Phase Equilibria in Hydrocarbon 1
Systems
XIX. Thermodynamic Properties of n-Butane B. H. SAGE,D. C. WEBSTER, AND W. N. LACEY California Institute of Technology, Pasadena, Calif.
Specific volumes and latent heats of vaporization of k-butane were experimentally d e t e r mined at temperatures f r o m 70" t o 250" F. From these and other published data t h e changes i n enthalpy, entropy, and fugacity with temperature and pressure were c a l c u lated. The results of this work are presented in tabular and graphical form.
-
T
HE thermodynamic properties of industrial fluids are of value in many types of engineering calculations. The experimental information for n-butane is scattered and incomplete. Several investigators (1, 2, 16) measured the vapor pressure of this material from below the atmospheric boiling point to the critical temperature. The work of Dana and co-workers (%')from 0" to 140" F,is perhaps the most reliable in the temperature range covered in the present investigation. They also determined the specific volume of the saturated liquid and of the saturated gas, the latent heat of vaporization (constant temperature), and the specific heat of the saturated liquid throughout all or a greater part of the temperature interval 0" to 140" F. Recently Jessen and Lightfoot (4) measured the deviation of gaseous n-butane from the behavior of a perfect gas a t pressures below one atmosphere for a temperature of 30°F. Other investigators (6, IO) determined the deviation of n-butane from the perfect gas laws a t 32" F. for a pressure of one atmosphere. In an earlier paper of this series, data were published (14) upon the specific heat of saturated liquid n-butane and of the gas a t atmospheric pressure throughout the temperature interval from 70" to 250" F. Information was also reported (5) upon the Joule-Thomson coefficient of n-butane gas from atmospheric pressure to vapor pressure at temperatures from 70" to 220' F. In the present paper are presented the results of a study of the pressure-volume-temperature relations of this material a t pressures from atmospheric to 3000 pounds per square inch absolute throughout the range from 70" to 250°F. Several direct measurements of the latent heat of vaporization a t temperatures higher than those reported by Dana are included. From these data the variations in enthalpy (also known as heat content and as total heat), entropy, and fugacity with temperature and pressure are computed. Materials The n-butane used in this investigation was obtained from the Phillips Petroleum Company, who submitted the following special analysis: 99.7 mole per cent n-butane, 0.3 mole per cent isobutane. This material was further purified by
two successive fractionations in a column (1%')packed with glass rings. The middle fraction of each distillation was condensed a t liquid air temperatures under a pressure less than 0.02 inch of mercury to remove traces of noncondensable gases. Even after this treatment the material exhibited approximately 0.15 pound per square inch change in vapor pressure between the dew and bubble points (saturated gas to saturated liquid) a t 160" F. It is probable that the fractionations did not remove all of the isobutane, which was the principal impurity in the original sample.
Experimental Methods The methods employed for the pressure-volume-temperature measurements were described previously (15): In principle they consisted in varving the effective volume of a steel cell, in which a known quantity of n-butane was confined, by the addition or withdrawal of mercury. The resulting equilibrium pressure was then measured at a known temperature. The quantity of n-butane added to the apparatus was determined by weighings with appropriate corrections for air buoyancy, as well as weight and balance calibrations. It is believed that the quantity of n-butane added was known within 0.05 per cent in the measurements of the specific volume of the condensed liquid. An uncertainty of about 0.1 per cent was involved in the weight of the sample employed for the study of the pressurevolume-temperature relations of the superheated gas. The pressures existing within the equilibrium chamber were determined by means of a pressure balance with a sensitivity of 0.05 pound per square inch. This instrument was calibrated before and after the experimental work against the vapor pressure of carbon dioxide at 324 F. The carbon dioxide used in the two calibrations was prepared from widely different sources. The first sample was prepared by purification of the commercial product. The second was made by heating sodium bicarbonate, dr ing, and purifying the gas by successive sub1imat:ons. The cazbration from these two samples of gas agreed withm 0.04 per 1 Previoua articles in this aeriea appeared in INDUETRIAL AND ENQINXaRrNt3 CHIMIBTRY during 1934,1935.1936, and in June, 1937.
