An experimental study of the equation of state of liquid xenon

J. Chem. Thermodynamics 1973, 5, 633-650

An experimental study of the equation of state of liquid xenon W. B. STREETT and L. S. S A G A N

Science Research Laboratory, U.S. Military Academy, West Point, N.Y. 10996, U.S.A. and L. A. K. STAVELEY

Inorganic Chemistry Laboratory, The University of Oxford, Oxford, U.K. (Received 4 January 1973) The gas-expansion method has been used to measure the density of liquid xenon at 17 temperatures from 165.00 to 289.74K and at pressures up to 3815 arm. The 530 experimental points have been ftted to the Strobridge equation, which has been used to estimate, at regular intervals of pressure and temperature, the following properties: density; isothermal compressibility; thermal expansivity; thermal pressure coefficient; configurational internal energy; and entropy relative to the saturated liquid. Within the range of the experiments, the configurational internal energy is very nearly a linear function of density. The experimental results, together with estimated third virial coefficients and published values of vapour pressure, second virial coefficient, and sound velocity in the liquid phase, have been used to estimate the following properties of the saturated liquid on the liquidvapour coexistence curve: enthalpy of vaporization; configurational internal energy; isothermal compressibility; thermal expansivity; thermal pressure coefficient; adiabatic compressibility; and heat capacity. The results have been used, together with published pressure, temperature data for the melting curve, to estimate the following properties of the saturated liquid on the liquid-solid coexistence curve: density; isothermal compressibility; thermal expansivity and thermal pressure coefficient.

1. Introduction T h e liquefied rare gases are o f p a r t i c u l a r i m p o r t a n c e in the d e v e l o p m e n t o f theories o f liquids, p a r t l y because o f their m o l e c u l a r simplicity, a n d p a r t l y because a c o n s i d e r a b l e a m o u n t o f i n f o r m a t i o n is n o w available for these elements on the r e l a t i o n between p o t e n t i a l energy a n d i n t e r m o l e c u l a r separation. Extensive values o f physical a n d t h e r m o d y n a m i c p r o p e r t i e s for these gases are required to test theoretical predictions, a n d a substantial p a r t o f these can be derived f r o m precise m e a s u r e m e n t s o f their p, V, T equations o f state. I n previous p a p e r s we r e p o r t e d e x p e r i m e n t a l studies o f the e q u a t i o n s o f state o f liquid a r g o n (1) a n d liquid k r y p t o n . (2) I n this p a p e r we r e p o r t a similar s t u d y o f liquid xenon, carried out at pressures u p to 3 8 1 5 a r m a n d at t e m p e r a t u r e s f r o m 165.00 to 2 8 9 . 7 4 K . t (The latter t e m p e r a t u r e is the critical t e m p e r a t u r e ; the t r i p l e - p o i n t t e m p e r a t u r e is 161.38 K.) T h e results consist o f 530 p, V, T points, m e a s u r e d a l o n g t Throughout this paper atm = 101.325kPa; calLh = 4.184 J.

634

W. B. S T R E E T T , L. S. S A G A N , A N D L. A. K. S T A V E L E Y

17 isotherms, covering a density range from 1.5 to more than 3 times the critical density. The measurements extend from pressures slightly above the vapor pressure to pressures just below the melting pressure; hence the results cover virtually the entire liquid range from the triple point to the critical temperature. The results have been fitted to the Strobridge equation, which has been used for interpolation and, in combination with additional data from the literature, for calculating thermodynamic properties of the liquid.

2. Experimental method The p, V, T measurements have been made by the method of gas expansion. A brief description of the apparatus and method is presented here; a more complete descrip1 " J (3) In this method a small quantity of fluid is confined in a cell tion has been publ'st~ea. of fixed volume (about 3.64cm3), under a measured pressure at a fixed temperature, and expanded to a pressure of about 1 arm into a known volume in a thermostat at room temperature. Accurate measurement of the pressure in the expansion volume allows the mass of fhiid to be calculated (using the first two terms of the virial equation for xenon
3. Results The experimentalp, V, Tresults are recorded in table 1, where for each of 17 temperatures the amount of substance density e is recorded as a function of pressure. For most temperatures the measurements extend from just above the vapour pressure to just below the melting pressure. Exceptions are the isotherms at 275, 283, and 287 K, for which measurements extend only to 300 atm. These were taken to obtain detailed information about curvatures of the isochores at densities from about 1.5 to 2 times the critical density (see section 6C).

EQUATION OF STATE OF LIQUID XENON

635

TABLE 1. Experimental results for amount of substance density e at pressure p and temperature T (atm = 101.325kPa) p at--m

c p m o l d m -3 at-m

T = 165.00K 4.08 22.41 7.62 22.42 7.76 22.43 16.38 22.46 26.43 22.50 32.46 22.52 32.69 22.53 47.37 22,58 64.75 22.64 75.89 22,67 87.18 22.71 T = 170.00 K 4.29 5.97 7.34 11,51

22,16 22.16 22.17 22.19

18,79 19,86 21.87 24.88 25.01 32.24 33.24 49.35 62.30 83.37 100.64 137.08 171.08 205.07 218.66

22.22 22.22 22.23 22.24 22.24 22.26 22.27 22.33 22.38 22.47 22.52 22.64 22.75 22.87 22.91

T----- 180.00K 6.63 21.63 7.11 21.64 8.75 21.64 10.90 21.65 12.56 21.66 16.32 21.68 19.11 21.69 19.69 21.69 21.70 21.70 25.20 21.72 25.35 21,72 25.94 21.72 27.06 • 21.72 32.66 21.75 32.95 21.75 32.82 21.75

33.26 33.39 49.27 62.27 83.78 105.81 137.22 171.08 214.18 239.06 273.05 304.33 345.12 388.63 440.29 483.81

c m o l d m -~ 21.75 2i.75 21.82 21.88 21.97 22.05 22.17 22.29 22.45 22.53 22.64 22.75 22.87 23.00 23.14 23.25

T = 190.00K 7.71 11.18 16.22 21.98 27.02 35.34 48.95 62.66 82.17 103.11 137.11 172.48 204.43 273.11 305.75 343.83 405.03 481.20 547.84

21.08 21.10 21.13 21.16 21.18 21.23 21.29 21.35 21.45 21.54 21.69 21.83 21.96 22.20 22.32 22.45 22.63 22.87 23.04

