Thermodynamic Properties of Chlorotrifluoromethane L. F. ALBRIGHT ANZ) J. J. MARTIN University of Michigan, Ann Arbor, Mich.
S
EVERAL chlorofluoro derivatives of methane and ethane have been used for some time as refrigerants. Recently chlorotrifluoromethane (CClFa), commercially known as "Freon13," has found acceptance as a low-temperature refrigerant, and as a result there haa been a demand for a knowledge of its physical and thermodynamic properties. Vapor pressure measurements ranging from -218" to 84" F. (approximately the critical temperature) have been reported by several investigators (8, 10, 13, fb, 16). However, differences as great as 2% were noted in their results. Gas density measurements (P-V-T) on "Freon-13" have been made (10,16),but the range of temperature was not great and only low densities and high densities near the critical were studied, with no measurements in the intermediate range from one third the critical density to the critical density. Saturated liquid densities from - 190" to 77" F. have been reported (IO),as well as critical constants (8,161. Specific heat values were calculated (10,16)from spectroscopic data reported in the literature ( 7 ) . Some of the thermodynamic properties of the saturated vapor and liquid (11, 16) and the superheated vapor (16)have been calculated from the above physical properties; however, small but definite disagreements of the values reported for these p h y e ical propertiee and the lack of data over desirable ranges of variables led to the present investigation.
VAPOR PRESSURE
The vapor pressure measurements were made by a static method in three sets of equipment, each designed for different pressures. The apparatus for pressures below atmospheric ie shown in Figure 1. That for 15 to 200 pounds per square inch absolute was similar to the 200- to 560-pounds-per-square-inchabsolute equipment, shown in Figure 2. The calibrated pressure gages could be read to within 0.1% of the total pressure being measured. Vapor ressures were measured by first evacuating the isotent scope witg the mercury diffusion pump to a pressure of less than 5 microns of mercury. The isoteniscope was then filled by condensing freon vapors into it. The temperature of the bath waa held constant and temperature-pressure readings were made when equilibrium was established. The readings were checked by boiling off some of the liquid and making new readings a t approximately the same temperature. Three to six such boiloffs and subsequent readings were made for each loading of the isoteniscope, and three to four loadings were made for each approximate temperature. A11 readings were averaged to give a composite vapor pressure point. Each of the seven points shown in Table I was determined by this procedure. Two vapor pressure equations have been developed. The first, loglop
FREONS AND STANDARDS USED
36.76130 - 2623.988/T 11.80586 logioT
+ 5.71495 X 10-aT
(1)
represents the experimental data within 0.08% from -200' to -15" F.and within 0.14% from -15" to 80" F. The second, The 'Freon-13" used in the experimental work was furnished by E, I. du Pont de Nemours &. Co. The sample used for the vapor pressure, saturated liquid density, and the critical temperature measurements was reported to be 99.9% pure, while that used in the P-V-T studies was analyzed as 99.7% pure, with air being the chief impurity. The vapor pressures of both samples were measured a t several temperatures and no differences were observed. Temperature standards were two platinum resistance thermometers that had been calibrated by the National Bureau of Standards. The thermometer readings were considered accurate to 0.02" F. Agitated baths were used to obtain the temperature conditions for all CONNECTION TO HIGH PRESSURE runs. Below -112' F. the baths were cooled VAPOR PRESSURE by liquid air similar to the method described EQUIPMENT AT I3 OF FIGURE 2 by Henning (6). Temperatures between -112" and 32" F. were obtained by cooling with a tube filled with dry ice and acetone. Water baths and electrically heated oil baths were used above 32" F. Figure 1. Low Pressure Vapor Pressure Equipment Pressures below atmospheric were measured I. Freon supply cylinder 9. Auxiliary mercury manometer 2. P&os drying tube IO, 11. I-liter flasks with mercury manometers read with a cathe3. Isotenisoope 12. Reeovery cylinder 4. Small mercury manometer 13. Vacuum pump tometer. Pressures above atmospheric were 5 Lar e mercury manometer 14. Hyvac pump 15. Bath for isotenisco 6: Mcl?md gage measured with Bourdon tube gages calibrated A,B C D E F G gJ,K,and 7. Mercury diffusion pump 8. Line to Hyvac pump L L 2 pias: &o&L against an American dead-weight gage tester. 188
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1952 D OIL LEG
Various equations to represent the isometrics, including the following, were tested
CONNECTION TO LOW PRESSURE VAPOR PRESSURE EQUIPMENT
.mP MERCURY LEG
+ B T + C/TS p = A + B T + C/T' p =A
AT STOPCOCK K OF
1
189
FIGURE I
(31 (4)
where A, B, and Care volume fun.ctions. Equation 3 is the form proposed by B a t t i e and Bridgeman ( 1 ) and employed by Benedict, Webb, and Rubin (9). Equation 4 predicts greater curvature of the isometrics and proved to represent the data slightly better than Equation 3. The constants for Equation 4 were determined and are shown graphically in Figure 5. The isometric constants can be represented as well as density functions of a polynomial form. A graphical procedure W&B used to determine these functions as
+ 0.01594 d8 - 0.0003964 d' B = 0.1027 d + 2.328 X 10-8 d4 + 4.944 X lo-' d4 C = (-23.55 d* + 0.0287 d4 - 5.816 X de) X lo8 A = -2.837 d2
U
U
Figure 2. High Pressure Vapor Pressure Equipment 1.
:
4. 5. 6. 7. 8. 9.
Metalisotenison *inch brass ho% valve %&ow Meroury leg with valve
10.
Pressuresage Safety NPt-0 disk
14.
Oillee
BuEer tank Nitm en valve 12: 0 to l ~ p o u n n - p 0 r - ~ a r e inchg e 13. Needlev%
I1
15.
I/c-inob tee
Supply oylinder Constant temperature bath
Dead-weight gage
loglop = 56.34405
- 3351.281/T
19.16910logioT
+ 9.20366 X
10-*T
(2)
(5) (6) (7)
A comparison of the values predicted by Equation 4 combined with Equations 6,6,and 7, and the experimental data are shown in Table 11.
-
OIL LEO MERCURY LEO
represents the data within 0.08% from -15' to 80' F., but is not Although the first equation represents the vapor pressure data f&Iy well at the higher temperatures, it was felt the use of the second equation was better in calculating the slope of the vapor preasure curve between -16' and 80' F., which is required in the ClausiueClapeyron relation. so accurate below this temperature range.
P-V-T RELATIONSHIP OF THE GAS
The e uipment, shown in Figure 3, to measure gas density waa essentid the same as that used by Bennrng and M c h e s s (3,4 ) . $he volume of the gas density bulb and !ts connectiqne was determined by weighmg the bulb and connections filled m t h water and empty. For pressures up to 300 oundwper square inch this volume was approximately 4100 m?, while for lugher ressurea a smaller bulb waa used, the volume being abou~600ml. !'he freon waa added to and removed from the gas density bulb from a wei hed charging cylinder. In all cases the amount of freon loade! and that removed a eed within 0.1% and generdly within 0.04%. The average of g e s e two amounts was taken aa the true amount in the vapor density bulb during the measurements. The calibrated ressure gage could be read within 0.3% of the total pressure in tge worst case. The observed pressures, densities, and temperatures are reported in Table 11. The observed pressures were corrected to constant density by an approximate equation of state. A large scale plot of the jsometrics, Figure 4, shows definite curvature in the neighborhood of the vapor pressure curve, especially near half the critical density.
2
Figure 3.
Pressure-Volume-Temperature Equipment
I . PreMuregage 2. Bath 3. AirmtiRer 4. SEfeW N p t W disk 5. Char ngline 6. Varidle eonneation 10. Needlevalve 11. MoLsodgagge
12.
Needlevalve
13. Line to Hyvao pump 14. Hyvao urn 15. Vapor $ens& bulb
Lunkenhdmer needle valve Oil-mcrcury leg 19. Dead-weight gage 80. Valve to nitrogen prcn-
I6,17.
18.