1188
1
I
OCTOBER, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
1189
Taking this relation as a reference basis and determining a t each of a series of temperatures, the differences between the measured vapor pressure and PR, "residual" values were obis tained. The residual vapor pressure, related to the experimentally measured pressure, P , and the reference pressure PR, of Equation 1, by the expression:
e,
P=Pg-P
(2)
The residual pressure is plotted as a function of temperature in Figure 2. The experimental points shown for the authors' work represent the data employed in determining the full line, used in calculating the values of vapor pressure recorded in Tables I and 11. The data of Dana and co-workers ($2) and of Seibert and Burrell (18) are included for comparison. Dana's work agrees with that of the authors with an average deviation of less than 0.4 pound per square inch, but the work of Seibert and Burrell shows values from 7 to 25 pounds higher than those reported in this paper. AlPRESSURE LB. PER SQ. IN. though the authors' vapor pressure measurements are consistent with one another to within FIQURE1. SPECIFIC VOLUME OF CONDEHSED LIQUID 0.1 pound per square inch, it is believed that an uncertainty as great as 0.5 pound per square cent, and successive calibrations with the second sample at inch may exist in the absolute value a t the higher temperawidely differing specific volumes agreed within 0.01 per cent. tures. The temperature of the determinations was ascertained by The direct measurement of the effect of pressure and temmeans of a copper-constantan thermocouple used in conjunction perature upon the specific volume of gaseous n-butane at low with a special potentiometer with a sensitivity of 0.1 microvolt. It is believed that the temperature of the contents of the aptemperatures is difficult. Minute traces of oil seriously imparatus was known within 0.02" F., with the exception of the pair the accuracy of these measurements in the vicinity of work at 250" F., in which an uncertainty as great as 0.1"F. may saturation because of the high solubility of n-butane in such have existed. materials. A considerable amount of time was expended in endeavoring to obtain accurate pressure-volume-temperature Results measurements in the superheated region a t low temperatures. The results of this work indicated that errors as great as 1.5 Figure 1 presents some of the results which were obtained per cent might be involved in the direct measurement of the for the condensed liquid region. The specific volume is shown specific volume of the saturated gas at temperatures below as a function of pressure for seven temperatures. The experi130" F. by the methods employed. At temperatures above mental points were chosen indiscriminately and from two dif160" F. the solubility of n-butane in heavier hydracarbons deferent sets of measurements w o n samdes of widely differing weight. The full curve a t t6e left-hand ends of the isotherms depicts the relation of the specific volume of the saturated liquid to pressure. For the condensed liquid, the isobaric thermal expansion, (bV/bT),, and the isothermal compressibility, ( b V / b P )T, both in0.0 crease with a n increase in temperature but dei creaee with a n increase in pressure. It is believed that the specific volumes of the condensed region and the saturated liquid, included g -1.0 as parts of Tables I and 11, respectively, are a known with an accuracy of 0.1 per cent. The vapor pressure was determined from a A special set of measurements in the two-phase P -10.0 region. Although there was an appreciable change (0.15 pound per square inch a t 160" F.) A in vapor pressure from saturated liquid to saturated gas, it was limited almost entirely to A states in the vicinity of saturated gas. For the - 20.0 vapor pressure measurements, the system was 0 AUTHORS maintained a t a quality of approximately 0.1. 0 DANA ET AL. It was found that the relation of vapor pressure a SEIBERT a. BURRELL to absolute temperature could be approximately expressed by the relation : P
TEMPERATURE
OF.