613.12 653.93 746.42

23.21 23.31 23.54

T = 200.00K 7.99 20.50 10.16 20.52 14.88 20.54 21.71 20.59 28.38 20.62 49.01 20.74 62.56 20.81 82.98 20.93 105.49 21.03

p atm 137.11 170.43 205.79 239.11 273.11 307.11 341.11 409.11 477.11 545.12 613.12 681.13 817.16 953.18 1021.20

c m o l d m -3 21.19 21.35 21.50 21.64 21.77 21.89 22.02 22.24 22.46 22.66 22.85 23.03 23.37 23.68 23.82

p a-~-

c moldm -£

137.11 20.15 171.11 20.35 205.11 20.53 239.11 20.70 273.11 20.86 307.10 21.01 338.38 21.16 409.11 21.43 477.11 21.68 545.11 21,91 613.12 22.13 681.13 22.33 749.14 22.52 817.15 22.69 885.16 22.88 953.18 23.04 T ~ 210.00K 1021.20 23.19 10.43 19.88 1089.22 23.35 14.90 19.92 1157.24 23.50 24.51 19.98 1225.27 23.64 47.72 20.15 1293.29 23.78 69.03 20.27 1361.32 23.91 105.69 20.48 1433.44 24.04 138.13 20.66 1501.47 24.16 171.11 20.83 1569.51 24.28 205.11 20.99 1623.94 24.38 277.18 21.31 T = 230.00K 345.18 21.58 413.19 21.82 21.96 18.64 481.19 22.05 28.22 18.70 549.20 22.28 36.12 18,79 617.20 22.47 44.56 18.87 685.21 22.66 49.60 18,91 821.23 23.01 56.49 18.98 957.26 23,33 68.96 19.10 1093.30 23.63 82.98 19.22 !229.35 23.90 103.79 19.37 1297.38 24.03 137.66 19.63 172.74 19.85 T = 220.00K 205.11 20.02 15.14 19.28 245.91 20.27 21.56 19.34 273,11 20.40 28.64 19.40 307.10 20.57 36.60 19.46 341.10 20.72 41.64 19.50 409.11 21.03 48.32 19.55 477.11 21.29 55.67 19.61 545.11 21.53 62.75 19.66 613.12 21.77 68.96 19.71 681.13 21.98 75.90 19.75 749.14 22.18 84.06 19.81 817.15 22.37 101.75 19,93 885.16 22.56

atm p

c m o l d m -8

953.18 1021.20 1093.30 1229.35 1365.41 1501.47 1637.54 1773.63 1868.89 1924.69

22.73 22.90 23.07 23.36 23.65 23.89 24.14 24.36 24,52 24,61

T = 240.00K 21.25 17.82 29.22 17.95 34.78 18.01 42.45 18.10 62.74 18.33 82.70 18.53 103.10 18.72 137.10 19.01 171.10 19.27 205.10 19.50 239.10 19.72 273.10 19.93 307.10 20.10 345.18 20.29 413.18 20.60 481.19 20.90 549.19 21.17 617.20 21.40 685.21 21.62 753.22 21.84 821.23 22.04 889.25 22.23 957.26 22.42 1025.28 22.59 1093.30 22.75 1161.32 22.91 1229.35 23.06 1297.38 23.21 1365.40 23.35 1501.47 23.62 1637.54 23.87 1773.63 24.11 1909.72 24.34 2045.82 24.56 2181.93 24.76 2249.98 24.86 T = 250.00K 27.04 17.01 29.90 17.08

W. B. STREETT, L. S. SAGAN, A N D L. A. K. STAVELEY

636

TABLE 1--continued p at-m 36.33 40.89 48.38 55.53 63.09 69.70 82.70 103.10 123.50 143.90 171.10 205.10 239.10 273.10 307.10 341.10 409.10 477.11 545.11 617.20 685.21 753.22 821.23 889.25 957.26 1025.28 1093.30 1161.32 1229.35 1297.38 1365.40 1501.47 1637.54 1773.63 1909.72 2045.82 2181.93 2318.04 2454.17 2556.27

c p m o l d m -fi atm 17.19 17.27 17.39 17.49 17.59 17.67 17.84 18.07 18.27 18.47 18.70 18.97 19.21 19.43 19.63 19.82 20.16 20.48 20.77 21.03 21.28 21.49 21.71 21,91 22,10 22,28 22,45 22.62 22,78 22.93 23.07 23.35 23.62 23.86 24.10 24.32 24.53 24.74 24.93 25.07

T = 260.00K 32.70 16.07 35.21 16.14 38.48 •6.22 42.09 16.31 45.29 16.39 48.70 16.47 55.57 16.61 62.66 •6.74 68.27 16.85 82.69 17.07

96.30 109.90 123.50 137.10 171.10 205.10 239.10 273.10 307.10 345.18 413.18 481.19 549.19 617.20 685.21 753.22 821.23 889.24 957.26 •025.28 1093.30 1229.34 1297.37 1365.40 1501.47 1773.63 1909.72 2045.82 2181.92 2318.04 2726.45 2590.30 2454.17 2896.64

c mol d m - a

p atm

•7.27 17.44 17.60 17.76 18.11 18.41 18.69 18.93 19.16 19.38 19.77 20.10 20.40 20.67 20.92 21.16 21.38 21.59 21.78 21.98 22.15 22.49 22.65 22.80 23.09 23.62 23.85 24.07 24.29 24.51 25.09 24.91 24.72 25.32

211.90 239.10 273.10 307.10 341.10 413.18 481.19 549.19 617.20 685.21 753.22 821.23 889.24 957.26 1025.28 1093.30 1161.32 1229.34 1297.37 1365.40 1501.47 1637.54 1773.62 1909.71 2045.82 2181.92 2318,04 2454.17 2590.30 2726.45 2998.76 3203.01

T=270.00K 46.58 15.23 53.66 15.47 62.46 •5.73 69.28 15.90 75.89 16.05 82.69 16.19 89.49 •6.32 96.29 16.45 102.69 16.56 •09.89 •6.69 123.50 16.90 137.10 17.08 156.82 17.35 171.10 17.51 184.70 17.66 198.30 17.79

c p mol d m - 3 arm 17.92 18.16 18.43 18.69 18.91 19.35 19.70 20.03 20.32 20.59 20.84 21.07 21.29 21.50 21.69 21.88 22.06 22.23 22.39 22.55 22.85 23.13 23.40 23.64 23.88 24.10 24.31 24.52 24.72 24.90 25.26 25.51

T=275.00K 48.76 14.57 56.05 14.90 62.85 15.16 69.08 15.34 82.69 15.72 96.29 16.03 •09.90 16.29 123.50 16.52 •37.•0 16.73 150.70 16.93 164.30 17.10 •77.90 17.27 191.50 17.42 205.10 17.56 2•8.70 17.70 232.30 •7.82 245.90 17.94 259.50 18.07

273.10 286.70 293.50 307.10

c p mol din- 3 arm 18.18 18.28 18.34 18.45

T = 280.00K 55.43 14.05 62.45 14.43 68.87 14.71 75.88 14.97 82.69 15.19 96.29 15.56 109.89 15.85 123.50 16.13 137.10 16.36 150.70 16.58 164.30 16.77 177.90 16.95 191.50 17.11 205.10 17.26 239.10 17.62 273.10 17.93 307.10 18.21 341.10 18.45 375.10 18.69 409.10 18.90 481.18 19.31 549.19 19.65 617.20 19.97 685.20 20.25 821.23 20.76 957.26 21.20 1093.30 21.60 1229.34 21.96 1365.40 22.28 1501.47 22.61 1637.54 22.88 1773.62 23.16 1909.72 23.41 2045.82 23.65 2181.92 23.89 2318.04 24.11 2454.17 24.31 2590.30 24.52 2726.45 24.71 2998.76 25.07 3271.10 25.41 3543.48 25.73 T = 283.00K 55.42 13.39 62.24 13.90