8-e
SATURATED LIQUID DENSITY AND CRITICAL CONSTANTS
Eleven liquid density points were measured between - 224.0 and 78' F. with calibrated glass floats by the method explained b Benning and McHarness (6). The results are reported in d b l e I11 and a plot of these data is shown in Figure 6. The critical density was found by extrapolating the rectilinear TABLB I. EXP~RIMENTAL VAPORPRESSURE DATACOMPARF+D diameter the average of the saturated li uid and vapor densities, TO VAPORPRESS^ EQUATION to the cdtical temperature. The critica? temperature was measured aa the t e perature a t which the liquid meniscus disappeared Experimenta~Data visuaUy in seged-off lass tubes, and was found to be 83.93' F. Ex tl., Calculated, % Deviation lb.%q. lb./sq. d E ! x 100) The saturated vapor tensity o w e was found by 'the intersection Point 1, F. T, ' R. in. aba. in. ab#. of the experimental isometrics with the vapor ressure curve. 80.37 640.06 837.9 s w . 2 0 . iafi 1 The vapor deneity curve and the calculated rectfhear diameter +0.14 2 32.00 491.69 286.9 286.3 are shown in Fiy e 6 The critical density from the rectilinear 3 -16.22 444.47 137.44 137.33 -0.08 diameter is 36.0 poudds per cubic foot. 4 -72.19 387.60 44.38 44.416 +0.08
(
5 6 7
-114.77 -148.86 -198.19
344.92 310.84 261.60
14'.623 4.674 0.4797
14.623 4.873 0.4797
0.00 -0.02 0.00
An equation to represent the saturated liquid density data was determined aa follows:
INDUSTRIAL AND ENGINEERING CHEMISTRY
190
Vol. 44, No. 1
2100
2000.
- .__
1900. 1800.
1700 1600
1500 1480
1300 1200
1100. $IO00 L
900
300 200 loo 0
E
-80 -60- 4
Figure 4.
dL = 36.07
Experimental Isometric Data for “Freon-13”
+ 0.01566 ( t , - t ) + 1.110 ( t c - t ) ’ / * + 6.665 ( t , + 3.245 X low6(Ic- t)* t)1’3
VI
=
1105; Vz = Vg
(8)
The critical pressure was calculated to 561.3 pounds per square inch absolute b y substituting the critical temperature in the vapor pressure equation. SPECIFIC HEAT OF THE GAS
The specific heat of the gas a t infinite volume was calculated from the fundamental vibration frequencies assigned by Plyler (9):
356; V3 = 781; Vc Vs = Vs = 1212; V,
= 450; = Vs =
561 cm.-l
Plyler measured all these values except the 356 crn.-’ which w a s measured by Kahovec and Wagner ( 7 ) . The method of calculating the specific heat from the spectroscopic data assuming linear harmonic oscillation is outlined by Wenner ( 1 4 ) . The values so calculated are represented within 0.5% by the equation em = 0.01602
+ 0.00028232’
- 1.159 X 10-72‘2 B.t.u. per pound per
R.
(9)
191
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1952
C VERSUS DENSITY
I
I
I
I
Variation of A , B, and C with Density
Figure 5.
B VERSUS DENSITY I
I
I
I
with respect to absolute temperature, The latent heat equation from -200" to -15" F. is
m
L
-
2.30259 pJ
(U
- VL) X
2623*988- 6.12721 + 87150 X [TThe constant pressure heat capacity a t zero prawure may be obtained by adding R to cv and is
+
- 15" to 80" F. is
-
g, = 0.03504 0.0002823T 1.159 X lO-'T2 B.t.u.
per pound per
The equation from
lO-ST]
R. (IO)
CALCULATION OF THERMODYNAMIC PROPERTIES
Calculations of the thermodynamic tables are based on a datum of zero enthalpy and entropy for the saturated liquid at -40" F. The thermodynamic calculations were made first for the saturated liquid and vapor and then for the superheated vapors. SATURATED LIQUID AND VAPORS. The thermodynamic properties of the saturated liquid and vapor were calculated at temperature intervals of IO" F. from -200" to 40' F. and 5 O F. intervals from 40" to 80" F. as shown in Table IV. The vapor pressures were calculated from Equation 1 or 2 depending on the temperature. The s a t u r a t e d l i q u i d v o l u m e s were obtained from Equation 8. S a t u r a t e d v a p o r volumes were obtained by solving simultaneously either Equation 1 or 2 and Equation 4. The latent heats were calculated from the Clausius-Clapeyron equation
*,
dT
1
T(v
- V L ) x ;iT
.
(11)
The slope of the vapor pressure curve was evaluated by differentiating Equation 1 or 2
DENSITY,
Figure 6.
LBS./CU
F
Saturated Liquid and Vapor Density for "Freon-13"
(12)
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
192 L = 2.30259 p J (V -
VL)
X
TABLE11. EXPERIMENTAL ISOMETRIC DATACOMPARED
pv- + 8.32501
t,
9.2037 X 10-sT]
(13)
F.
-71.46 -68.35 -37.07 -1.64 34.92 71.56 107.10
The entropy of vaporization was determined by dividing the latent heat by the absolute temperature. The enthalpies and entropies of the saturated vapor were determined by calcdating the enthalpy and entropy changes along suitable constant volume and temperature lines, utilizing the equation of state and the specific heat equation. At constant temperature
-51.77 -21.82 16.54 49.86 77.45 106.57 -21.12 13.08 46.90 82.11 122.25 154.96 -4.22 1.13 40.32 78.19 107.02 145.18 171.79 12.63 20.17 51.75 75.88 112.62 140.29
=
[-1.050
f 0.0004309T -
-
26.15 x 1091[; T4
rv'a. +
0.004424 [-0.00009782
=
32.27 58.80 84.16 115.32 146.28 171.30
3
+
49.30 62.33 94.55 127.71 165.16 190.71 212.05
- ut11 - + 9.15 X
8.611 X lop7
A
-
10'
(17)
The specific heat at a definite volume, cv, used in Equations 16 and 17 was calculated from c z m (Equation 9), specific heat at infinite volume, as follows
Ti] f 0.0001412 [Tz2 - Ti2] -3.862 21.79
Equation 8 Experimental Data E Temp., x pt dL l.lated calcudL (calcd.-exptl. calcd. x 100) Points F. te - t 50.86 -0.08 50.90 1 78.08 5.85 56.57 f0.04 14.11 56.55 2 69.82 63.98 1-0.05 31.81 63.95 3 52.12 4-0.03 67.64 67.66 4 40.14 43.79 71.52 -0.04 58.76 71.55 5 25.18 75.60 -0.03 75.62 6 6.73 77.20 -0.05 81.81 81.77 7 -26.14 110.07 -0.09 90.11 90.03 8 -78.84 162.77 96.38 +o.os 209.18 96.30 9 -125.25 100.66 +0.05 241.96 100.51 10 -158.03 108.46 -0.02 108.48 11 -224.05 307.98
v
+ JvAp
l
= 0.01602 [ Tz
x
TABLE111. EXPERIMENTAL SATURATED LIQUID DENSITIES COMPARED TO LIQUID DENSITY EQUATION
At constant volume
J
OF STATE
.