FIQUREI 2. RESIDUAL VAPORPRESSURE-TEMPERATURE DIAGRAM
=
/ /
/
(5)
If the values of the specific volume and the isobaric thermal expansion from Equations 3 and 4, respectively, are substituted in Equation 5, a relation is obtained between the isobaric change of Z with temperature and the isothermal change of heat content with pressure:
0.98
/
;- (%)J$)
JESSEN L LIGHTFOOT
I
J
The value of Z throughout the temperature range investigated was calculated by integration of Equation 6, using inTEMPERATURE 'F. formation concerning the absolute value of Z a t each presF~~~~~ 3, c~~~~~~~~~~~~~ F~~~~~OF GASEOUS ~ - B U T A ~ sure and a temperature of 220° F. obtained from the experimental pressure-volume-temperature measurements. AT ATMOSPHERIC PRESSURBI Several other investigators (4, 6, 10) determined the deviations of n-butane from the creases to such an extent that satisfactory measurements perfect gas laws for several temperatures a t atmospheric were obtained except in the close vicinity of s a t u r a t e d pressure. Since their exgas, For these reasons none perimental methods obviated the difficulty with traces of of the experimental pressureheavier hydrocarbons experivolume-temperature me a s enced by the authors, their urements below 160" F. for data permit a check upon the the superheated region are values of 2 calculated from recorded in this paper. Fortunately data upon the the Joule-Thomson coefficient an extended temperaover Joule-Thomson coefficients, ture interval. Figure 3 prewhich are functions of state, sents the variation in Z with furnish an admirable way to temperature for a pressure determine the variations in 14.696 p o u n d s per square the specific volume of a gas inch. The full curve reprewith temperature. From a sents the values of Z calcuknowledge of the isobaric lated from the Joule-Thomspecific heat at a single presson coefficient and the disure throughout the temperar e c t l y measured values a t t u r e r a n g e a n d t h e Joule220°F. The data of LightThomson coefficient, 50 IO0 150 200 250 foot (4) at 86°F. and the ( d T / d P ) H it , is possible to calculate (13) the derivative, PRESSURE LE. PER SQ. IN. other experimenters (6, 10) (bH/bP) T , throughout the FIQURE 4. COMPRESSIBILITY FACTOR-PRESSURE DIAGRAM at 32" F*weewithin FOR GASEOUS %-BUTANE range of pressure and temperature through which the Joule-Thomson coefficient is known. Values of (W/dP), for n-butane calculated in this manner -I were reported in an earlier paper of this series 50
100
150
200
250
-
$1;
(6)*
The specific volume is related to the pressure, temperature, specific gas constant, b ( b = R / M , where R is the molal gas constant and M is the molecular weight), and the compressibility factor, 2,by the expression:
$
0.200
f
2
0.175
>I
v =ZbTp
(3)
w
0.150
4
-1
This equation differentiated with respect to temperature at a constant pressure becomes :
(%Ip (%)JF) =
9
23
0.125
0
+-i5 Zb
(4)
W ln
K
50
The specific volume and the isobaric thermal expansion are to (dH/ap)y by the ing general thermodynamic equation :
too
150
PRESSURE
200
LB. PER SQ.
250
300
IN.
FIGURE 5. RESIDUAL SPECIFIC VOLUME-PRESSURE DIAGRAM FOR GASEOUS n-BUTANE
OCTOBER, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
limits (0.2 per cent) with those predicted from the present data. The authors' measurements a t 250", 190", and 160' F. are in substantial agreement with the Joule-Thomson data. Figure 4 presents the variation in Z with pressure for a series of temperatures as determined from the Joule-Thomson data. The points shown for saturated gas are taken from direct measurements by Dana and co-workers (2). Since their work is considered by them to have an accuracy of 1.O per cent, the agreement is satisfactory. The results from the authors' pressure-volume-temperature measurements a t the higher temperatures are included for comparison. The values of specific volume for the superheated gas reported in Table I are considered trustworthy to within 0.2 per cent. The residual specific volume, may be defined in the following way :
v,
v= -
-bT P
v=
(1
- 2)bT
(7)
P