69.75 75.88 82.69 96.29 109.90 123.50 137.10 150.70 164.30 177.90 191.50 205.10 218.70 232.30 245.90 259.50 273.10 286.70 300.30

c mol 14.30 14.60 14.84 15.25 15.58 15.87 16.13 16.35 16.56 16.74 16.92 17.08 17.24 17.38 17.52 17.65 17.77 17.88 18.00

T = 287.00K 62.79 13,06 69.55 13.63 76.16 14.01 82.69 14.33 96.29 14.82 109.90 15.20 123.50 15.53 137.10 15.80 150.70 16.05 164.30 16.28 177.90 16.48 191.50 16.67 205.10 16.84 218.70 17.02 232.30 17.18 245.90 17.31 273.10 17.56 300.30 17.80 T = 289.74K 62.24 12.17 69.21 13.05 75.88 13.54 82.69 13.93 90.72 14.30 96.84 14.51 109.89 14.93 123.50 15.28 137.10 15.58 150.70 15.84 164.30 16.08

E Q U A T I O N O F STATE O F LIQUID X E N O N

637

TABLE 1--continued p atm 177.90 191.50 205.10 218.70 232.30 245.90 259.50 273.10 286.70

e p tool dm- s atm 16.30 16.49 16.67 16.83 16.99 17.15 17.28 17.41 17.54

c p tool din- 3 atm

307.10 341.10 375.10 409.10 443.10 477.10 511.11 545.11 579.11

17.75 18.02 18.25 18.48 18.70 18.90 19.09 19.27 19.44

617.20 685.20 753.22 821.23 889.24 957.26 1025.28 1093.30 1161.32

c m o l d m -3

p atm

19.61 19.92 20.19 20.45 20.69 20.92 21.13 21.33 21.51

1229.34 1297.37 1365.40 1501.47 1637.54 1773.62 1909.71 2045.81 2181.92

e p m o l d m -3 atm 21.70 21.88 22.04 22.36 22.66 22.94 23.19 23.44 23.67

c m o l d m -3

2318.04 2454.17 2590.30 2722.36 2998.76 3271.10 3543.48 3815.90

23.89 24.10 24.31 24.50 24.88 25.23 25.56 25.86

4. Least squares fit to the Strobridge equation A n e q u a t i o n o f s t a t e w h i c h h a s b e e n f o u n d u s e f u l i n d e s c r i b i n g p , 1I, T b e h a v i o u r o v e r a w i d e r a n g e o f d e n s i t i e s is d u e t o S t r o b r i d g e . <1°) T h e e q u a t i o n c a n b e w r i t t e n as follows •

p = R T c +(A1 R T + A2 + A a / T + A J T 2 +As/T4)c 2 + + ( A 6 R T + A7)c a + A s Tc 4 + (Ag/T 2 + A l o / T 3 + A11/T 4) e x p ( A 1 6 c2)c a + + ( A l ~ / T 2 + A l a / T a + A 1 4 / T 4) e x p ( A ~6 c2)c5+A15 c 6.

(1)

W i t h t h e e x c e p t i o n o f A ~ 6 , t h i s e q u a t i o n is l i n e a r i n t h e c o n s t a n t s Ai, a n d i t is a s i m p l e m a t t e r t o e v a l u a t e t h e s e c o n s t a n t s u s i n g l i n e a r l e a s t - s q u a r e s t e c h n i q u e s . (2~ T h e 530 e x p e r i m e n t a l p , V, T p o i n t s i n t a b l e 1, t o g e t h e r w i t h 14 s a t u r a t e d l i q u i d p , V, T p o i n t s obtained by extrapolating our isotherms to the saturation vapour pressure, have been fitted t o e q u a t i o n (1) w i t h t h e u s e o f a w e i g h t e d l i n e a r l e a s t - s q u a r e s t e c h n i q u e d e s c r i b e d b y H u s t a n d M c C a r t y . ° ~ T h e c o n s t a n t s o b t a i n e d f r o m t h i s fit a r e r e c o r d e d i n t a b l e 2. TABLE 2. Constants for equation (1). With these constants the equation is valid only in the p, V, T region covered by the experiments that is, for temperatures from 165.00 to 289.74 K, and pressures between the vapottr pressure curve and the melting curve. The included density range is about 1.5 to 3.1 times the critical density. A~ = -- 0.16568907× 10 -1 dmSmo1-1 Az = 0.70469920 × 101 atm dm n m o l - z As = --0.44719386 × 1 0 a a t m d m 6 K m o l - 2 A4 = 0.45147418 × 10~arm dm 6 K ~tool-2 A6 = --0.23699824 × 101° arm dm 6 K 4 mol- z A6 = --0.78770471 × 1 0 - 2 d i n 6 tool -2 A7 = 0.24831111 atmdm9 tool -3 A8 = 0.19478457 × 1 0 - 4 a t m d m 1 2 K - l m o 1 - 4 A, = --0.11848171 × 105 a t m d m ° K 2 m o 1 - 3 A~o = 0.12666999 × 108 atmdmOKSmol -n All = --0.14045036 × 10l° atm dm 9 K 4 mol- 3 A ~ = --0.44260325 × 102 atmdml~K2mo1-5 A~8 = --0.15261577 × 10~ atm dm is KSmo1-5 Aa4 = 0.27129925 × 107 atmdm~SK4mol -n A15 ---- 0.83197174 × 10-~atmdmlSmo1-6 A~6 = -- 0.0040 dm 6 m o l - 2 R = 0.082057 dm 3 arm K - 1 tool- ~

638

w.B. STREETT, L. S. SAGAN, AND L. A. K. STAVELEY

One measure of the effectiveness of equation (1) in representing the experimental results is the magnitude of the difference Ac between the experimental and calculated densities. We have examined the values of Ac for each of the 530p, V, T points, and found the maximum value to be 0.15 per cent and the average value less than 0.03 per cent of c. In other words, with the constants in table 2, equation (1) represents all experimental densities within the estimated accuracy of the experiment. Calculated values of c were obtained from equation (1) using an iterative technique based on the formula

ci+ l = c~-f(cl)/f'(c~),

(2)

where f(c) is equation (1) in the form f(c) = 0 and f ' ( c ) is the first derivative with respect to c. A first estimate of 20 tool d m - 3 for c will cause the iteration to converge for any point in the experimental range. Although equation (1) is explicit in p, it is less suitable for calculating p at fixed values of c and T. The magnitude of (~p/~c)r is of the order of 100 atm dm 3 m o l - 1 over most of the experimental range; hence the inherent scatter in c of about 0.01 tool dm -3 leads to errors of roughly 1 atm in the calculated pressures--a relatively large error in the low-pressure range.