7'082 ''1
cu dT
TO EQNATION
Experimental Data Corrected Corrected Calcd. X ' , Deviation Exptl. pressure Ca1cd.-Cor. Density pressure, Density Pressure x 100) Calcd. lb./sq. in. abs. Lb./Cu. Ft. Lb./Sq. In. Abs. Lb./Sq. In. kbs.( lb./cu. fi. Isometric Density, 1.15 Lb./Cu. Ft. $0.43 41.94 41.85 1.15 41.76 $0.26 42.36 42.35 1.15 42.25 +O. 15 46.50 46.50 1.15 46.43 $0.21 51.06 50.95 1.15 50.95 55.68 f0.38 55.50 1.15 55.47 60.25, 4-0.48 59.95 1.15 59.96 f0.56 64.65 64.25 1.15 64.29 Isometric Density, 1.68 Lb./Cu. Ft. -0.40 1.68 62.99 62.74 63.05 1.6816 -0.13 1.68 68.79 68.70 68,80 1.6803 f0.21 1.68 75.92 76.08 75.90 1.6795 +O. 47 1.68 81,96 82.35 81.90 1.6787 f0.31 1.68 85.21 87.48 87,lO 1.6779 +0.26 1.68 92.62 92.86 92.45 1.6770 Isometric Density, 2.91 Lh./Cu. Ft. +0.05 110.8 2.91 110.7 110.8 2.9115 +0.08 123.2 2.91 123.2 123.1 2.9101 +o.oo 134.8 2.91 134.8 134.8 2.9087 +0.07 146.5 2 91 146.6 146.7 2.9066 f0.12 159.5 2.91 159.8 160.1 2.9044 f0.06 170.3 2.91 170.7 170.8 2.9030 Isometric Deneity, 4.27 Lb./Cu. Ft.. -0.13 159.0 158.8 159.3 4.27 4.277 f0.00 161.8 161.8 4.27 162.1 4.277 f0.11 183.0 183.2 4.27 183.2 4.275 +a 10 203.0 203.2 203.1 4.27 4.272 t0.00 218.0 218.0 218.0 4.27 4.270 -0.04 237.4 237.3 4.27 237.2 4.267 -0.04 250.7 250.6 4.27 250.4 4.265 Isometric Density, 6.00 Lb./Cu. Ft. +O. 51 214.4 215.5 214.4 6.000 6.003 -0.05 220.4 220.3 6.000 220.4 6.001 f0.08 247.1 247.3 6,000 247.0 5.997 +0.08 266.0 266.2 6.000 265.7 5.995 +0.04 294.2 294.3 6.000 293.8 5.991 +0.03 314.9 315.0 314.3 6.000 5.988 Isometric Density, 8.27 Lb./Cu. Ft. 283.5 8.27 283.4 285.3 +O. 67 8.277 f0.41 8.273 315.8 8.27 315.7 316.8 344.5 8.27 344.5 346.0 f0.43 8.269 f0.26 8.27 379.9 380.9 379.8 8.265 8.261 414.0 8.27 414.4 414.8 +0.10 +o. 18 8.27 440.9 441.7 440.5 8.258 Isometric Density, 10.82 Lb./Cu. Ft. 10.831 384.6 10.82 354.4 365.1 f0.20 375.3 10.82 375.2 376,6 +0.37 10.829 -0.05 428.5 10.82 428.5 428.3 10.823 -0.06 10.817 479.8 10.82 479.9 479.6 536.0 -0.07 536.4 10.82 10.810 536.0 573.9 -0.17 574.9 10.82 10.805 574.3 10,801 605.8 10.82 606.5 605.2 -0.21
0.04377 [loglovz - log~~vll - [O.Mx)4309 4-
AH, =
Vol. 44, No. 1
0.00885
+-p--
[& - &]
X 10'
1.076 X v5
+ 0.18506 vAp
x
1 (16)
INDUSTRIAL A N D ENGINEERING CHEMISTRY
January 1952
ISOMETRIC DATACOMPARED TABLE11. EXPERIMENTAL
t,
O
F.
Experimental Data Expel. pressure lb./sq. in. i b s .
Densit lb./cu.
k.
TO
Isometric Density, 12.77 Lb./Cu. Ft. 12.77 408.0 12.77 417.6 12.77 478.2 12.77 544.3 12.77 601.6 12.77 662.1 12.77 715.7 12.77 758.0
408.4 417 .O 478.2 544 1 601.7 661.2 714.6 758.5
+O.lO -0.14
19.76 19.76 19.75 19.74 19.73 19.72 19.71 19.70
513.8 527.3 628.3 738.3 846.1 947.3 1008.8 1092.3
Isometric Density, 19.75 Lb./Cu. Ft. 19.75 513.7 19.75 527.2 19.75 628 3 19.75 737.6 846.9 19.75 19.75 948.7 19.75 1010.3 19.75 1094.3
513.3 527.4 626.6 736.9 846.4 949.9 1009.9 1094.8
-0.08 10.04 -0.27 -0.09 -0.06 +o, 12 -0.04 4-0.05
83.86 85.59 116.56 147.51 182.44 219.06 260.35
26.78 26.78 26.76 26.75 26.73 26.71 26.69
558,3 568.3 724.0 873.8 1041.6 1217.5 1415.3
Isometric Density, 26.75 Lb./Cu. Ft. 558.3 26.75 568.3 26.75 723.9 26.75 873.9 26.75 1042.1 26.75 1218.7 26.75 1417.4 26.75
559.8 568.5 722.6 874.3 1043.7 1219.5 1416.4
+o
83.91 86.82 116.31 150.42 186.21 222.51 261.19
28.05 28.05 28.03 28.02 28 00 27.98 27.97
559.3 571.3 734.3 910.3 1093.8 1278.3 1475.3
Isometric Density, 28.0 Lb./Cix. Ft. 559.3 28.0 571.3 28.0 734.1 28.0 910.0 28.0 1093.8 28.0 1278.9 28.0 1476.6 28.0
561.3 572.4 732.0 909.5 1094 .O 1279.7 1476.7
+0.35 +o. 19 -0.29 -0.06 10.02 10.06
561.3 578.0 830.8 1088.8 1352.3 1618.8 1879.0
Isometric Denaity, 35.9 Lb./Cu. Ft, 561.3 35.9 35.9 578.0 830.6 35.9 1088.8 35.9 1352.9 35.9 35.9 1620.3 1881.5 35.9
561.2 579 . O 830.8 1088.8 1352.8 1620.3 1881.4
10.02 +0.17 t0.02
562.3 904.1 1262.5 1651.5 2036.0
Isometrio Density, 44.45 Lb./Cu. Ft. 44.45 562.2 44.45 904.0 44.45 1262.2 44 45 1651.7 44.45 2037.3
515.3 856.7 1211.4 1595.7 1984.1
-9.12 -5.52 -4.19 -3.51 -2.68
12.783 12.782 12.776 12.769 12.761 12.754 12.747 12.742
77.94 82.00 111.15 144.46 178.32 210.51 229.82 256.95
84.00 86.52 121.64 157.21 193.26 229.59 264.87 83.93 119.46 154.92 192.31 229.35
35.94 35.94 35.92 35.90 35.88 35.86 35.84 44.53 44.50 44.47 44.44 44.41
-200 --- 190 180 170 - 160 150 ---130 140 --110 120
Pressure Lb./Sq. In. kb8. 0.4329 0.7480 1.238 1.967 3.104
Volume, Cu. Ft./Lb. Liquid Vapor 0.009466 61.33 0.009574 36.74 0.009685 22.99 0.009801 14.942 0.009920 9.750
[e] bT2 dv (18) The enthalpies and entropies of the saturated liquid were determined by subtracb ing the latent heats and entropies of v a p o r i z a t i o n , respectively, from the thermodynamic values of the saturated vapors. SUPERHEATED VAPOR. The enthalpies and entropies of the superheated vapor were calculated at constant volumes and temperature by using Equations 14, 15, 16, and 17 from -200" to 500' F. and from 0.03 (slightly higher than the critical volume) to 60 cubic f e e t per pound. Large enthalpy-pressureand entropypressure diagrams with constant temperature lines were then drawn. The enthalpy and enbropy values were read from these charts at pressures from 1.0 to 561.3 pounds per square inch absolute and at temperatures from -2OOO to 500' F. The volumes at these pressures and temperatures were determined with the aid of a compressibility chart, which was constructed from
+o.oo
-0.04 +0.02 f0.02 -0.01 +0.07
1 0 27 04
-0.18 +0.05 +0.04 +0.07 -0.07
+0.01
+o.oo -0.01 +o. 00 -0.01
'NAMIC PROPERTIES TABLEIV. THERMODY
Tyy.,
OF
+ JT
% Deviation (Calcd*-Cor* x 100) Calod.