This quantity, as defined by Equation 7, uses perfect gas behavior as a reference basis. Figure 5 presents the residual specific volume of n-butane as a function of pressure for a series of temperatures. Extrapolation of the data t o low pressures indicates that the residual specific volume is not zero a t infinite dilution, which is in accord with the general theory of imperfect gases. Actual gases never exhibit all of the characteristics of a perfect gas, even a t infinite dilution. Experimental evidence (3,6,11) indicated that the Joule-Thomson coefficient, I 4 ,which is zero for a perfect gas, is finite at zero pressure for actual gases. The isobaric heat capacity per unit weight is also finite under these conditions, since nearly the same intramolecular energies are involved as are encountered in the vicinity of atmospheric pressure. The Joule-Thomson COefficient and the isobaric specific heat are related to the residual specific volume by the following general equation : pCp =
_V
-T
(g),
(7-4)
1191
would also equal zero. Since this is incompatible with Equation 7A, both p and C, being finite, 41 will not be equal to zero. On the other hand, the equation would be satisfied if _V a t infinite dilution were finite and either constant or a function of temperature. I n the latter case, could be equal to zero, but only for a temperature a t which -T(b_V/bT), was equal to p C,. At other temperatures 1would be finite. Although Equation 7 becomes indeterminate a t zero pressure, the limiting value of a t infinite dilution may be obtained from it by independent differentiation of the numerator and denominator. Upon substitution of unity as the limiting value of 2 and simplification, the following equation for the limiting case of infinite dilution results:
V = -bT ( bP E )T
(7B)
If it is assumed that the fugacity is equal to the pressure a t zero pressure, the following integral expression (9) may be conveniently used to determine graphically the fugacity of the gas as a function of pressure: I n Pf
=
-_ blT J o ' p E I d p
(8)
The change in fugacity with pressure in the condensed liquid region was ascertained by graphical evaluations of the following integral equation in which fi refers to the fugacity of the saturated liquid and, therefore, of the saturated gas:
h-- -t T
Lfp
vdp
(9)
Tables I and 11 give the fugacity of the superheated gas, the condensed liquid, and the saturated states, respectively. The fugacity is closely related to isothermal changes in enthalpy and entropy. Lewis and Randall partially defined the fugacity of a one-component system in terms of its free energy, F, by the following differential expression (8):
If the residual specific volume, ,V' were constant and equal to zero at infinite dilution, its first derivative, (by/bT)p,
dk
=
bT (d Inf)
(10)
They also defined the free energy of a system in the following way (7) : F=H-TS
(11)
If Equation 11 is differentiated a t a constant temperature, the following expression is obtained: m'
dF = dH
25
- TdS
(12)
_I
If Equations 10 and 12 are combined, a relation between the entropy, enthalpy, and fugacity for an isothermal process results:
a w a
2
2
0.0
b(d lnf) = dTH - dS
I
I-3
(13)
Equation 13 may be rewritten in the following integrated form where subscripts A and B refer to two states a t the same temperature.
- 5.0
' b h f " =HB -HA fA T ao I Sq-S
&TU. PER LB. PER
- ( S B - SA)
(14)
~
0.02
a03
OF.
FIGURE6. ISOTHERMAL CHANGESIN ENTHALPY AND ENTROPY FOR CONDENSED LIQUID
Equation 14 affords a convenient means of checking the consistency, for any one temperature, of Of thermodynamic properties such the those presented in Tables I and 11.
VOL. 29, NO. 10
INDUSTRIAL AND ENGINEERING CHEMISTRY
1192
PROPERTIES OB WBUTANE, SINGLE-PHASE REQIONS TABLEI. THERMODYNAMIC P
7-70'
Satd.gas Satd.liquid 14.696 20 30 40 50 60 70 80 90 100 125 150 175 200 225 250 275 300 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000
V
j
2.907 0,02754 6.451 4.680 3.043
....
.... . ... .... , .. . .,.. .,.. .... .. .'.. ..... ...
I . .
....
,---190°
v
En --
60 70 80 90 100 125 150 175 200 225 250 275 300 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000
H
29.37 164.65 5.67 29.37 14.27 166.97 19,22 166.36 28.23 164.92
.... ....
. .. . . . . . . .. . . . . . ....... *
.. .... .. .. .. .. .. ... . . ... . ., . ... . ... ...
.., . . . .. ,
.. .
33.49 35.91 38.47 41.22 44.15 47.27 50.60 54.15 57.94 61.98 66.30
I
S 0.3109 0.01075 0.3396 0.3279 0.3125
.... .... .... .... .... ....
6.08
.. . .
6.57 7.10 7.66 8.25 8.86 9.49 10.15 10.82 11.50 12.20 12.90
F. (174.4)-
H
0 00j97 0.00660 0.00529 0.00405 0.00286 0.00168 0.00058 -0.00047 -0.00148 -0.00247 -0.00343 S
0.5275 141.0 202.06 0,03262 141.0 82.94 8,013 14.44 215.33 5.851 19.53 215.00 3.855 28.96 214.35 2.855 38.16 213.65 2.255 47.13 212.94 1.8548 55.90 212.18 1.5688 64.44 211.38 1.3546 72.78 210.59 1.1867 80.90 209.76 1.0530 88.81 208.90 0.8095 107.67 206.68 0.6461 125.21 204.36
0.3237 0.14033 0.4217 0.4105 0,3964 0.3859 0.3776 0.3706 0 3647 0.3590 0.3541 0.3494 0.3390 0.3305
0.03244 143.9
82.75
....
