A Rational Basis for the Thermodynamic Treatment of Real Gases and Mixtures of Real Gases

From the general laws of thermodynamics and two isothermal assumptions, one of which states that at constant temperature the energy of a pure gas approaches a function of the temperature in the following manner: U₁=f₁(T)+ζ₁p and the other that at constant temperature and composition the ratio of the equilibrium pressure of a gas in a mixture to the product of the mole fraction of the gas in the mixture multiplied by the total pressure of the mixture approaches unity in the following manner: pₑᵢpxᵢ=1+ξᵢp where ζ₁ and ξᵢ are bounded parameters, it has been shown that the following relations hold for real gases or mixtures of real gases at infinitely low pressures:(a). The ratio of the equilibrium pressure of a gas to the product of its mole fraction in the mixture multiplied by the total pressure of the mixture is unity.(b). The ratio of the equilibrium concentration of a gas to its concentration in the mixture is unity.(c). The ratio of the sum of the equilibrium pressures (or equilibrium concentrations) of the component gases to the total pressure (or concentration) of the gas mixture is unity.(d). The entropy, energy, heat content, thermodynamic potentials and heat capacities at constant volume and at constant pressure of a mixture of gases are equal respectively to the sums of the entropies, energies, heat contents, thermodynamic potentials and heat capacities of the component gases existing each by itself with the same value of its volume, temperature and chemical potential as in the mixture. The above statement holds when the component gases exist each by itself with the same value of its volume and temperature as in the gas mixture and with the ratio of its concentration to its concentration in the gas mixture equal to unity.(e). The energy, heat content and heat capacities of pure gases and of gas mixtures of constant composition are functions of the temperature.(f). The difference between the heat capacity at constant pressure and that at constant volume of a pure gas or of a gas mixture is equal to the product of the total number of moles present multiplied by the gas constant R.(g). The pressure-volume product for a pure gas or for a gas mixture is equal to the product of the total number of moles present multiplied by RT where R is a universal constant and T the Kelvin temperature.