5. Comparison with other measurements As noted above, the saturated liquid densities of Terry et aL (6) were used to calibrate our apparatus; hence there is forced agreement between those results and the saturated liquid densities obtained by extrapolating our experimental isotherms to the saturation curve. In table 3 these densities are compared to those reported recently by Theeuwes and Bearman, <12) over the temperature range 170 to 240 K. Their densities are higher than ours, by amounts ranging from about 0.18 to 0.36 per cent. TABLE 3. Amount of substance density e of saturated liquid xenon. Comparison of the data of Theeuwes and Bearmanc12>with values calculated from equation (I)

T/K 170.00 180.00 190.00 200.00 220.00 240.00

c/mol dm - 3 Theeuwes and Bearman This work 22.194 21.668 21.135 20.565 19.277 17.834

22.134 21.609 21.063 20.491 19.242 17.802

A representative comparison with the compressed liquid densities of Theeuwes and Bearman, (13) for p < 300atm, is shown in table 4. In this case their densities are systematically higher than ours by about 0.l per cent, which is within the estimated errors of the two experiments. We are unable to account for the poorer agreement between saturated liquid densities.

EQUATION OF STATE OF LIQUID XENON

639

TABLE 4. Comparison of amount of substance densities c calculated from equation (1) with values reported by Theeuwes and Bearman(la~ (atm = 101.325kPa) T/K

p/atm

170.00 170.00 200.00 200.00 240.00 240.00

11.85 119.28 61.75 279.42 36.47 256.03

c/mol dm -3 Theeuwes and Bearman Equation (1) 22.196 22.830 20.835 21.785 18.070 19.847

22.176 22.838 20.818 21.794 18.040 19.826

TABLE 5. Comparison of amount of substance densities c calculated from equation (1) with the values reported by Michels et al. a4~ (atm = 101.325kPa)

T/K

273.15 273.15 273.15 286.65 286.65 286.65

p/atm 65.80 645.42 1802.30 96.23 760.04 1815.66

clmol dm - 3 Michels et al. equation (l) 15.534 20.409 23.434 14.919 20.409 23.153

15.484 20.341 23.392 14.875 20.348 23.118

In table 5, densities calculated from equation (1) are compared to the experimental results of Michels et al. (~4~ at 273.15 and 286.65 K. Their densities are systematically higher than ours by about 0.3 per cent.

6. Derived properties A. GAS AND SATURATED LIQUID To examine the dependence, at regular temperature intervals, of the configurational internal energy of liquid xenon on density, we need values at these temperatures of AH~, the molar enthalpy increase when the liquid evaporates to give the infinitely dilute gas. This quantity is given by the equation

A~/~ = Ansv + ( U ~ - Hsv),

(3)

where AHsv is the molar enthalpy of evaporation at the saturation vapour pressure p, and ( H ~ - H s ~ ) the further enthalpy increase when the vapour at this pressure is expanded to zero pressure. Only one calorimetric determination of AHs~ appears to have been made, by Clusius and Riccoboni (t 5) at the normal boiling temperature, and the data required in using this value of AH~ as the basis for calculating AH~v at higher temperatures are not available. However, two very careful studies of the vapour pressure of liquid xenon have been made, by Michels and Wassenaar (16) and by Theeuwes and Bearman. (~2) (The recent measurements of Bowman, Aziz, and Lira (~7) 43

640

W.B. STREETT, L. S. SAGAN, AND L. A. K. STAVELEY

do not seem t o be o f quite such high precision, and we have not used them.) From these vapour pressure results we have estimated dp/dT, and hence AHsv. Michels and Wassenaar fitted their values o f p to an equation with four parameters, while Theeuwes and Bearman used one with eight parameters which, not surprisingly; gives a somewhat better fit with experiment over the whole temperature range. From 200 to 270 K we have used Theeuwes and Bearman's data. Over this range, the values of d p / d T so obtained and those derived from the equation of Michels and Wassenaar are in good agreement, the average numerical difference being 0.22 per cent. "Below 200K the values of d p / d T from the two sets of measurements diverge increasingly. From 165 to 190 K we have preferred to use the data of Michels and Wassenaar, primarily because their measurements extended to the triple-point temperature (161.7K) whereas those of Theeuwes and Bearman ended at 175 K. The value of 3011 calthmo1-1 for AHsv at the normal boiling temperature (165.02K) derived from Michels and Wassenaar's vapour pressure equation is in fair agreement with the directly determined figure of 3020 calth tool- 1 of Clusius and Riccoboni. In using the Clapeyron equation to estimate AHoy from values of dp/dT, it is of course also necessary to know Vs~ and Vsl, respectively the molar volumes of vapour and liquid at the saturation vapour pressure, Values of Vsl have been taken from the present work. Calculation of Vs~ requires a knowledge o f the appropriate virial coefficients. The second virial coefficient B presents no problem, since Brewer has measured this quantity directly at 223.15, 198.15, and 173.15 K. His values, together with a value (4) of B = - 154.25 cm 3 m o l - 1 at 273.15 K, give the equation: B/cm 3 m o l - 1 = 92.31 - 225.20/TR+ 33.08/T2 - 37.65/T3,

(4)

where T R = T/Tc, with the critical temperature Tc = 289.74K. The third virial coefficient C has not been measured below 273 K, and we have .therefore calculated it from the following formula suggested by Chueh and Prausnitz: (19) C / V 2 = (0.232TR-°'z5 + 0.468Ta- 5){1 --exp(1 - 1.89T2)} x x [-0.6 e x p { - ( 2 . 4 9 - 2 . 3 0 T R+ 2.70TRa)}]. (5) The value given by this formula at 298 K is 6185 cm 6 tool-2, as compared with the experimental figure of (5970_+ 790) cm 6 tool -2 obtained by Chen and Present (2°) from a re-analysis of available data. Since Chueh and Prausnitz advise against using their equation at low temperatures where C becomes negative, we have ignored the third virial coefficient below 210 K. The enthalpy correction for the imperfection of the saturated vapour, (H~, + H~v), is given by the equation: (H ° - H ~ ) = - R T{(B - BI)/Vs., - ( 2 C - C~)/2 V2},

(6)

where Bt = T ( d B / d T ) and C1 = T(dC/dT). Values o f B I and C1 were estimated from equations (4) and (5). The molar configurational energy U~ of saturated liquid xenon, is defined by the equation: Utsl = -AH~, + R T - pV~, = - H s , , - ( H~,- H~v) + R T - pV~I.

