound at a pressure of 3000 pounds per square inch, and pressure changes of 0.01 pound could be detected when using the low-pressure plunger. The instrument was calibrated against the vapor pressure of carbon dioxide in a manner similar to that described by Bridgeman (S),using a value of 505.56 pounds er square inch for the vapor pressure of carbon xioxide at 32' F. It was necessary to correct the readings of the pressure balance for the constant head of oil and the varying head of mercury in the connecting fluid system between the interior mercury surface and the plunger of the pressure balance. It is believed that pressures were determined within 0.1 pound at pressures below 1000 pounds per square inch, and within 0.2 pound at higher pressures. No effort was made to increase the accuracv of mesFIGURE 3 . SPECIFIC VOLUNE-PRESSURE DIAGRAM I N THE CRITICAL REGION sure measurements to better than 0.1 pound per square inch even at the low pressures. In order t o make use of the full sensitivity of the low-pressure plunger, several sets of measurements agreed within the experimental unmodifications would have t o be made in the connecting fluid certainty. system to avoid the possibility of surface energy effects and other complications such as the effect of pressure and temperature upon Experimental Results the calibration constant of the gage. Figure 2 presents some of the results obtained in the gaseThe apparatus employed for the determination of the conous region. The ratio PVM/RT is plotted against the equistant-volume specific heats and the Joule-Thomson coefficient librium pressure a t each of a series of temperatures. I n this has already been described in previous publications (14, 15). ratio, I' is the specific volume, M is the molecular weight, The isochoric specific heat measurements are considered and R is the molal gas constant. Only a portion of the experitrustworthy within 2 per cent a t the low temperatures and mental points has been presented, but the ones shown are may have a somewhat larger error at the higher temperatures. taken a t random from the results for four different samples
JUNE, 1937
ILUDUSTRIAL AND EKGINEERING CHEMISTRY
of ethane. I n order to verify the accuracy of the low-pressure data, another set of pressure-volume-temperature measurements was made in an apparatus similar t o that employed by the Bureau of Standards (1) for the determination of the deviation of actual gases from perfect gas behavior. The results obtained from these measurements cannot be distinguished from the other points on the scale presented in Figure 2 . The reproducibility of the experimental points is consistent with the accuracy of the individual measurements previously described. These data agree reasonably well with the interpolated values from the work of Beattie. In general, the values are between 0.1 and 0.4 per cent larger than the specific volumes obtained from his work. This disagreement, which is largest a t the lower pressures, may be due to inaccuracies in pressure measurements in one or t.he other set of data, since this appears to be the most likely source of error a t low pressures. Figure 3 shows a pressurevolume diagram for the critical region on a somewhat enlarged scale. There is a rapid change in specific volume with both pressure and temperature, which makes the determination of an equation of state or of other generalizations for this region extremely difficult. The specific volumes of the saturated liquid and gas were determined by the breaks in the isothermal pressure-volume relations which occurred a t these points. Although the experimental work of Porter upon the specific volume of the saturated gas does not quite extend t o these temperatures, an extrapolation of his data would indicate somewhat larger specific volumes ( 2 per cent) for the saturated gas than those found in this investigation. This difference might be accounted for by possible impurities in one of the samples but is more likely to be due to the method employed by Porter, which is not as satisfactory for the determination of saturated gas densities in the critical region as the one employed in the present work. It has been found that the law of rectilinear diameters (4) appears to be valid for ethane throughout the critical region. Figure 4 presents a temperature-volume diagram for the condensed liquid and the critical region. The rapid change in the isobaric thermal expansion with both pressure and temperature in this region is apparent.