0.13941
57 164.5 0,03121 175.6 0.03088 187.4 0.03057 199.6 0.03030 212.7 0.03005 226.5 0.02982 241.1 0.02961 256.5 0.02994 272.8 0.02927 290.0
82:39 82.19 82.11 82.14 82.24 82.42 82.65 82.93 83.26 83.63 84.02
o:i3057 0.13400 0.13165 0.12948 0.12746 0.12556 0.12377 0.12208 0.12047 0.11894 0.11746
... ... ... .,.
1.7999 0.02856 6.847 4.981 3.266 2.390 1.8669
....
.... ....
. . .. . ... .... ....
.... ....
.... ....
. ... .. .... ..
....
.... 97 i54:o
. .. . ... . . ...
.... .... ....
I
V
....
0.00942
F. (51.62)--
-100'
....
....
0.02739 31.23 0:02?23 0.02709 0.02697 0.02687 0.02676 0.02665 0.02655 0.02646 0.02638 0.02631 0.02628
Satd.gas Satd,liquid 14.696 20 30 40
F. (31.30)"-
0.02838
....
H
-130'
V
S
47.08 174.18 0.3125 47.08 23.32 0.04295 14.33 178.48 0.3607 19.33 177.98 0.3492 28.48 176.96 0.3345 37.29 175.78 0.3232 45.74 174.45 0.3139
.... .... .... . .. . ... . .. .. .. .. .... .. .. .. .. 49.72 ... .
0:02820 bi:25 0.02805 57.00 0.02789 60.99 0.02774 65.24 0.02761 69.76 0.02749 74.57 0.02736 79.69 0.02724 85.14 0.02711 90.93 0.02700 97.08 0.02691 103.6 -220"
V
....
F. (243.5)-
.... .... .... i0i:h o:i0Qo4
97 209:i 0 39 214.6 0,03284229.2 0.03232 244.6 0 03195 260.8 0.03160 277.9 0.03129 295.8 0.03102 314.8 0.03075 334.8 0.03055 355.9 0.03036 378.2
.... .... .... .... .... .... ....
0.02946
....
F. (80.78)H
S
71.12 183.52 0.3152 71.12 42.00 0.07518 14.38 190.38 0.3814 19.41 189.94 0.3701 28.67 189.07 0.3556 37.64 188.11 0,3447 46.30 187.07 0.3369 54.68 186.00 0.3283 62.76 184.83 0.3215 70.53 183.62 0.3157
.... .... .... .... .... .... .... .... .... .... . . . . .... .... .... .... .... . . . . .... .... . . . . . . . . 74.47 42.18 0.07392 . . . . . . . . . . ..
24:07 o:04009 0 : 02922 79: 06 42:50 0 : 07216 24.55 0.03861 0.02901 735.18 ,42.86 0.07049 26.05 0.03721 0.02881 91.03 43.27 0.06891 25.59 0.03586 0.02861 97.23 43.71 0.06741 26.15 0.03458 0.02844 103.8 44.18 0.06597 26.74 0.03336 0.02829 110.8 44.68 0.06459 27.35 0.03218 0.02815 118.2 45.20 0.06327 27.97 0.03104 0.02799 126.1 45.76 0.06200 28.61 0,02994 0.02785 134.5 46 33 0.06078 29.26 0.02886 0.02771 143.3 46.91 0.05959 29.92 0.02782 0.02760 152.7 47.51 0.05844
H S 0.3604 187.0 209.44 0.3266 0.03476 187.0 105.11 0.17311 8.398 14.47 228.38 0.4414 6.136 19.58 228.10 0.4302 4.048 29.06 227.54 0.4163 3.003 38.34 226.96 0.4060 2.377 47.42 226.35 0.3978 1.9583 56.32 225.71 0.3910 1.6601 65.02 225.06 0.3851 1.4365 73.54 224.37 0.3799 1.2625 81.88 223 64 0.3752 1.1232 90.03 222.89 0.3708 0 8715 109.6 220 88 0.3611 0.7022 128 1 218.72 0.3525 0.5791 145.5 216.42 0.3445 0.4844 161.7 213.99 0.3370 0.4082 176.7 211.41 0.3306 0 03472 187.4 105.07 0.17300
o
f
.... .... .... .... .... .... .... .... . . . . .. .. . . . . ... . . . . . .... .... ...... . .. .... .. . ... . 23.63 0.04164 .... ....