(7)

The results of these calculations are summarized in table 6 at 165K and at 10K intervals from 170 to 270K. The least certain values o f AH~v and hence of U~ are probably those at the highest temperatures, primarily because of the uncertainty in the

E Q U A T I O N OF STATE OF LIQUID X E N O N

641

TABLE 6. Thermodynamic properties of liquid and gaseous xenon; B and C are the second and third viral coefficients, respectively; Vs~ and V~ are molar volumes of saturated vapour and liquid, respectively; AHs~ is the molar enthalpy of vaporization to give saturated vapour; H ° is the molar enthalpy of infinitely dilute gas; H~v is the molar enthalpy of saturated vapour; 2xH,~ is the molar enthalpy of vaporization to give infinitely dilute gas; and U ~ is the molar configurational internal energy of saturated liquid (calth = 4.184 J; atm = 101.325 kPa) T K

p atm

B cm a mol- a

C cm 6 mol- 2

Vsv cm a tool- ~

Vst cm 3 tool- ~

165 170 180 190 200 210 220 230 240 250 260 270

0.99855 1.3196 2.192 3.441 5.133 7.396 10.312 13.973 18.477 23.926 30.433 38.131

--405 --381.8 --341.5 --307.7 --279.0 --254.3 --232.9 --214.1 --197.6 --182.9 --169.7 --157.8

-----650 3435 5100 6040 6515 6690 6680

13141 10174 6377.3 4198.8 2888.4 2039.8 1477.4 1091.4 818.0 618.4 468.4 351.7

44.65 45.16 46.27 47.48 48.81 50.35 51.97 53.92 56.21 58.99 62.45 67.02

r K"

dp/dr atm K - i

AHoy calt~ m o l - 1

H~ -- Hsv calth m o l - £

165 170 180 190 200 210 220 230 240 250 260 270

0.05754 0.07125 0.1047 0.1465 0.1967 0.2574 0.3273 0.4066 0.4959 0.5958 0.7078 0.8346

3011 2971 2889.5 2798 2705.5 2604 2485.5 2349.5 2195.5 2018 1809.5 1553.5

30.1 37.6 56.3 80.7 111.4 154.1 203.2 262.7 334.8 423.0 532.1 672.6

AHg caltn tool- 1 3041 3008.5 2946 2878.5 2817 2758 2688.5 2612.5 2530.5 2441 2341.5 2226.5

-- UL calth mol- 1 2714 2672 2590.5 2505 2426 2350 2264.5 2173.5 2078.5 1978.5 1871 1751.5

e r r o r s i n t r o d u c e d by n e g l e c t i n g virial coefficients h i g h e r t h a n t h e t h i r d , b u t a c o m p a r i s o n o f the c o n t r i b u t i o n s m a d e at 270 K b y C a n d CI w i t h t h o s e d u e t o B a n d B1 gives t h e i m p r e s s i o n t h a t e v e n at t h i s ' t e m p e r a t u r e ( w h i c h is r e l a t i v e l y h i g h in r e l a t i o n to To) t h e v a l u e s o f AHsv a n d U~ a r e r e a s o n a b l y reliable. A n u m b e r o f useful t h e r m o d y n a m i c p r o p e r t i e s c a n be e s t i m a t e d f r o m t h e p, V, T e q u a t i o n o f state a n d f r o m p u b l i s h e d d a t a o n t h e v e l o c i t y o f s o u n d in x e n o n . T h e f o l l o w i n g m e c h a n i c a l coefficients f o r t h e s a t u r a t e d l i q u i d h a v e b e e n c a l c u l a t e d f r o m e q u a t i o n (1): t h e i s o t h e r m a l c o m p r e s s i b i l i t y 1¢r = - ( 1 / V ) ( S V / ~ p ) r ; t h e t h e r m a l e x p a n s i v i t y ~p = (1/V)(~V/~T)p; a n d t h e t h e r m a l p r e s s u r e coefficient 7v = (~P/~T)v.

642

W.B. STREETT, L. S. SAGAN, AND L. A. K. STAVELEY

The thermal expansivity along the saturation line, ~ , has been calculated f r o m the equation

c~o = . . ( 1 - ~d~v),

(8)

where ?~ is the slope d p / d T o f t h e v a p o u r pressure curve (column 7 intable 6). Measured values o f the velocity o f sound u in saturated liquid xenon, reported by Aziz et al., (21) have been used to calculate the adiabatic compressibility, fls = - ( 1 / V ) ( 0 V/~p)s, from the equation fls = 1/P u2. (9) The mechanical and adiabatic coefficients o f the saturated liquid on the liquid-vapour coexistence curve are recorded in table 7. With these coefficients, heat capacity can be calculated f r o m the relations:

Cv = TVa2p/(flr-fls),

(10)

Cv = C.fls/flr, C,~ = Cv + T V . . ( ? v - ?,,),

(12)

(11)

TABLE 7. Mechanical and adiabatic coefficients for saturated liquid xenon on the liquid + vapour coexistence curve (atm = 101.325 kPa) T 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00

104xr atm - 1 1.82 2.13 2.52 3.03 3.69 4.61 5.92 7.92 11.17 17.18 30.80 80.90

10a~p K- 1 2.35 2.49 2.69 2.93 3.23 3.61 4.11 4.80 5.83 7.53 10.98 21.95

Yv atm K - 1 12.91 11.69 10.64 9.67 8.74 7.83 6.94 6.06 5.21 4.38 3.57 2.71

104fls

103ct~ K- 1

atm- ~

2.34 2.47 2.65 2.87 3.13 3.46 3.87 4.41 5.16 6.32 8.41 14.00

0.87 0.98 1.11 1.27 1.47 1.74 2.09 2.59 3.33 4.53 6.78 12.14

where C~ is the heat capacity measured along the saturation curve. The calculated heat capacities are shown in figure 1, together with a single experimental value o f Cp reported by Clusius and Riecoboni °5) for a temperature a few kelvins above the triple-point. The measured value o f Clusius differs f r o m our calculated value by less than 1 per cent, which is remarkably g o o d agreement under the circumstances. However, it would be unwise to assume that the heat capacities in figure 1 are accurate to within 1 per cent over the entire temperature range. The mechanical coefficients in equations (10) to (12) are obtained f r o m first derivatives calculated f r o m equation (1) at one o f the boundaries o f the fitted p, V, T surface. At such a boundary, the small inherent scatter in the p, V, T results, as well a s the surface fitting process itself, can

EQUATION OF STATE OF LIQUID XENON 40 - - y

~

N--F~F

643

C-

c,, 30

7 20

10 ~,>-3---~ -

t 0 ~

c__~__~..~._:~__~.~.~ I

160

I

I

200

l

1

240 7'/K

I

280

FIGURE I. Heat capacities of saturated liquid xenon calculated from p, V, T and velocity of sound measurements. The square represents the only available directly measured value of Cp by Clusius and Riccoboni.C15~

lead to significant errors in estimating these derivatives. In the case of krypton, (2) we found that heat capacities calculated in this way, using the velocities of sound from the same source, (21) agreed with experimental values (zz) within the estimated accuracy of the experiments (about 4 per cent), except for the region within 10 K below the critical temperature, where the difference was as much as 10 per cent. Therefore it seems reasonable to suggest that the heat capacities of xenon, recorded in figure 1, are accurate to within at least 10 per cent. B. COMPRESSED LIQUID Equation (1) has been used to calculate densities at regular intervals of pressure. These are recorded in table 8. For the same pressures, values of fir, %, 7v, the configurational internal energy U t, and the entropy relative to the saturated liquid AS(T), have been calculated and are recorded in tables 9 to 13. Values of U t in table 12 have been calculated from

Ut

=

U~l+

{r(Op/ST)v-p} dV,

(13)

Vsl

using values of U~ from table 6. The relative entropy AS(T) in table 13 has been calculated from AS(T) =

f~(SP/6T)v

dV.