408.3 417.8 478.3 544.3 601.3 c61.3 414.8 754.6
62.51 66.78 97.79 132.44 163.49 196.18 225.88 250.57
e* = csm
EQUATION OF STATE (COntd.)
Calcd. Correoted Corrected Density Pressure Pressure Lb./Cu. bt. Lb./Sq.In.Abs. Lb./Sq.In.Abs.
193
SATURATED "FREON-13"
Enthalpy above -40' F. (B.t.u./Lb.) Liquid Latent Vapor -34.551 73.096 38.545 -32.429 72.029 39.600 -30.298 70.970 40.672 -28.208 69.904 41.696 -26.083 68.808 42.725
Entropy above -40' F. (B.t.u./Lb./O R.) Liquid Vapor Vaporization -0.10081 0.28147 0.18066 -0.09313 0.26708 0.17395 -0 .OS575 0.25375 0.16800 -0.07858 0.24131 0.16273 -0.07213 0.22960 0.15747
4.464 6.455 9 .os0 12.48 16.81
0.01004 0.01017 0.01031 0.01045 0.01060
6.976 4.950 3.605 2.681 2.031
-24.010 -21 ,902 -19.792 -17.671 -15.527
67.783 66 696 65.596 64.473 63.316
43.773 44.794 45.804 46.802 47.789
-0.06491 -0.05844 -0 05209 0.04590 -0.03977
-
0.19896 0.18980 0.18106
0.15396 0.15019 0.14687 0.14390 0.14129
22.23 28.89 36.98 46.68 58.19
0.01075 0.01091 0.01109 0.01127 0.01146
1.5642 1.2232 0.9689 0.7766 0.6289
- 13.387 -11.241 -9.052 -6,843 -4.604
62.138 60.941 59.672 68.362 56.993
48.751 49.700 50 620 51.519 52.389
-0.03286 -0.02806 -0.02230 -0.01665 -0.01106
0 17275 0.16484 0.15716 0.14977 0.14259
0.13889 0.13678 0.13486 0.13312 0.13153
71.71 87.43 105.6 126.4 150.1
0.01167 0.01189 0.01213 0.01239 0.01268
0.5139 0.4234 0.3512 0.2930 0.2454
-2.320 0.000 2.363 4.809 7.484
55.546 54.023 52,416 50.668 48.630
53.226 54.023 54.779 55.477 56.114
0.01686
0.13558 0.12872 0.12199 0.11524 0.10814
0.13009 0.12872 0 12744 0.12620 0.12500
30 40
176.8 206.8 240.4 277.9 319.6
0.01299 0.01335 0.01375 0.01422 0.01477
0.2066 0.17443 0.14732 0.12437 0.10455
10.052 12.696 15.443 18.247 21.370
46.638 44.479 42.100 39.472 36.450
56 690 57.175 57.543 57.719 57.820
0.02234 0.02789 0 03351 0.03921 0.04516
0 10146 0.09470 0.08777 0 08061 0.07295
0.12280 0 12259 0.12128 0.11982 0.11811
45 50 55 60 65
342.2 365.9 390.8 417.0 444.5
0.01509 0.01546 0.01588 0.01637 0.01696
0.09565 0.08734 0.07945 0.07189 0.06468
22.979 24.651 26.418 28.310 30.322
34.769 32.958 30.946 28.677 26.137
57.748 57.609 57.364 56.987 56.459
0.04826 0 05143 0.05473 0.05824 0.06193
0.06889 0.06466 0.06013 0.05518 0.04981
0.11715 0.11609 0.11486 0.11342 0.11174
70 75 80
473.4 503.7 535.5
0.01771 0.01874 0.02047
0.05767 0.05027 0.04131
32.515 35.110 38.E27
23.193 19.382 13,565
55.708 54,.492 52.092
0.06591 0.07059 0.07672
0.04379 0.03625 0.02513
0.10970 0.10185 0.10684
83.93
561.3
0.02772
0.02772
45.271
....
45.271
0,08898
.....
0.08898
- 100
- 90 - 80
--70 60 -- 40 50 -30 -20 - 10
0 lG 20
-0.00548 0 00000 +0.01096 0.00545 t
0.20863 0.21887
I
INDUSTRIAL AND ENGINEERING CHEMISTRY
194
TABLE v. THERMODYNAMIC PROPERTIES O F Pressure Lb./Sq. 1n.Abs. 0.0 H 1.0 v H 1.5
S V H S
2.0
v
H S 2.5 V H S 3.0 V H S 4.0 V H S 6.0 V H S 8.0
V
H
S
10.0 15.0 20.0
v
H S V H S
-200 38.66
-180 40.88 28.51 40.70 0.1722
-160 43.15 30.61 43.02 0.1797 20.35 42.95 0.1719 15.22 42.88 0.1662 12.14 42.81 0.1618 10.09 42.74 0.1581
-140 45.48 32.71 45.38 0.1870 21.75 45.33 0.1793 16.29 45.28 0.1736 13.00 45.22 0.1693 10.82 45.17 0.1656 8.077 45.07 0.1599 5.338 44.84 0.1517
-120 47.87 34.78 47.80 0.1940 23.15 47.75 0.1864 17.33 47.70 0.1807 13.85 47.66 0.1764 11.52 47.62 0.1728 8.612 47.54 0.1673 5.705 47.37 0.1591 4.251 47.20 0.1533 3.376 47.02 0.1486
v
H
S 25.0
v
H
S 30.0 V H S 40.0 V H S
60.0
80.0
100.0 150.0
V H S V H S
v
H
S V H
S 200.0
v
H
S
SUPERHEATED "FREON-13"
Temperature. O F. -100 -80 50.32 52.83 36.85 38.93 50.26 52.78 0.2011 0,2078 24.54 25.93 50.22 52.75 0.2000 0.1933 18.38 19.42 50.19 52.72 0.1876 0.1944 14.69 15.52 52.69 50.15 0.1902 0.1834 12.22 12.92 50.12 52.66 0,1799 0.1866 9.671 9.149 50.05 52.61 0.1810 0,1742 6.069 6.421 49.91 52.50 0.1662 0.1732 4.528 4.795 49.78 52.38 0.1605 0.1674 3.602 3.819 49.64 52.27 0.1560 0.1828 2.368 2.518 49.29 51.98 0,1475 0.1547 1.749 1.866 48.91 51.69 0.1413 0.1487 1.476 51.39 0,1438 1.215 51.07 0.1397
- 60 55.40 40.98 55.36 0.2143 27.31 55.33 0.2066 20.46 55.31 0.2010 16.35 55.28 0.1968 13.61 55.26 0.1933 10.19 55.22 0.1877 6.772 55.12 0.1799 5.062 55.03 0.1742 4.034 54.93 0.1694 2.665 54.69 0.1616 1.981 54.40 0.1567 1.570 54.19 0.1510. 1.295 53.96 0.1470 0,9526 53.37 0.1406
VOl. 44, No. 1
VAPOR
-40 58.04 43.05 58.00 0.2207 28.68 57.98 0.2130 21.49 57.96 0.2076 17.18' 57.93 0.2032 14.31 57.91 0.1997 10.72 57.88 0.1942 7.124 57.80 0.1864 5.325 57.72 0.1807 4.248 57.64 0.1763 2.811 57.43 0.1683 2.092 57.22 0.1624 1.661 57.02 0.1579 1.874 56.80 0.1540 1.014 56.37 0.1477 0.6532 55.42 0.1384 0.4705 54.45 0.1311
-20 60.74 45.11 60.71 0.2270 30.06 60.69 0.2192 22.53 60.67 0.2139 18.00 60.65 0.2095 15.00 60.63 0.2060 11.23 60.60 0.2005 7.471 60.53 0.1927 5.589 60.46 0.1871 4.460 60.39 0.1827 2.955 60.21 0.1748 2.202 60.03 0.1691 1.749 59.85 0.1644 1.448 59.67 0.1608 1.072 59.27 0.1545 0.6950 58.51 0.1456 0.5052 57.71 0.1387 0.3900 56.82 0.1330
0 63.51 47.16 63.48 0.2331 31.43 63.47 0.2252 23.56 63.45 0.2200 18.84 63.43 0.2156 15.69 63.42 0.2121 11.75 63.39 0.2066 7.819 63.33 0.1988 5.851 63.27 0.1933 4.670 63.20 0.1889 3.098 63.05 0.1810 2.311 62.89 0,1754 1.839 62.74 0.1709 1.524 62.58 0.1671 1.130 62.26 0.1612 0.7350 61.58 0.1524 0.5371 60.88 0.1458 0.4180 60.11 0.1403 0.2569 58.08 0.1291
20 66.35 49.23 66.33 0.2392 32.81 66.32 0.2315 24.58 66.30 0.2261 19.66 66.28 0,2217 16.37 66.27 0.2182 12.27 66.24 0.2128 8.167 66.19 0.2060 6.115 66.13 0.1994 4.883 66.08 0.1951 3.241 65.93 0.1872 2.418 65.80 0.1816 1.926 65.66 0.1771 1.597 65.52 0.1734 1.186 65.22 0.1675 0.7750 64.63 0.1589 0.5694 64.01 0.1525 0.4451 63.44 0.1473 0.2781 61.59 0.1369 0.1929 59.60 0.1280
250.0 V H S
300.0 V H 400.0
S V
561.3
S V
H
H
S
the equation of state. The thermodynamic results of the above calculations are reported in Table V and Figure 7. DISCUSSION OF RESULTS FOR PHYSICAL PROPERTIES
The smoothed vapor pressure data of Riedel (IO)and Whitney (16)agree within 0.3% of the values calculated from the equation. The data of the other investigators (8, 18, 13) differ from the equation by 1.5% or more. The equation of state, Equation 4, was compared where possible with the P-V-T data of Riedel (10) and Whitney (16).
