James A. Beattie

The Compressibility of Gaseous Krypton. II. The Virial Coefficients and Potential Parameters of Krypton

The second and third virial coefficients of a sample of krypton containing 0.90 mole percent xenon have been determined from our compressibility measurements over the temperature range 0° to 300°C and to a density of 10 mole per liter. They are listed in Table II. The parameters of the Lennard‐Jones (6, 12) potential for krypton are μ=2.044×10−58 erg‐cm6, λ=0.438×10−102 erg‐cm12, e=238.4×10−16 erg, b0=58.40 cm3 per mole, θ=172.7°K, σ=3.591×10−8 cm, r0=4.030×10−8 cm. The representation of the second virial coefficient is quite satisfactory. The third virial coefficients diverge more than those of xenon from the theoretical values for a Lennard‐Jones (6, 12) potential as tabulated by Bird, Spotz, and Hirschfelder. The observed second virial coefficients agree moderately well with the tabulated values of Buckingham and Corner for an inverse sixth and inverse eighth power attractive and an exponential repulsive potential when the tables are used in conjunction with the values of the arguments derived by Kane ...

The Compressibility of Krypton. I. An Equation of State for Krypton and the Weight of a Liter of Krypton

The compressibility of krypton containing 0.90 mole percent xenon has been measured from 0° to 300°C and over the density range 1 to 10 mole per liter. The constants of the Beattie‐Bridgeman equation of state for the sample and for pure krypton were determined. The constants for pure krypton are R=0.08206, A0=2.4230, a=0.02865, B0=0.05261, b=0, c=14.89×104 in units of standard atmos, liter per mole, and °K(T°K=t°C+273.13). The equation for the sample studied reproduced the observed pressures with an average deviation of 0.16 percent. The weight of one liter of Kr at a pressure of one standard atmosphere is calculated from the molecular weight (83.7) and the above constants to be 3.745 g per liter at 0°C and 3.474 g per liter at 70°F.

The Compressibility of Gaseous Xenon. I. An Equation of State for Xenon and the Weight of a Liter of Xenon

The compressibility of xenon containing 0.14 mole percent of krypton has been measured from 16.65° (the critical temperature) to 300°C and over the density range 1 to 10 mole per liter. The constants of the Beattie‐Bridgeman equation of state for the sample used and for pure xenon have been determined from these measurements. The constants for pure xenon are R=0.08206, A0=4.6715, a=0.03311, B0=0.07503, b=0, c=30.02×104 in units of normal atmos, liter per mole, and °K (T°K=t°C+273.13). The weight of one liter of Xe at a pressure of one standard atmosphere is calculated from its molecular weight (131.3) and the above parameters to be 5.897 g per liter at 0°C and 5.467 g per liter at 70°F.

The Second Virial Coefficient for Gas Mixtures

The second virial coefficients B for methane, normal butane, and three mixtures of these gases were evaluated from the experimental data, and the interaction term B12 computed for methane‐n‐butane from 150° to 300°C. The results were used to study the methods of combination of constants in an equation of state. Computation of B12 from a Lennard‐Jones expression similar to that used for a pure gas with σ and θ evaluated as σ12=½(σ11+σ22) and θ12=θ11½θ22½ where the subscripts 1 and 2 refer to the pure components gave exceptionally good results. This suggested a new method of combination of constants in the equation of state which led to the best results of any method so far used.

The Vapor Pressure, Orthobaric Liquid Density, and Critical Constants of Isobutane

The vapor pressures and orthobaric liquid densities of isobutane (propane−2‐methyl) were measured from 30° to 125°C. The equation log10p (normal atmos.)=4.31269–1126.71/T  (T=t∘C (Int.)+273.13) gives a fair representation of the vapor pressures.The critical constants of isobutane are determined by the compressibility method. They are: tc=134.98±0.05°C (Int.), pc=36.00±0.05 normal atmos., vc=0.263 liters per mole (4.53 ml per g), dc=3.80 moles per liter (0.221 g per ml). The uncertainty in the critical volume and density is 2 percent.

The Compressibilities of Gaseous Mixtures of Methane and Normal Butane. The Equation of State for Gas Mixtures

The compressibilities of three gaseous mixtures of methane and normal butane have been measured from 100° to 300°C and from 1.25 to 10 mole/liter (maximum pressure 350 atmos.). The data on these three systems and the two pure hydrocarbons are used to study several methods of combination of constants in the Beattie‐Bridgeman equation of state extended to apply to gas mixtures. The best results were obtained with square‐root combination for A0 and for c and Lorentz combination for B0; but square root combination for A0 and linear combination for B0 and for c are a fair compromise between accuracy of representation of the data on mixtures and simplicity of expression.

The Vapor Pressure and Critical Constants of Neopentane

The vapor pressure of neopentane has been measured from 50° to the critical point. The equation, log10p(atmos)=3.901633−1136.462T+4.99118×10−4T  (T=t∘C+273.16), gives a fair representation of the observations.A study of the compressibility of neopentane in the critical region gives for the critical temperature, pressure, volume, and density the values: tc = 160.60°±0.05°C (Int.), pc = 31.57±0.03 normal atmospheres, Vc = 0.303 liter per mole (4.20 ml per g), dc = 3.30 mole/liter (0.238 g per ml). The uncertainty in the critical volume and density is 1 percent.

The Critical Constants of Propane

The critical constants of propane (C3H8) are: tc = 96.81±0.01°C, pc = 42.01±0.02 normal atmospheres, vc = 0.195 liter per mole (4.43 cc per gram), dc = 5.13 moles per liter (0.226 gram per cc). The uncertainty in the critical volume and density is 1 percent.

Determination of the Lennard‐Jones Parameters from Second Virial Coefficients Tabulation of the Second Virial Coefficient

Values of B/(2πNσ3/3) to four decimal places as a function of θ/T are computed from θ/T=0.20 to 1.00 for a Lennard‐Jones (6, 12) potential. The equation B/(2πNσ3/3) = (θ/T)¼[1.064–3.602(θ/T)] computes the tabulated values fairly well. Thus σ and θ can be determined from experimental B values by plotting BT¼ against 1/T and finding the slope and intercept of the best straight line through the points. For methane and n‐butane this method gave parameters that computed B values agreeing with observed values within the experimental uncertainty.

Experimental Study of the Absolute Temperature Scale. XI. Deviation of the International Practical from the Kelvin Temperature Scale in the Range 0° to 444.6°C

The deviations of the International Practical Temperature Scale from the thermodynamic Celsius scale were determined at eleven temperatures in the range 0° to 444.6°C by a comparison of the indications of four platinum resistance thermometers with those of two constant‐volume nitrogen‐gas thermometers in a stirred‐liquid thermostat. In each gas thermometer several different ice‐point pressures were used to permit corrections to be made for the imperfection of the thermometric fluid. The arithmetic means of the observed differences between temperatures on the thermodynamic Celsius scale as it was defined in 1954 and those on the IPTS at the eleven temperatures, each weighted in accordance with the number of observations, are represented by the equation t(therm.)−t(Int.)=[−0.0060+(0.01t−1)(0.04106–7.363×10−5t)](0.01t), where t in the right‐hand member is on the IPTS. The standard deviation of a determination of Δt of unit weight from the equation is 18×10−4 deg.