(14)

644

W . B . STREETT, L. S. SAGAN, AND L. A. K. STAVELEY

TABLE 8. Amount of substance density c of xenon at T and p (atm = 101.325kPa)

T/K

170

180

190

200

210

p/atm 5 10 15 25 50 100 200 400 600 800 1000 1500 2000 2500 3000 3500

22.149 21.622 22,169 21.644 22.189 21.667 22,228 21.712 22.32421.820 22.506 22.025 22.840 22.395 23.020

21.071 21.098 20.521 19.905 21.12420.551 19.941 21.17520.611 20.012 21.299 20.754 20.179 21.530 21.017 20.483 21.941 21.47620.999 22.622 22.219 21.810 23,182 22.818 22,453 23.328 22.992 23.775 23,462

220 230 240 c/moldm -a

19.284 18.563 19,369 18.670 17,892 19,569 18.914 18.202 19.923 19.333 18.710 20.50720.000 19,479 21.397 20.98020.559 22.086 21,718 21.351 22,65722.322 21.990 23.149 22,840 22.533 24.163 23.894 23,629 24.498

250

260

16.995 17.411 16.501 18.046 17.329 18.943 18.389 20.136 19.712 20.98620.623 21.662 21.337 22.230 21.933 23,369 23.114 24.265 24.037 25.013 24,804

270

280

289

15,377 16.543 17,818 19.288 20.264 21.018 21.640 22.866 23.815 24.601 25.278

13.681 15,658 17.227 18.864 19.909 20.704 21.354 22.623 23,599 24.404 25,094 25.702

14,733 16.676 18.483 19.594 20.426 21.102 22.410 23,410 24.231 24,934 25.552

270

280

289

TABLE 9. Isothermal compressibility x r of xenon (atm = I01.325 kPa)

T/K

170

180

190

1.81 1.80 1.78 1.75 1.69 1.57 1.38

2.12 2.10 2.08 2.04 1.95 1.79 1.55 1.23

2.51 2.48 2.46 2.40 2.27 2.06 1.74 1.35 1.11

200

210

2.98 2.94 2.86 2.68 2.38 1.97 1.48 1.20 1.02 0.89

3.66 3.59 3.47 3.20 2.79 2.23 1.63 1.30 1.09 0.94

p/atm 5 10 15 25 50 100 200 400 600 800 1000 1500 2000 2500 3000 3500

220 230 240 104xr/atm- 1

4.51 4.32 3.91 3.30 2.55 1.80 1.41 1.16 1.00 0.74

5.89 5.55 4.88 3.97 2.93 1.98 1.52 1.24 1.06 0.78

250

260

7.51 11.03 6.31 8.57 12.61 21.74 62.20 4.85 6.07 7.82 10.48 14.89 22.02 3.40 3.96 4.65 5 . 5 1 6.59 7.80 2.19 2.42 2.68 2.97 3.29 3.61 1.65 1.78 1.92 2 . 0 8 2.24 2.40 1.33 1.42 1.51 1.61 1.72 1.81 1.12 1.19 1.26 1 . 3 3 1.40 1.47 0.81 0.85 0.89 0.93 0.97 1.00 0.64 0.67 0.69 0.72 0.74 0.77 0.55 0.57 0.59 0.61 0.62 0.50 0.51 0.53 0.45 0.46

EQUATION OF STATE OF LIQUID X E N O N

645

TABLE I0. Thermal expansivity ~p of xenon (atm = 101.325 kPa)

T]K

170

180

190

2.34 2.33 2.32 2.29 2.23 2.12 1.94

2.48 2.47 2.45 2.42 2.34 2.21 2.00 1.72

2.68 2.66 2.64 2.59 2.50 2.34 2.09 1.77 1.56

200

210

2.90 2.87 2.82 2.69 2.49 2.19 1.83 1.60 1.44 1.32

3.21 3.17 3.09 2.93 2.67 2.31 1.88 1.63 1.46 1.33

220

p/atm 5 10 15 25 50 100 200 400 600 800 1000 1500 2000 2500 3000 3500

230 240 10actp/K- 1

3.56 3.45 3.22 2.88 2.43 1.94 1.66 1.48 1.34 1.12

4.09 3.93 3.60 3.13 2.57 2.00 1.69 1.49 1.35 1.12

4.63 4.10 3.43 2.71 2.05 1.72 1.50 1.35 1.11 0.96

250

260

270

280

289

5.77 4.83 3.81 2.88 2.10 1.74 1.51 1.35 1.10 0.95 0.85

6.02 4.32 3.06 2.15 1.75 1.51 1.35 1.09 0.94 0.83

8.44 17.73 5.01 6.06 3.26 3.49 2.20 2.24 1.76 1.77 1 . 5 1 1.50 1.34 1.33 1.07 t.06 0.92 0.90 0.81 0.80 0.74 0.72 0.66

7.59 3.73 2.28 1.77 1.49 1.31 1.04 0.89 0.78 0.70 0.65

TABLE 11. Thermal pressure coefficient ~v of xenon (atm = 101.325kPa)

T/K

170

180

190

12.93 12.96 12.99 13.06 13.20 13.49 14.03

11.71 11.74 11.78 11.84 12.01 12.33 12.93 13.97

10.65 10.69 10.73 10.81 11.00 11.36 12.00 13.11 14.05

200

210

9.72 9.76 9.85 10.06 10.45 11.15 12.32 13.29 14.14 14.90

8.77 8.82 8.91 9.15 9.58 10.33 11.56 12,56 13.42 14.18

p/atm 5 10 15 25 50 100 200 400 600 800 1000 1500 2000 2500 3000 3500

220 230 240 ~,v/atm K - 1

7.88 7.99 8.25 8.73 9.53 10.81 11.84 12.71 13.47 15.08

6.95 7.08 7.37 7.89 8.75 10.08 11.12 12.00 12.77 14.36

6.16 6.50 7.08 7.99 9.37 10.42 11,30 12.07 13.65 14.93

250

260

270

280

289

5.23 5.64 6.28 7.27 8.68 9.75 10.63 11.38 12.94 14.20 15.27

4.77 5.52 6.57 8.02 9.09 9.97 10.72 12.25 13.49 14.54

3.88 4.78 5.92 7.40 8.47 9.34 10.08 11.59 12.80 13.82 14.72

2.85 4.07 5.30 6.82 7.89 8.75 9.47 10.95 12.13 13.13 14.01 14.79

3.45 4.79 6.33 7.39 8.24 8.95 10.40 11.55 12.53 13.38 14.15

646

W . B . STREETT, L. S. SAGAN, A N D L. A. K. STAVELEY

TABLE 12. Configurational internal energy Ut of xenon (caleb = 4.184J; atm = 101.325kPa)