661
I n the course of this work the vapor pressure of ethane was determined a t several temperatures. These results agree reasonably well with those of other investigators (2, 18). Residual interpolation ( 5 ) of the present data to a temperature of 77' F. (25' C.) gives for the vapor pressure a value of 614.1 pounds per square inch; Beattie obtained a value corresponding to 608.0 pounds per square inch for the same temperature. Although these measurements were not made for the purpose of establishing the critical constants of ethane, interpolation of the data indicates that the following values are the critical constants for this material: pressure, 718.1 pounds per square inch; temperature, 90.6' F.; specific volume, 0.07553 cubic foot per pound. The critical tempera-
ture was estimated by
the derivative
(%)
a t the critical specific volume from higher temperatures to the temperature corresponding to the zero value of this derivative. This value agrees well with that obtained graphically from a density-temperature diagram by joining the lines corresponding t o the saturated liquid and gas densities by a smooth curve and then ascertaining the point of intersection with this curve of the line representing the locus of average of the densities of liquid and gas. The temperature corresponding t o this point is taken as the critical temperature. The critical pressure was obtained by residual extrapolation of the vapor pressure from 90' F. to the critical temperature. The critical volume was determined by a similar extrapolation of the average density of the saturated liquid and gas t o the critical temperature. Both of these latter extrapolations may be made with good precision. The results of over two thousand five hundred P-V-T measurements upon four different samples of ethane have been interpolated graphically, by residual methods, to even values of pressure and are reported as part of Table I. It is believed that the interpolated results have the following accuracies: temperature, 0.03' F.; pressure, 0.2 pound per square inch; specific volume, 0.1 per cent. Space does not permit a more detailed record of these results in the gaseous and condensed liquid region, but in Table I1 the equilibrium pressures for a series of specific volumes and temperatures for the critical region are given. These results is nearly indicate that the derivative independent of temperature in the single-phase region, and therefore the isochores upon the pressure temperature plane are substantially straight through the critical region. These P-V-T data permit the calculation of the fugacity of ethane as a function of pressure and temperature. At low pressures, the
(g),
c1 3
B
0 09
Q. U
L
0.08
3
V
w
0.07
I,
logf = log P
P 2 L.
(%F)T,
in which Z is e q u a l t o P V M I R T , is practically independent of pressure, which permitted the assumption that Z = 1- KP. The fugacity could then be computed by use of the following expression: derivative
I-
- 0.43429 K P
At the higher pressures where this simplification was not permissible, the following more general relation was employed:
006
Y % 0 05
=
70
80
90
100
TEMPERATURE
110
120
OF
FIGURE 4. SPECIFIC VOLUME-TEMPERATURE DIAGRAM 13THE LIQUIDAND CRITIC.4L REGIONS
SFp
Zd log P
Subscript 1 refers to values for a state a t which the fugacity has been determined by use of CONDENSED the Previous equation. I n t h e c o n d e n s e d l i q u i d region, where the change in specific 130
662
INDUSTRIAL AND ENGINEERING CHEMISTRY
I
00000
00000 00000 0000
VOL. 29, NO. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY
JUNE, 1937
volume with pressure was not large, the following relation was used:
RT In ffl
=
M J r
VdP
The graphical solution of these integral expressions permitted the accurate calculation of the fugacity, which is given with the specific volumes in Tables I and 111. It is of interest to compare the critical fugacity for ethane of 478 pounds per square inch with the similar value obtained earlier (17) for propane of 407 pounds. The corresponding values of fc/pc are 0.6656 and 0.6322, respectively. ~
~~
FOR ETHANE IN TABLE II. PRESSURES
v
80' F.
Cu.W l b . 0.050 0.0525 0.055 0.060 0.065 0.070 0.080 0.090 0.100 0.110 0.125 0.150 0.175 0.200
90°F. 95O F. L b . / s q . in. abs.
100'F.
110'F.
753.5 704.5 677.8
838.5 777.5 697.5 719.6 712.9
927.3 863.4 818.4 778.8 764.4 758.3 752.3 747.6 741.1 733.5 717.9 684.1 646.9 609.3
1018 940.2 887.8 838.2 816.9 806.2 793.2 784.8 774.0 763.2 743.2 703.9 663.1 623.1
1195 1095 1030 958.3 921.6 900.0 873.7 854.8 835.9 817.5 789.5 741.7 694.1 648.8
I
669.5
... ... ... ... ... ... ...
... ... .. .. .. ... ...
62513 598.9 568,3
667 4 644.7 614.8 582.0
.
I
.
...
CRITICAL REGION
THE
85' F.