(Continued on p a g e 2.96)
The data of Riedel a t densities up to about one third of critical density agree within 0.5% of Equation 4. The t w o isometrics reported by Whitney at, densities of about one third the critical density and the critical density agree within 1.07, of the equation. The saturated liquid density equation, Equation 8, was compared to the data of Riedel (IO). Agreement is within 0.1% except a t about - 1 8 0 O and 77" F. where the deviations are a8 high as 0.87,. The critical temperature, pressure, and density are compared with the results of other investigators.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
January 1952
195
TABLE V. THERMODYNAMIC PROPERTIES OF SUPERHEATED “ F R E O N -VAPOR ~ ~ ” (Continued) Pressure Lb./Bq. In. kba. 0.0 H 1.0 v H
S
1.5 V H
S
2.0 2.5
v
H S
v
H S 3.0 V H S 4.0 V H S 6.0 V H S 8.0 10.0
v
H S
v
H S
15.0 V
H S
20.0 25.0 30.0 40.0 60.0
v
H
S V H S V H S V H S V H
S
80.0 100.0
v
H 8
v
H S 150.0 V H S
200.0
v
H S
250.0 V
€1
S
300.0 V H
S
40 69.26, 51.28 69.24 0.2449 34.18 69.23 0.2375 25.61 69.21 0.2320 20.49 639.20 0.2277 17.07 69.19 0.2243 12.78 69.16 0.2187 8.515 69.11 0.2110 6:375 69.07 0.2055 5.092 69.02 0.2010 3.381 68.89 0.1932 2.525 68.77 0.1875 2.012 68.64 0.1832 1.670 68.52 0.1795 1.242 68.26 0.1736 0.8140 67.73 0.1652 0.5993 67.18 0.1589 0.4704 66.60 0.1540 0.2976 65.10 0.1442 0.2098 63.41 0.1358 0.1555 61.44 0.1285 0.1175 59.04 0.1213
400.0 V H 561.3
S V H S
80 72.24 75.28 55.40 53.35 72.22 75.26 0.2510 0.2569 35.54 36.91 72.21 75.25 0.2432 0.2491 26.65 27.68 72.19 75.24 0.2379 0.2436 21.31 22.14 72.18 75.23 0.2335 0.2393 17.75 18.44 72.17 75.22 0.2302 0.2360 13.29 13.81 72.15 75.20 0.2245 0.2303 8.859 9.204 72.10 75.16 0.2169 0.2226 6.635 6.895 72.06 75.12 0.2113 0.2170 5.301 5.511 72.01 75.07 0.2127 0.2069 3.520 3.662 71.90 74.97 0.1992 0.2050 2.631 2.738 71.79 74.87 0.1934 0.1993 2.097 2.183 71.68 74.77 0.1891 0.1950 1.741 1.813 71.56 74.66 0.1854 0.1913 1.296 1.351 71.33 74.45 0.1797 0.1856 0.8521 0.8892 70.85 74.03 0.1713 0.1773 0.6292 0.6681 70.36 73.58 0.1653 0.1713 0.4951 0.5191 69.88 73.11 0.1603 0.1664 0.3157 0.3334 68.51 71.94 0.1508 0.1572 0.2254 0.2399 67.03 70.67 0.1431 0.1499 0.1699 0.1833 65.42 69.26 0.1364 0.1438 0.1322 0.1447 63.66 67.77 0.1304 0.1382 0.07974 0.09448 58.24 63.82 0.1166 0.1272
Temperature. F. Riedel (10) MoNsbne (8) Whitney 6 6 ) Authors
83.84 83.84 83 89 83.93
60
100 78.38 57.46 78.36 0.2624 38.29 78.35 0.2547 28.71 78.34 0.2492 22.96 78.34 0.2450 19.13 78.33 0.2414 14.34 78.31 0.2361 9.549 78.27 0.2283 7.155 78.23 0.2226 5.719 78.19 0.2184 3.801 78.10 0.2106 2.842 78.00 0.2050 2.267 77.91 0.2007 1.885 77.81 0.1970 1.406 77.61 0.1914 0.9263 77.23 0.1832 0.6864 76.83 0.1772 0.5425 76.41 0.1724 0.3503 75.40 0.1633 0.2537 74.21 0.1564 0.1954 72.93 0.1505 0.1562 71.64 .0.1453 0.1056 68.69 0.1358 0.05708 61.40 0.1186
Lb./Sq. Pressure In. ‘Abs. 559.7 561.5 561 3
120 81.55 59.50 81.53 0.2680 39.66 81.52 0.2603 29.74 81.51 0.2548 23.79 81.50 0.2504 19.82 81.50 0.2471 14.85 81.48 0.2416 9.894 81.44 0.2338 7.414 81.40 0.2283 5.925 81.37 0.2241 3.940 81.29 0.2162 2.948 81.20 0.2106 2.353 81.11 0.2063 1.956 81.03 0.2026 1.459 80.84 0.1970 0.9638 80.47 0.1889 0.7157 80.11 0.1830 0.5663 79.75 0.1783 0.3670 78.77 0.1693 0.2671 77.75 0.1626 0.2068 76.63 0.1569 0.1664 75.45 0.1520 0.1155 72.80 0.1432 0.06887 68.45 0.1296
Lb./Cu. Densityh. 36.27 36.07
DISCUSSION O F THERMODYNAMIC RESULTS
The values for the thermodynamic properties of the saturated liquid and vapor presented in Table IV were compared wherever
Temperature, F. 140 160 84.77 88.05 \63.62 61.56 88.04 84.76 0.2734 0.2788 42.40 41.03 88.03 84.75 0.2657 0.2710 31.79 30.77 88.02 84.74 0.2602 0.2657 24.62 25.44 88.02 84.73 0.2560 0.2614 20.50 21.19 88.01 84.72 0.2525 0.2579 15.88 15.37 87.99 84.71 0.2525 0.2470 10.58 10.24 84.67 87.96 0.2447 0.2393 7.933 7.674 84.64 87.93 0.2390 0.2337 6.133 6.341 84.61 87.90 0.2348 0.2295 4.080 4.218 84.53 87.83 0.2271 0.2217 3.157 3.054 84.45 87.75 0.2216 0.2162 2.437 2.521 84.37 87.68 0.2117 0.2172 2.026 2.097 84.29 87.60 0.2082 0.2137 1.513 1.566 84.12 87.44 0.2026 0.2080 1.000 1.035 83.78 87.13 0.1944 0.2000 0.7433 0.7703 83.45 86.80 0.1941 0.1886 0.5892 0.6112 83.09 86.50 0.1895 0.1840 0.3830 0.3987 82.18 85.64 0.1752 0.1809 0.2924 0.2801 81.24 84.83 0.1686 0.1744 0.2180 0.2287 80.27 83.91 0.1631 0.1691 0.1764 0.1860 79.28 83.05 0.1584 0.1645 0.1241 0.1321 77.13 81.07 0.1501 0.1567 0.07766 0.08504 73.01 77.67 0.1382 0.1458
180 91.39 65.67 91.37 0.2843 43.77 91.36 0.2764 32.82 91.36 0.2711 26.26 91.35 0.2668 21.88 91.35 0.2631 16.41 91.33 0.2578 10.93 91.31 0.2501 8.192 91.28 0.2445 6.548 91.25 0.2401 4.356 91.18 0.2324 3.2e3 91.11 0.2270 2.606 91.03 0.2225 2.167 90.95 0.2190 1.620 90.80 0.2134 1.071 90.53 0.2054 0.7976 90.23 0.1996 0.6335 89.94 0.1950 0.445 89.16 0.1864 0.3048 88.40 0.1800 0.2390 87.59 0.1749 0.1950 86.75 0.1704 0.1398 84.90 0.1629 0.09173 81.83 0.1527
200 94.79 67.73 94.78 0.2895 45.14 94.77 0.2816 33.86 94.76 0.2763 27.08 94.75 0.2720 22.57 94.74 0.2684 16.92 94.73 0.2630 11.27 94.70 0.2552 8.450 94.67 0.2497 6.755 94.64 0.2453 4.495 94.58 0.2376 3.367 94.51 0.2322 2.689 94.45 0.2278 2.238 94.38 0.2243 1.672 94.24 0.2187 1.107 93.97 0.2107 0.8252 93.69 0.2048 0.6559 93.41 0.2003 0.4303 92.70 0.1918 0.3172 91.94 0.1856 0.2492 91.23 0.1806 0.2040 90.46 0.1761 ’ 0.1471 88.85 0.1689 0.09796 86.09 0.1592