T/K

170

180

190

--2674 --2677 --2680 --2686 --2701 --2730 --2782

--2592 --2595 --2599 --2606 --2622 --2654 --2710 --2806

--2506 --2510 --2514 --2521 --2540 --2575 --2637 --2740 --2825

200

p/atm 5 10 15 25 50 100 200 400 600 800 1000 1500 2000 2500 3000

210

220 230 Ut/calthmo1-1

--2430 --2434 --2443 --2464 --2503 --2572 --2683 --2773 --2849

--2352 --2357 --2368 --2392 --2436 --2511 --2632 --2727 --2808 --2916 --2877

--2270 --2282 --2310 --2360 --2444 --2574 --2675 --2759 --2832 --2979

--2175 --2189 --2222 --2280 --2374 --2514 --2621 --2709 --2784 --2936

240

250

260

270

--2090 --2130 --2198 --2304 --2455 --2568 --2659 --2737 --2892 --3012

--1981 --2033 --2115 --2234 --2397 --2516 --2611 --2690 --2848 --2969 --3068

--1926 --2028 --2164 --2341 --2465 --2563 --2644 --2804 --2926 --3025

--1803 --1939 --2097 --2287 --2417 --2518 --2601 --2763 --2885 --2983 --3065

TABLE 13. Entropy AS(T) of liquid xenon relative to liquid at saturation (calLh = 4.184J; a t m = 101.325kPa)

T/K

170

180

190

--0.009 --0.022 --0.035 --0.060 --0.121 --0.239 --0.455

--0.008 --0,022 --0,035 --0.063 --0.129 --0,254 --0.483 --0.878

--0,005 --0.020 --0.035 --0.065 --0.138 --0.274 --0.520 --0.936 -- 1.287

200

p/atm 5 10 15 25 50 I00 200 400 600 800 1000 1500 2000 2500 3000

--0.017 --0.034 --0.067 --0.148 --0.298 --0.563 -- 1.005 -- 1.371 --1.689 --1.972

210 220 230 AS(T)~al~hK-lmo1-1

--0.010 --0.030 --0.067 --0.158 --0.324 --0.613 -- 1.083 -- 1.465 --1.794 --2.084

--0.021 --0.065 --0.169 --0.355 --0.671 -- 1.170 -- 1.569 --1.908 --2.205 --2.831

--0.005 --0.058 --0.179 --0.390 --0.738 -- 1.268 -- 1.684 --2.033 --2.337 --2.970

240

250

260

270

--0.042 --0.187 --0.432 --0.817 -- 1.382 -- 1.814 --2.171 --2.481 --3,121 --3.639

--0.009 --0.194 --0.485 --0.914 -- 1.516 -- 1.964 --2.330 --2.645 --3.289 --3.807 --4.247

--0.195 --0.555 --1.040 -- 1.682 --2.145 --2.520 --2.838 --3.485 --4.002 --4.438

--0.181 --0.660 --1.217 -- 1.903 --2.382 --2.763 --3.085 --3.733 --4.247 --4.679

--5.055

EQUATION OF STATE OF LIQUID XENON

647

In principle, it is possible to calculate the change in heat capacity with volume or pressure, using the relations:

r(~2p/~r2)v dV,

(ACv)r =

(15)

VI

and = -

r(azv/

r2), dp.

(16)

Pl

However, because of the sensitivity of second derivatives to errors in the p, V, T data, this method is rarely feasible in practice. In order to obtain reliable estimates of these derivatives for the liquid phase, the p, V, T data must have a precision in density of about 10 .4 , or better, (with, of course, equivalent precision in pressure and temperature). In this work, the precision in density is about 3 x 10 -4, and values of the second derivatives in equations (15) and (16), calculated from equation (1), were found to be erratic. Hence these equations are not likely to yield reliable values of heat capacities for compressed liquid xenon. C. THE SHAPE OF THE DENSE FLUID ISOCHORES Calculated values of Yv are plotted in figure 2 for several values of c. From this diagram we conclude that the isochore at 15moldm -3 (about 1.8 times the critical density) is very nearly a straight line, while at higher densities the isochores have a negative curvature--that is, (~Zp/~T2)v < 0. Martin (23) has pointed out that the dense fluid isochores of most gases show similar behaviour. E v e n though second derivatives calculated from equation (1) are not suitable for calculating the pressure dependence of the heat capacity, they can provide qualitative information about the shape of the dense-fluid isochores. Of particular interest are inflexion points in the isochores--that is, points at which (OZp/OT2)v = 0. It follows from equation (15) that these points correspond to maxima or minima in Cv isotherms. Inflexion points in the isochores represented by equation (1) have been located by solving the expression (O2p/OT2)v = 0 for V at fixed values of T. The results are shown 1

I

t

1

I

I

I

I

[

I

I]

10 &

18 mol dm -3 5

-t

16 tool dm-3q I

180

I

I

200

I

I

220

I

15 m o t i d m - 3

240

260

-o----..-o

c-

280

T/K FIGURE 2. Temperature dependence of ?'v = (~p/~T)vfor isochores of liquid xenon. For c > 15 tool dm -3 (about 1.8 times the critical density) the isochores have a negative curvature.

648

W. B. STREETT, L. S. SAGAN, AND L. A. K. STAVELEY 18

I

i

i

i

16

-~ 14

12

i 260

1

I 280

I

300

T/K FIGURE 3. Locus of isochore inflexion points (Cv minima) in the c, Tplane; --©--, satarated iquid; --[]--, inftexion points derived from equation (1). in figure 3. The inflexion points correspond to minima in Cv, and the behaviour shown is similar to that of other classical simple dense fluids. (z4- 26) The locus of the in flexion points intersects the saturated liquid line at T ~ 260K and c ~ 16tool d m - a ; hence isochores for which c > 16tool dm -3 (about twice the critical density) do not have inflexion points. Theeuwes and Bearman, (27) however, concluded from an analysis of their p, V, T results that inflexion points exist in xenon isochores for densities up to at least 2.6 times the critical density. If they are correct, the locus of Cv minima would not intersect the saturated liquid line as in figure 3, but would remain roughly parallel to it as the temperature decreases. Recent experimental measurements (z8) of the velocity of sound in liquid and dense fluid krypton have confirmed that a plot of inflexion points for the isochores of krypton is similar to figure 3. This evidence, together with that summarized by Diller, (26) strongly suggests that the low-temperature high-density inflexion points for xenon isochores reported by Theeuwes and Bearman are false. It should be stressed that the curvature of the isochores in the vicinity of these points is so small that errors in the measured densities of a few parts in 104 can not only obscure the true inflexion points, but also introduce false inflexion points into equations obtained by least-squares curve and surface fitting. In other words, inflexion points in the fitted equations may not be present in the true p, 1I, T surface of the fluid. D. FLUID PROPERTIES AT THE MELTING CURVE The available data for the melting pressure of xenon as a function of temperature have been critically reviewed by Babb, (29) who used the best data to evaluate parameters for the Simon melting equation. The equation recommended by Babb is p/atm = 2575.87[{(T/K)/161.364} 1.5892_ 1]. (17)