1.1617 0.02963 7.237 5.273 3.458 2.549 2.003 1.6358 1.3735 1.1751
f
103.23 0.16565 102.73 0.16267 102.41 0.15997 102.21 0.15749 102.11 0.15517 102.09 0.15301 102.16 0.15097 102.28 0.14906 102.46 0.14724 102.69 0.14550
Thermodynamic Calculations The values of enthalpy and entropy recorded in Tables I and I1 are based upon the following experimental measurements: the isobaric specific heat of the saturated liquid (14), the isobaric specific heat of the gas a t atmospheric pressure (14), the Joule-Thomson coefficient of the gas (6),latent heat measurements by Dana and eo-workers (d), and several values measured directly by the authors a t a higher temperaturepressure-volume-temperature relations of the condensed liquid, the pressure-volume relations of the superheated gas a t 220"F., and the relation of vapor pressure to temperature from 70" to 250" F. These data are more than sufficient t o determine the variation of enthalpy and entropy with temperature and pressure and thus permit a check upon the consistency of the data. For present purposes the enthalpy and entropy of the saturated liquid a t 6O"F.were arbitrarily taken as zero. By meth-
-250'
V
f
F. (330.4)H
--MOO
V
0.7745 0.03090 7.627 5.564 3.659 2.704 2.131 1.7477 1.4742 1.2681 1.1072 0.9783
f
F. (120.99)H
102.3 192.94 102.3 61.84 14.41 202.67 19.48 202.29 28.83 201.51 37.93 200.71 46.77 199.87 55.36 198.97 63.70 189.05 71.79 197.10 79.63 196.11 87.22 195.11
5 0.3192 0.10764 0.4017 0.3905 0.3762 0.3655 0.3570 0.3497 0.3433 0.3376 0.3323 0.3274
.... ..... .... ..... . . . ..... .... .. ...... .. .. .. .... . .. . . .. . ... . .... 0.03070 106.0 61.84 0.10646 . . . . . . . . ... . .... ....
o:Oi037 iii:i 0.03009 121.0 0.02984 129.2 0.02959 138.1 0.02938 146.9 0.02917 156.6 0.02898 166.9 0.02880 177.8 0.02864 189.3 0.02850 201.5 0.02839 214.5
0i:92 62.08 62.30 62.57 62.89 63.26 63.67 64.11 64.58 65.07 65.59
o :i%o
0.10231 0.10043 0.09866 0.09698 0.09539 0,09388 0,09106 0.09244 0.08973 0.08844
S
0.2417 239.1 214.23 0.3267 0.03797 239.1 128.21 0.2055 8.780 14.49 241.82 0.4607 6.419 19.61 241.59 0.4496 4.240 29.13 241.10 0.4358 3.149 38.48 240.59 0.4256 2.4953 47.66 240.09 0.4175 2.059 56.64 239.55 0.4109 1.7485 65.47 238.98 0,4051 1.5165 74.14 238.39 0,4001 1.3340 82 64 237.78 0,3956 1.1896 90.99 237.14 0,3913 0.9286 111.2 235 46 0 3819 0.7535 130.4 233.62 0.3740 0.6270 148.7 231.61 0.3669 0.5303 166.1 229.41 0.3600 0.4530 182.4 227.03 0 3533 0.3901 197.6 224.46 0.3468 0.3366 211.8 221.66 0.3405 0 2904 224 9 218.56 0.3343 0:03689 25i:o 126 74 0.2018 0.03575 269.1 125.24 0.19734 0.03490 287.9 124.19 0.19356 0.03424 307.5 123 41 0 19022 0.03370 328.1 122.83 0.18718 0.03323 349 8 122.39 0.18437 0.03282 372.5 122.06 0.18175 0.03247 396.5 121 83 0 17931 0.03216 421.8 121.70 0.17701 0.03187 448.4 121.63 0.17484 0.03161 476.4 121.62 0.17276
a Figures in parentheses are vapor pressures, in pounds per squareinch absolute.