220 240 260 101.72 105.26 98.22 69.78 71.84 73.89 101.70 105.24 98.21 0.2946 0.2996 0.3045 46.51 47.88 49.25 98.21 101.70 105.24 0.2866 0.2918 0.2969 34.89 35.91 36.94 101.69 105.23 98.20 0.2813 0.2862 0.2911 27.92 28.73 29.55 98.19 101.69 105.23 0.2770 0.2820 0.2870 23.25 23.94 24.62 98.19 101.68 105.22 0.2735 0.2787 0.2836 17.43 17.95 18.46 98.17 101.67 105.21 0.2682 0.2732 0.2782 11.62 11.96 12.30 98.15 101.64 105.19 0.2603 0.2654 0.2704 8.965 9.252 8.707 98.12 101.62 105.16 0.2548 0.2599 0.2649 6.961 7.168 7.374 98.10 101.60 105. 4 0.2505 0.2557 0.l608 4.634 4.772 4.910 98.04 101.54 105.09 0.2428 0.2480 0.2530 3.471 3.574 3.678 97.97 101.48 105.03 0.2373 0.2424 0.2473 2.856 2.039 2.772 97.91 101.42 104.98 0.2330 0,2381 0.2430 2.307 2.377 2.446 97.84 101.35 104.92 0.2295 0.2345 0.2395 1.725 1.778 1.830 97.71 101.23 104.80 0.2291 0.2341 0,2239 1.143 1.179 1.214 97.46 100.99 104.57 0,2158 0,2210 0.2260 0.8527 0.8801 0.9070 97.20 100.76 104.29 0.2101 0,2153 0.2208 0.6781 0,7003 0.7221 96.94 100.49 104.10 0.2055 0,2108 0.2158 0,4605 0.4754 0.4455 96.26 99.83 103.52 0.1971 0.2024 0.2075 0.3291 0,3408 0.3523 95.57 99.26 102.93 0.1910 0.1964 0,2015 0,2689 0.2786 0.2590 94.90 98.64 102.38 0,1860 0,1914 0.1966 0,2125 0,2210 0.2293 94.05 97.90 101.77 0.1817 0.1871 0.1925 0,1541 0.1611 0,1677 92.73 96.51 100.29 0.1747 0.1803 0,1857 0.1037 0.1092 0.1146 90.14 94.27 98.30 0.1654 0.1713 0.1770 (Concluded on page 196)
possible with those reported by Riedel (11) and Whitney (16). The enthalpy and entropy values reported by these two investigatora agree within about 1.0 B.t.u. per pound and 0.003 B.t.u. per pound per O R., respectively, with values shown in Table IV. The values for the thermodynamic properties of the superheated vapor were compared to a lebs detailed pressure-enthalpy diagram of Whitney (16). The enthalpy values in the superheated gas region agree within about 2.0 B.t.u. per pound for the
196
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 44, No. 1
TABLE V. THERMODYNAMIC PROPERTIES OF SUPERHEATED “FREON-13” VAPOR(Concluded) Pressure Lb./Sq. In. Abs. 280 0 0 H 108.84 1 0 75.94 H 108.83 S 0.3092 .15 v 50.62 H 108.82 0.3017 S 2 0 v 37.97 H 108.82 0.2961 S 2 5 v 30.37 H 108.82 S 0.2920 3 0 v 25.30 H 108.81 S 0.2886 4 0 v 18.97 H 108.80 0.2830 S 6.0 V 12.64 H 108.78 0.2753 S 8 0 9.480 H 108.76 0.2698 S 7.580 10 0 V H 108.74 0.2666 S 5.047 15.0 V H 108.68 0.2579 S 20 0 v 3.782 H 108.63 S 0.2524 25.0 V 3.022 H 108.58 0.2480 S 2.515 30.0 V H 108.52 0.2445 S 1.883 40.0 V H 108.41 0.2390 S 60 0 V 1.250 H 108.19 0.2310 S 0.9339 80 0 v H 107.97 0.2253 S 100.0 v 0,7440 H 107.75 0.2209 s 150 0 V 0.4904 H 107.19 0.2126 S 0.3639 200 0 H 106.60 0.2065 S 0.2880 250 0 V H 106.05 0.2017 S 0.2373 300 0 V H 105.44 0.1976 S 0.1742 400 0 V H 104.26 0,1910 S 0.1197 561.3 V 102.34 H 0,1826 S
v
v
v
300 112.48 78.01 112.47 0.3140 51.99 112.46 0.3067 38.99 112.46 0.301.1 31.20 112.45 0.2968 25.99 112.45 0.2934 19.49 112.44 0.2879 12.98 112.41 0,2803 9.736 112.39 0.2747 7.787 112.37 0,2705 5.185 112.32 0.2627 3.885 112.27 0,2572 3.105 112.22 0,2529 2.586 112.17 0.2494 1.936 112.06 0,2438 1.285 111.85 0.2359 0.9608 111.65 0.2301 0.7658 111.44 0,2258 0.6053 110.91 0.2176 0.3754 110.35 0.2115 0.2974 109.82 0.2067 0.2455 109.27 0.2027 0.1806 108.18 0.1962 0,1246 106.48 0,1879
320 116.15 80.06 116.13 0.3187 53.36 116.13 0.3114 40.02 116.13 0,3058 32.02 116.13 0.3016 26.67 116.12 0.2982 20.00 116.11 0.2927 13.33 116.09 0,2850 9.995 116.07 0.2794 7.993 116.05 0,2752 5.323 116.00 0,2675 3.989 115.95 0,2620 3.189 115.90 0,2577 2.655 115.86 0,2541 1.988 115.75 0,2486 1.321 115.56 0,2407 0.9873 115.36 0,2350 0.7872 115.15 0,2306 0.5202 114.65 0.2225 0.3869 114.14 0.2164 0.3068 113.62 0.2117 0.2535 113.16 0.2077 * 0.1869 112.09 0.2013 0,1296 110.41 0,1931
340 119.86 82.12 119.85 0.3231 54.73 119.84 0.3161 41.05 119.84 0.3105 32.84 119.84 0.3064 27.36 119.84 0.3028 20.51 119.83 0.2974 13.68 119.81 0.2897 10.25 119.79 0.2842 8.200 119.7.7 0.2799 5.461 119.72 0.2722 4.093 119.67 0.2667 ‘3.272 119.63 0.2624 2.725 119.58 0.2589 2.040 119.49 0.2533 1.356 119.30 0.2455 1.014 119.11
0.2398 0.8087 118.92 0.2353 0.5350 118.44 0.2272 0.3982 117.97 0.2213 0.3161 117.46 0.2166 0.2614 116.98 0.2126 0.1930 115.94 0.2062 0.1342 114.50 0.1982
360 123.62 84.17 123.60 0.3275 56.11 123.59 0.3207 42.08 123.59 0.3153 33.67 123.59 0.3111 28.05 123.59 0.3075 21.03 123.58 0.3022 14.02 123.56 0.2944 10.51 123.54 0.2889 8.406 123.53 0.2848 5.600 123.48 0.2769 4.197 123.44 0.2713 3.356 123.39 0.2671 2.794 1.23.35 0.2635 2.093 123.25 0.2580 1.391 123.08 0.2501 1.040 122.89 0.2445 0.8301 122.72 0.2401 0.5497 122.27 0.2319 0.4095 121.82 0.2261 0.3254 121.32 0,2214 0.2692 120.86 0.2174 0,1992 119.98 0.2110 0.1390 118.41 0.2032
constant temperature, entropy, and volume lines. The entropy values of the two diagrams agree within about 0.003 B.t.u. per pound per O R. for the same pressures and enthalpies. The major disagreements of the two charts are a t high temperatures and high pressures. Both Whitney and Riedel used essentially the same method for calculating the thermodynamic properties of “Freon-13” as that used in the present investigation. Differences of the various thermodynamic values are, consequently, due to the different equations for the various physical properties. In general, all