EQUATION OF STATE OF LIQUID XENON

649

This equation has been used, with equation (1), to calculate densities and mechanical coefficients for the saturated liquid along the melting curve, and these are recorded in table 14. The densities are in g o o d agreement with values obtained f r o m a large-scale graphical extrapolation o f the experimental isotherms, and errors resulting f r o m the extrapolation are believed to be less t h a n about 0.2 per cent. Errors in the mechaflical coefficients in table 13 are estimated to be about 3 per cent or less. The thermal TABLE 14. Amount of substance densities c and mechanical coefficients for saturated liquid xenon on the melting curve (atm = 101.325 kPa) T

p at-m

170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 289.00

222.51 488.61 763.56 1047.18 1339.28 1639.69 1948.26 2264.84 2589.29 2921.48 3261.28 3608.58 3927.47

c " mol dm- a 22.91 23.26 23.58 23.87 24.15 24.41 24.66 24.90 25.14 25.37 25.60 25.83 26.03

104xr atm- 1

10aap K- 1

~'v atm K- 1

7 atm K- ~

10act~ K- f

1.35 1.13 0.98 0.86 0.77 0.69 0.63 0.58 0.54 0.50 0.46 0.43 0.41

1.91 1.63 1.44 1.30 1.18 1.08 0.98 0.90 0.83 0.76 0.70 0.65 0.61

14.15 14.39 14.74 15.07 15.32 15.47 15.54 15.53 15.45 15.32 15.15 14.96 14.76

26.16 27.06 27.93 28.79 29.63 30.45 31.26 32.05 32.83 33.60 34.36 35.10 35.76

-1.62 -1.44 -1.29 -1.18 -1.10 -1.04 -1.00 -0.96 -0.93 -0.91 -0.89 -0.88 -0.86

expansivity ~ measured along the melting curve is negative because the effect o f increasing temperature is more than offset by increasing pressure, resulting in an increase in density with increasing temperature along this line. E. D E P E N D E N C E OF I N T E R N A L E N E R G Y ON DENSITY With regard to the dependence o f the energy U I o f liquid xenon on the mass density p, it is k n o w n that for simple liquids this dependence is remarkably nearly given by the equation: g I = U°(T)-ap. (18) As the energy Ug o f unit a m o u n t o f an ideal monatomic gas is 3RT/2, we have

U t = U , - Ug = {U°(T)-3RT/2}-ap.

(19)

U p to about 190K, plots o f U t against p for liquid xenon are linear within experimental error. A t higher temperatures, they develop a slight S-type curvature, but even at 270 K a plot o f U t against p is very nearly a straight line. The intercept o f this line at p = 0, namely { U°(T)-3RT/2}, decreases with rising temperature. A t 190 K, this intercept is such that U°(T) is about 3RT; U°(T) falls as the temperature rises, and at 270 K itis approximately 2RT. With respect to the dependence o f U t on p, and also o f U°(T) on temperature, the behaviour o f liquid xenon is very similar to that already reported for liquid krypton. (2) We believe that the physical interpretation o f the change

650

w . B . STREETT, L. S. SAGAN, AND L. A. K. STAVELEY

o f U°(T) with rising t e m p e r a t u r e is t h a t it reflects the g r a d u a l change o f the v i b r a t i o n o f the molecules in the liquid f r o m a n a p p r o x i m a t e l y s i m p l e - h a r m o n i c m o t i o n at low t e m p e r a t u r e to a m o r e a n h a r m o n i c m o t i o n , a n d eventually t o t r a n s l a t i o n a l movement. F i n a n c i a l s u p p o r t for this w o r k was p r o v i d e d b y the U.S. A r m y Research Office, D u r h a m , N o r t h Carolina. REFERENCES 1. Streett, W. B.; Staveley, L. A. K. J. Chem. Phys. 1969, 50, 2302. 2. Streett, W. B.; Staveley, L. A. K. J. Chem. Phys. 1971, 55, 2495. 3. Streett, W. B. J. Chem. Eng. Data 1971, 16, 289. 4. Dymond, J. H.; Smith, E. B. The Virial Coefficients of Gases. Clarendon Press: Oxford. 1969, p. 205. 5. Streett, W. B.; Staveley, L. A. K. Adv. Cryog. Eng. 1968, 13, 363. 6. Terry, M. J.; Lynch, J. T.; Bunclark, M.; Mansell, K. R.; Staveley, L. A. K. J. Chem. Thermodynamics 1969, 1, 413. 7. Mathias, E; Onnes, H. K.; Crommelin, C. A. Commun. Phys. Lab. Univ. Leiden 1912, 131a. 8. Mathias, E.; Crommelin, C. A.; Meihuizen, J. J. Physica 1937, 4, 1200. 9. Goldman, K.; Scrase, N. G. Physica 1969, 44, 555. 10. Strobridge, T. R. Nat. Bur. Stand. (U.S.) Tech. Note 123 1962. 11. Hust, J. G.; McCarty, R. D. Cyogenics 1970, 7, 200. 12. Theeuwes, F.; Bearman, R. J. J. Chem. Thermodynamics 1970, 2, 507. 13. Theeuwes, F.; Bearman, R. J. J. Chem. Thermodynamics 1970, 2, 501. 14. Michels, A.; Wassenaar, T. ; Louwerse, P. Physica 1954, 20, 99. 15. Clusius, K.; Riccoboni, M. Z. Phys. Chem. 1938, 38B, 81. 16. Michels, A.; Wassenaar, T. Physica 1950, 16, 253. 17. Bowman, D. H.; Aziz, R. A.; Lim, C. C. Can. J. Phys. 1969, 47, 267. 18. Brewer, J. Determination of Mixed Virial Coefficients. U.S. Air Force Office of Scientific Research, No. 67-2795, 1967. 19. Chueh, P. L.; Prausnitz, J. M. J. Am. Inst. Chem. Eng. 1967, 13, 898. 20. Chen, C. T. ; Present, R. D. J. Chem. Phys. 1972, 57, 757. 21. Aziz, R. A.; Bowman, D. H.; Lim, C. C. Can. J. Chem. 1967, 45, 2079. 22. Gladun, C.; Menzel, F. Cryogenics 1970, 10, 210. 23. Martin, J. J.; Hou, Y. C. J. Amer. Inst. Chem. Eng. 1955, 1,142. 24. Rowlinson, J. S. Liquids and Liquid Mixtures, 1st Edn. Butterworths: London. 1959, p. 98. 25. Verbeke, O.; Van Itterbeek, A. Equation of State of Liquefied Gases in Physics of High Pressure and the Condensed Phase, Van Itterbeek, A., Editor. North Holland Publ. Co. : Amsterdam. 1965, p. 148. 26. Diller, D. E. Cryogenics 1971, 11,186. 27. Theeuwes, F.; Bearman, R. J. J. Chem. Thermodynamics 1960, 2, 513. 28. Streett, W. B.; Ringermacher, H. I.; Butch, J. L. J. Chem. Phys. 1972, 57, 3829. 29. Babb, S. E. Rev. Mod. Phys. 1963, 35, 400.