ods previously described (17), the variation in these quantities with temperature and pressure throughout the condensed liquid region was established. I n general, residual methods were employed, increasing the accuracy of the calculations several fold over simple graphical methods. Figure 6 shows the isothermal change in enthalpy and entropy from saturation for a series of temperatures. The enthalpy progressively increases with an isothermal increase in pressure a t low temperatures but decreases with a n isothermal increase in pressure a t the higher temperatures, reaches a minimum, then increases again with a progressive increase in pressure. On the other hand, the entropy always decreases with a n increase in pressure a t a constant temperature and at a greater rate a t the higher temperatures. Figure 7 presents the variation in the latent heat of vaporization with temperature. The full curve represents the values chosen for this work, and the dotted curve results from values calculated by use of the Clapeyron equation. Since
OCTOBER, 1937
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perimental data. It is believed that this inconsistency is probably due to the lower perJ.U l centage accuracy in the experimental measI50 urements of vapor pressure a t these lower 3 t e m p e r a t u r e s . The specific heats of the 2 saturated liquid and the gas a t atmospheric pressure are also involved in determining the 6 125 enthalpy of both the saturated liquid and the 2 ; saturated gas. Since these data were deter8 mined only with an accuracy of approxi5 100 mately 1.5 per cent, it is not surprising that B appreciable divergences appear in the latent + heat data calculated in such widely different W d ways. The entropy of the saturated gas a t 130" F. TEMPERATURE 'F. was d e t e r m i n e d , as previously indicated, FIGURE7. LATENTHEATOF VAPORIZATION FOR BUTANE from the latent heat of v a p o r i z a t i o n , the absolute temperature, and the entropy these latter values agreed with the experimentally determined of lthe saturated liquid a t this temperature. The isothermal changes in entropy in the superheated gas region latent heats a t temperatures in the vicinity of 130" F., the value a t this temperature was used for calculating the enwere obtained by evaluation of the following integral expresthalpy and entropy of the saturated gas. sion : Using the values of enthalpy and entropy so determined for the saturated gas a t 130"F. as a basis, the entire thermodyS A - 8s = b l n (15) namic behavior in the superheated region was calculated by use of the Joule-Thomson coefficients and the pressure-volume relaThe residual thermal expansion, (dV/bT),, in Equation 15 tions a t 220" F. The isothermal change in enthalpy was dewas obtained from the derivative, (bH/bP),, and the residual termined by graphical integration of the values of (bH/bp), volume,- by means of the relation : previously reported ( 5 ) . The change in enthalpy with ternperature a t atmospheric pressure was determined by residual integration of the atmospheric isoTABLE11. THERMODYNAMIC PROPERTIES OF WBUTANE, SATURATED GAS, baric specific heats (13). Proper combinations AND SATURATED LIQUID of these changes in enthalpy with pressure and Saturated Gas Saturated Liquid with temperature gave the values for the superheated region and the saturated gas reported in P f V H S I v H S 4.20 0.0157 67.6 3.027 163.88 0.3108 28.21 0.02747 30 Tables I and 11, respectively. The full curve in 40 84.3 2.301 160.11 0.3116 37.05 0.02802 13.80 0.0284 46.67 0.02850 22.09 0.0407 50 98 0 1.8568 173.51 0.3124 Figure 7 was established from the differences in 54.11 0.02891 29.29 0.0527 109.7 1.6556 177.22 0.3132 60 62.37 0,02926 35.65 0.0639 the enthalpy of the saturated gas and the satu70 120.1 1.3377 180.49 0.3142 70.48 0,02960 41.50 0.0741 129.3 1.1728 183.38 0.3152 80 rated liquid, and was in good agreement (0.2 per 90 137.7 78.44 0 02993 46.80 0 0834 1.0433 186.00 0.3161 86.27 0 03025 51.89 0.0919 cent) with both sets of direct latent-heat meas100 145.5 0.9393 188.42 0.3172 0 03104 63.70 0.1105 105.3 162.6 0.7492 193.77 0.3196 125 urements. At the lower temperatures the small 150 177.3 0.6203 198.33 0 3218 123 7 0 03183 74.30 0.1267 0 03264 83.17 0.1408 0.3237 141.4 0.5259 202.14 discrepancy between the latent heats of vaporiza175 190.3 0 03342 91.55 0.1534 205.29 0.3252 158.6 200 202.0 0.4536 tion calculated by use of the Clapeyron equation 225 212.7 0.3959 207.88 0.3261 175.2 0 03422 99.40 0 1646 0 03497 106.68 0.1755 250 222.5 0.3489 209.97 0.3267 191.2 and those obtained from the isothermal differ0 03580 113.63 0.1856 275 231.7 0.3095 211.68 0.3270 206.6 0.03671 120.37 0.1950 ences in the enthalpy of the saturated gas and 300 240.2 0,2761 212.97 0.3270 221.6 liquid indicates some inconsistency in the exm'
;:+ L:(%)pdp
250
200
150
IO0
I70
180
190
200
ENTHALPY
210
220
2 30
240
B.T.U. PER LB.