Temperature, F. 380 400 420 127.41 135.09 131.23 86.22 88.28 90.33 127.40 131.22 135.08 0.3319 0.3362 0.3404 60.22 57.48 58.85 135.07 127.39 131.22 0.3253 0.3297 0.3342 43.10 44.14 45,W 135.07 127.39 131.21 0.3197 0.3244 0.3286 36.13 34.49 35.31 127.39 131.21 135.07 0.3156 0.3201 0.3246 30.11 28.74 29.41 135.07 127.38 131.21 0.3120 0.3166 ’ 0.3210 22.58 21.55 22.06 135.06 127.37 131.20 0.3066 0.3111 0.3156 15.05 14.36 14.71 135.04 127.35 131.18 0.3078 0.2989 0.3034 11.28 10.77 11.03 135.02 127.34 131.16 0.3023 0.2934 0.2979 9.025 8.612 8.819 127.32 131.15 135.01 0.2981 0.2881 0.2937 6.015 5.738 5.877 134.97 127.28 131.11 0.2815 0.2859 0.2904 4.509 4.301 4.405 127.24 131.06 134.93 0.2848 0.2758 0.2804 3.439 3.522 3.605 127.20 131.02 134.89 0.2717 0.2762 0.2807 3.002 2.864 2.933 127.15 130.98 134.85 0.2771 0.2681 0.2726 2.250 2.145 2.197 127.07 130.90 134.77 0.2716 0.2626 0.2671 1.498 1.427 1.463 126.89 130.74 134.61 0.2637 0.2547 0.2592 1.120 1.067 1.094 126.71 130.57 134.46 0.2491 0.2536 0.2581 0.8946 0.8516 0.8732 126.54 130.40 134.29 0.2537 0.2446 0.2492 0.5935 0.5645 0.5789 126.12 129.99 133.89 0.2366 0.2411 0,2456 0.4429 0.4207 0.4318 125.66 129.56 133.48 0.2399 0.2307’ 0.2353 0.3525 0.3345 0.3435 125.22 129.13 133.09 0,2352 0.2261 0.2307 0.2924 0.2771 0.2847 124.78 128.71 132.69 0.2314 0.2221 0.2268 0,2172 0,2053 0.2112 123.88 127.90 131.87 0.2252 0.2158 0.2205 0.1526 0.1435 0.1481 122.45 126.55 130.59 0,2175 0.2081 0.2128
440 460 480 138.98 142.90 146.84 92.39 94.42 96.50 138.96 142.89 146 83 0.3445 0.3486 0.3526 61.58 62.95 64.33’ 138.96 142.89 ‘146.83 -0.3385 0.3428 0.3470 46.19 47.22 48.25 138.95 142.88 146.83 0.3331 0,3374 0.3416 36.95 37.77 38.59 138.95 142.88 146.82 0.3289 0.3331 0.3373 30.79 31.48 32.16 138.95 142.88 146.82 0.3254 0.3297 0.3339 23.09 23.61 24.12 138.94 142.87 146.82 0.3200 0,3242 0.3285 15.39 15.73 16.08 138.93 142.85 146.80 0.3122 0.3165 0.3208 11.54 11.80 12.05 138.92 142.84 146.79 0.3067 0.3110 0.3153 9.232 9.438 9.645 138.90 142.82 146.77 0.3025 0.3068 0.3111 6.151 6.289 6.426 138.86 142.78 146.74 0.2947 0,2990 0.3033 4.612 4.716 4.820 138.82 142.75 146.70 .0.2892 0.2936 0.2979 3.687 3.770 3.852 138.79 142.72 146.66 0.2850 0.2893 0.2935 3.071 3.140 3.209 138.75 142.68 146.63 0.2814 0.2858 0.2901 2.301 2.354 2.405 138.67 142.61 146.56 0.2760 0.2803 0.2845 1.533 1.568 1.603 138.52 142.46 146.43 0.2680 0.2724 0.2767 1.146 1.173 1.199 138.87 142.32 146.28 0.2625 0.2668 0,2710 0.9160 0.9371 0.9585 138.22 142.17 146.14 0.2581 0.2624 0.2668 0.8079 0.6221 0.6365 45.79 137.83 141.79 0.2588 0,2501 0,2545 0,4538 0.4648 0.4759 45.44 137.43 141.43 0.2530 0.2443 0.2487 0.3615 0.3705 0.3794 45.09 137.07 141.05 0.2484 0.2397 0.2441 0.2999 0.3075 0.3151 44.74 136.68 140.69 0.2447 0.2359 0.2403 0,2232 0,2290 0.2347 135.95 140.01 144.02 0.2297 0.2341 0.2385 0.1572 0.1616 0.1659 134.69 138.83 142.90 0.2220 0.2266 0.2310
500 150.82
.lgE:i8 0.3566 65.70 150.80 0.3610 49.27 150.80 0,3459 39.42 150.80 0.3416 32.85 150.80 0.3381 24.63 150.79 0.3327 16.41 150.77 0.3249 12.31 150.76 0.3195 9.851 150.74 0.3152 6.564 150.71 0.3075 4.922 150.68 0.3020 3.936 150.65 0.2977 3.279 150.61 0,2942 2,457 150.55 0.2887 1.638 150.41 0.2809 1.226 150.28 0.2753 0.9798 150.14 0,2709 0.6511 49.80 0.2630 0.4869 49.4.5 0.2572 0,3883 49.11 0.2526 0,3227 48.79 0.2489 0,2405 148.11 0,2428 0,1701 147.03 0,2354
of the equations used by Riedel and Whitney with the exception of Whitney’s equation of state a,greequite closely with those of the present investigation. Whitney’s equation of state, however, differs from Equation 4 up to ‘2% at densities of one third the critical density and up to 6% at the critical density. In addition, his equation, which is a simplified (4-constant) Beattie-Bridgeman equation, predicts tbe isometrics as straight lines, and Whitney’s calculations consequently indicate no change in cv with a change in volume, for ( d2p/dT2)y in Equation 18 is equal to zero. This change of the specific heat with volume was found in the
January 1952
INDUSTRIAL A N D ENGINEERING CHEMISTRY
197 present study to be significant at high densities. The differences between Whitney’s thermodynamic r e s u 1t s B n d t h s e of the present investigation are as a result considered to be mainly due to the disagreement between the two equations of state. Since exact thermodynamic formulas were used in the calculations of the enthalpy and entropy values, the .results are thermodynamically consistent. Multiplication and division calculations were made with the aid of a 10-place calculating m a c h i n e . Whenever logarithms were needed, a 6-place table was used. Representative points along the saturated vapor line and throughout the superheated vapor region were checked by traveling to them by alternate routes. The enthalpy and entropy values of Tables IV and V were further tested for cons i s t e n c y b y p l o t t i n g them against pressure on large scale graphs. Smooth and consistent curves were obtained for all thermodynamic values. It is regarded that Tables TV and V accurately reproduce all the empirical relationships put into them. The thermodynamic properties presented in Table IV, Table V, and Figure 7 cover the range of conditions normally e n c o u n t e r e d when “Freon-13” is used as a refrigerant. NOMENCLATURE
A
function of density in equation of state B = function of density in equation of state C = function of density in equation of state cpo = specific heat of gas a t zero pressure in B.t.u. per pound per O R. cy = specific heat of gas at constant volume, u, in B.t.u. per pound per O R. cvm = specific heat of gas a t infinite volume in B.t.u. per pound pe? O R. d = density of gas in pounds per cubic foot dL = d e n s i t y of l i q u i d i n pounds per cubic foot AHT = change of enthalpy in B.t.u. per pound with volume a t c o n s t a n t temperature =
198
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Vol. 44, No. 1
AH. = change of enthdlpy in B.t.u. per pound with temperature
LITERATURE CITED