:
...
iii'
108.2 703.9 692,6 664.3 630.5 595.5
663
The isochoric specific heat increases rapidly with an increase in temperature in the two-phase region and discontinuously decreases to a much lower value when the saturated liquid state is reached a t 90.5' F. The magnitude of this discontinuity was established by the following exact r e l a t i ~ n s h i p : ~
where CV"is the specific heat a t constant volume for the twophase region adjacent t o bubble point and CV' is the corresponding value for the single-phase (liquid) region adjacent 4 Inasmuch as this relationship is not in general use, its complete derivation follows: For a change of state of a system which results in a change in temperature during which the system remains a t bubble point (as saturated liquid), the change in internal energy of the system is the same whether the system remains strictly a t bubble point or is infinitesimally away from bubble point in either the one-phase or two-phase regions. Strictly speaking, these three quantities, d E B s t d , d E ' , and d E " , do differ by quantities which are second-order differentials and which therefore are negligible compared t o the quantities themselves. For these particular changes of state, we may then write: dE" = dE'
If specific volume and temperature are considered t o be the independent vari. ables, the above equation, by application of the fundamental equation of partial differentiation, may be written in the follouing form:
I n this equation dV and dT are the changes in V and T accompanying the differential change in E , while the system is kept a t saturation conditions. AS SATUTABLE 111. THERMODYNAMIC PROPERTIES O F ETHANE RATED GASAND SATURATED LIQUID
P 525 550 575 600 625 650 675 700 715.5
t"
f
63.7 67.6 71.3 75.0 78.5 81.9 85.3 88.6 90.6b
375.5 390.4 404.7 418.4 431.8 444.7 457.6 470.1 477.7
t = temperature in b
Critical state.
--Satd. V 0.1992 0.1838 0.1695 0.1567 0.1433 0,1293 0.1142 0,0974 0,0755
H
Gas-
95:3 92.8 90.0 86.6 82.4 76.9 68.2
..
S 0.186 0,1799 0.1736 0.1668 0,1595 0.1509 0,1396 0.1227
....
r-Satd.
V
Liquid--
H
0,0459 0,04705 7:9 0,04795 1 2 . 0 0,04920 1 6 . 3 0,05079 2 0 . 8 0,05293 2 5 . 6 0.05614 3 1 . 3 39.6 0,0618 .. 0.0755
The partial derivative by CV'.
S
0.007 0.0142 0.0215 0.0291 0,0373 0.0462 0.0673 0.0722
(g)" .
.
may be designated by CV" and the derivative
Upon rewriting,
satd.
The subsoript, satd., designates the last derivative as applying t o a change during which saturation is maintained. By utilizing the general relation,
....
F.; other units as in Table I. the previous equation becomes:
These P-V-T measurements, when combined with a knowledge of a single specific heat quantity throughout the temperature range involved, are sufficient to determine the thermodynamic properties of the material. I n the critical region, however, and a t low pressures, additional thermal information greatly increases the accuracy of the resulting values for the thermodynamic properties. I n this work numerous isochoric specific heat determinations
0 500
where E is internal energy.
As an illustration,
For the two-phase region of a pure substance, the following equality exists:
(">" DT v
=
["I
dT
satd.
Combination of the last two equations produces the equation given in the text.
-------
INDUSTRIAL AKD ENGINEERING CHEMISTRY
664
t o bubble point condition. The quantities required for the evaluation of this expression were obtained by residual graphical differentiation based upon P-V-T measurements. This discontinuity does not reduce t o zero a t the critical point but steadily decreases as the specific volume is reduced. The satisfactory agreement of these values computed from P-V-T measurements with those indicated from direct specific heat determinations serves as an adequate check upon the consistency of these independent experimental measurements. These data, combined with the Clapeyron relation, were used as the basis for evaluation of the heat contents and entropies reported in Table 111. They were also used along with the
0175
z %
OI5O
a
; a W m
OIZ5
+ +a
? -
0100
L
0 075
I00
200 PRESSURE
FIGURE 6.