FIGURE 8. TEMPERATURE-ENTHALPY DIAGRAM FOR GASEOUS BUTANE
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VOL. 29, NO. 10
modynamic paths in and between the oneand two-phase regions. I n general, the data showed a consistency better than 0.2 per cent, with the exception of the two-phase region a t temperatures below 130" F. where uncertainties as great as one per cent are involved.
Nomenclature T t
P
P ~
Ti
Ti H S
F
f 6
2 C p
temperature, ' F. abs. (" R.) = temperature, O F. = pressure, lb./sq. in. abs. = residual pressure, lb./sq. in. = specific volume, cu. ft./lb. = residual volume, cu. ft./lb. = enthalpy, B. t. u./lb. = entropy, B. t. u./lb./" F. abs. = Lewis' free energy, B. t. u./lb. = fugacity, lb./sq. in. = specific gas constant = compressibility factor = isobaric heat capacity, B. t. u./lb. =
Acknowledgment This investigation was conducted as a part of a general study of the thermodynamic behavior of simple and complex hydrocarbon mixtures which is being carried on by Research Project 37 of the American Petroleum Institute, whose financial support has made the work possible. The assistance of Jeanne Thomson is acknowledged in connection with the calculations.
Literature Cited (1) Burrell and
Robertson. U. S. Bur. Mines, Refrig.
T
(g)p (g),-I=
_V p
The change in entropy with temperature a t atmospheric presCP sure was calculated by graphical evaluation o f S T dT. Using the value of the entropy of the saturated gas a t 130"F. as a basis, all of the changes in entropy in the superheated region were calculated by proper combinations of the isothermal and isobaric changes discussed above. Discrepancies in the entropy of vaporization similar to those found in the enthalpy of vaporization were encountered. The authors believe that the values of enthalpy and entropy relative to the datum state are trustworthy within 1.5 per cent. I n either the condensed liquid or the superheated gas region the isothermal changes in these quantities are probably reliable within 0.5 per cent. Numerous diagrams representing the thermodynamic behavior of n-butane can be drawn from the tabulated data. Figure 8 shows a temperature-enthalpy diagram for the superheated gas. Several lines of constant entropy are included in order to show the interrelation of these variables. The temperature-entropy diagram affords the most satisfactory means of presenting the thermodynamic behavior of the single-phase and two-phase regions of a pure substance. Figure 9 presents such a diagram for n-butane. Lines of constant pressure, specific volume, and enthalpy are included in the single-phase regions. Lines of constant quality are also shown in the twophase region. The over-all consistency of the thermodynamic properties was checked by the application of several general thermodynamic equations of state to a variety of ther-
York,
McGraw-Hill Book Go., 1923. (8) Ibid., p. 191. (9) Ibid., p. 195. (10) Oudinoff, Bull. SOC. chim. Belg., 23,266 (1909). (11) Roebuck and Osterberg, Phgys. Rev., 48,450(1935). 28, (12) Sage. Davies, Sherborne, and Laoey, IND. ENO. CHEIM.,
i328 (1936).
Sage, Kennedy, and Laoey, Ibid., 28,601 (1936). Sage and Lacey, Ibid., 27,1484(1935). Ibid., 28, 106 (1936). Sage, Schaafsma, and Lacey, Ibid., 26, 1218 (1934). Sage, Webster, and Laoey, Ibid., 29, 658 (1937). Seibert and Burrell, J. Am. Chem. Soc., 37,2683 (1915). RECEIVIOD March 17, 1937