at constant volume J = 0.18506, factor for converting cubic feet, pounds per square inch, pounds to B.t.u. per pound L = latent heat of vaporizatjon in B.t.u. per pound p = pressure in pounds per square inch absolute AST = change of entropy in B.t.u. per pound per O R. .with volume a t constant temperature A S , = change of entropy in B.t.u. per pound pdr O R. with temperature a t constant volume T = absolute temperature, " R. ( " R. = " F. plus 459.69) t = temperature, O F. tc = critical temperature (83.93" F.) v = gas volume in cubic feet per pound VL = liquid volume in cubic feet per pound
(1) Beattie, J. A.,and Bridgeman, 0. C., Proc. Am. Acad. Arts Sci., 63, 229-308 (1928). (2) Benedict, M., Webb, G. B., and Rubin, L. C., J . Chem. Phys., 8, 33445 (1940). (3) Benning, A. F.,'and McHarness, R. C., IND.ENO. CEEM.,31, 912-16 (1939). (4) Ibid., 32, 698-700 (1940). (5)Ibid., pp. 814-16. (6) Henning, F.,2. Instrumentenk., 33, 33 (1913). (7) Kahovec, L.,and Wagner, J., 2. physilc. C h m . , B48, 177 (1941). (8) McNabney, R.,unpublished thesis, Western Reserve University, 1941. (9) Plyler, E.K.,private communication, 1949. (10) Riedel, L.,2. ges. Kttlte-Id., 48,9-13 (1941). (11) Ibid., pp. 89-92. (12) Ruff, O.,and Keim, R., 2. anorg. u. allgem. Chem., 201, 255 (1931). (13) Thornton, N. V., Burg, A. B., and Schlesinger, H. S., J . Am. Chem. Sw., 55, 3177 (1933). (14) Wenner, R. L.,"Thermochemical Calculations," 1st ed., New York, McGraw-Hill Book Co., 1941. (15) Whitney, J. H.,private communication with E. I. du Pont de Nemours & Co., 1948. RECEIVED October 13, 1950.
ACKNOWLEDGMENT
The authors wish to thank E. I. du Pont de Nemours & Co. for its generous financial assistance in this investigation. The suggestions of A. F. Benning and R . C . McHarness of Du Pont Co. are especially appreciated.
Phase Equilibria in Hvdrocarbon N
Systems 4
VOLUMETRIC BEHAVIOR OF THE NITROGEN-ETHANE SYSTEM H. H. REAMER, F. T. SELLECK, B. H. SAGE, AND W. N. LACEY California Institute of Technology, Pasadena 4, Calif.
N
ITROGEN is found in many petroleum reservoirs and may be considered as a component of natural gaa. Since mix-
turea of nitrogen and p a r a f i hydrocarbons do not form ideal solutions ( I f ) at elevated prwurea, a knowledge of the volumetric behavior of such mixtures is of industrial interest. Keyes and Burks (12) investigated the volumetric behavior of mixtures of nitrogen and methane with an accuracy adequate for most purposes. The work has been supplemented by the measure ments of Eilerts, Carlson, and Mullens (9)upon the effect of nitrogen on the volumetric behavior of natural gas. Burnett (7) recently summarized the thermodynamic properties of nitrogen. The volumetric behavior of the nitrogen-ethane system does not appear to have been established a t the higher pressures. The present study is concerned with the volumetric behavior of three mixtures of nitrogen and ethane at pressures up to 10,000 pounds per square inch in the temperature interval between 40" and 460" F. The influence of temperature and pressure upon the volume of ethane has been investigated in some detail. Beattie and coworkers ( 4 ) determined the volumetric behavior up to approximately 3,000 pounds per square inch with good accuracy. These studies have been extended recenly to somewhat higher pressures (19). Barkelew, Valentine, and Hurd (1) reviewed available experimental information concerning ethane and prepared a tabulation of thermodynamic data. The compressibilities of nitrogen and mixtures of hydrogen and nitrogen were determined over a wide range of temperatures and pressures by Wiebe and Gaddy (18). Volumetric studies of the nitrogen-carbon dioxide system were made by Haney and Bliss (10). The characteristics of nitrogen at pressures near 1 atmosphere were carefully determined by Baxter and Starkweather ( 8 ) . Benedict (6)studied the influence of pressure and temperature
upon the volume of nitrogen a t elevated preasurea. Beattie and Bridgeman established constants for this compound for their equation of state (3). Roebuck and Osterberg (16)and Deming and Deming (8)measured the Joule-Thomson coefficient of nitrogen over an extended range of pressures. The thermodynamic properties of this compound were made available recently (16). This background of experimental information serves to establish the volumetric behavior of the components of the nitrogen-ethane system with an accuracy adequate for present needs. MATERIALS
The nitrogen used in this investigation was obtained from the Linde Air Products Division of the Carbide and Carbon Chemicals Corp. which reported it to contain less than 0.0005 mole fraction of material other than nitrogen. This sample was passed over activated charcoal a t a low temperature and by means of a mass spectrometric analysis, .the purified material was found to contain less than 0.0002 mole fraction of. impurities. Before use the nitrogen was stored in a steel vessel at elevated pressures. The ethane was obtained from the Phillips Petroleum Co. which reported it to contain less than 0.001 mole fraction of impurities. This material was subjected to a single fractionation in a column packed with glass helices a t a reflux ratio of approximately 40 to 1. The central fraction from this distillation yielded less than 0.2 pound per square inch change in vapor pressure as a result of a change in quality-Le., the weight fraction gas of a heterogeneous system, from 0.2 to 0.8 a t a temperature of 70" F. Difficulty in obtaining satisfactory improvement in purity by fractionation had been experienced with other sources of ethane. This behavior may have resulted from the formation of an azeotropic mixture with one of the impurities which would have rendered simple fractionation ineffective as a means of purification. The ethane was stored in a weighing bomb ( 1 7 ) until ready for use.