300
400 LES PER SQ
500 IN
600
urements (14) by the authors, and for t h a t reason it was considered unnecessary t o attempt to improve upon the accuracy of the results obtained by Eucken. The JouleThomson measurements a t pressures below 600 pounds per square inch are reported in Table IV and are depicted as a function of pressure for a series of temperatures in Figure 6. The solid lines a t pressures above 250 pounds per square inch were determined from the P-V-T measurements here presented and from the specific heat data of Eucken. At lower pressures the Joule-Thomson measurements of the authors and the specific heat data of Eucken were employed t o calculate the isothermal changes in heat content and entropy, since it is believed t h a t these direct thermal measurements give more accurate values than do the specific volume data in the evaluation of these changes a t low pressures. The agreement of the thermal measurements with those predicted from the P-V-T determinations even a t low pressures indicates a satisfactory degree of consistency between these two sets of data. It was also found that the values of heat content and entropy based upon the isochoric specific heat data in the critical region agreed within small limits (1 per cent) with values calculated from the atmospheric specific heat measurements and the isothermal changes in these quantities as determined from the P-V-T and Joule-Thomson data. This a g r e e m e n t is considered satisfactory since direct calculation of i s o t h e r m a l changes in heat content and entropy with pressure is somewhat uncertain in this region. Space does not permit a detailed description of the graphical m e t h o d s employed for the calculation of the variation in heat content and entropy with pressure and temperature in the various regions. I n general, residual methods
EXPERIMEXTAL AKD CALCULATED JOULE-THOMSON COEFFICIENTS
(g)
derivative in the following relations to determine the changes in heat content and entropy with specific volume in the critical region:
The use of these relations instead of the approach previously described (17) for the c a l c u l a t i o n of the thermodynamic properties of h y d r o carbon gases and liquids permits a more accurate evaluation of the isothermal changes in heat content and entropy in this region. The specific heat data of Eucken (6) were employed to calculate the changes in heat content and entropy with temperature a t atmosp h e r i c pressure. These data agreed s u b s t a n t i a l l y with t e n t a t i v e experimental meas-
VOL. 29, NO. 6
FIQURE 7. TEMPERATURE-HEAT CONTENT DIAGRAM
JUNE, 1937 TABLEIv. P
70°F.
L b . / s q . in.
INDUSTRIAL AND ENGINEERING CHEMISTRY JOULE-THOMSON COEFFICIENTS O F GASEOUS
ETHANE
100' F.
130" F.
160' F.
190' F.
F . / l b . / s q . in.
665
be expected for any gas, since a t zero pressure the following relation applies:
220' F. 7
111. The tabulated values of heat content
FIGURE 9. TEMPERATURE-EXTROPY DIAGR.4M
INDUSTRIAL AND ENGINEERING CHEMISTRY
666
VOL. 29, NO. 6 thermal change in volume. This fact is also i n d i c a t e d b y t h e nearly linear isochoric change in pressure with volume throughout the range of pressures and temperatures covered by Figure 9. I n order to show the behavior of the two-phase and critical regions in greater detail, those portions of Figure 9 have been presented on an enlarged scale in Figure 10. Lines of constant quality are also included in the two-phase region. The discontinuity of the isochoric specific heats shown in Figure 5 is indicated in this figure by the change in slope of the isochores a t the saturation line.
Acknowledgment
region. The change in specific heat with pressure may be directly evaluated from the pressure-volume-temperature measurements by integration of the following expression:
(g)-T(g), =
Graphical integration of this expression yielded the results shown a t the lower pressures in Figure 8. The values a t the higher pressures were obtained by graphical differentiation of the isobaric lines on a temperature-heat content diagram such as Figure 7. The points indicated in Figure 8 are for a pressure of 600 pounds per square inch and were independently obtained from the Joule-Thomson measurements. These values were calculated from the following relation:
The agreement of these two sets of data was considered t o indicate that the Joule-Thomson measurements were in good agreement with the P-V-T data a t this pressure. Figure 8 shows that the assumption often made of the constancy of the specific heats with isothermal change in pressure may introduce an error of several fold in calculating the heat effects attending an isobaric change in state. The thermodynamic properties of a pure substance may best be summarized by means of a temperature-entropy diagram. Figure 9 presents such a diagram for ethane. Lines of constant heat content, pressure, and volume throughout the single-phase portion of the diagram are included. The constant-volume lines are nearly parallel throughout this region, which indicates that there is only a small change in the isochoric specific heat with an iso-
This experimental w o r k w a s prosecuted as part of the work of Research Project 37 of the American Petroleum Institute, and t o this organization the authors wish to express their appreciation for the financial aid and encouragement which have made this investigation possible. The assistance of T. Vermeulen is acknowledged for his determinations of the isochoric specific heats in the c r i t i c a 1 region. Jeanne Thomson materially aided in the calculation of the thermodynamic properties reported.
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