The Entropy and Thermodynamic Potentials of Real Gases and Mixtures of Real Gases and a Mass Action Law for Chemical Reaction Between Real Gases: II. Integrated Equations

The general thermodynamic equations derived in the first paper are integrated by means of a new equation of state for gas mixtures. Thus the energy, heat content, entropy and thermodynamic potentials $F_{V,T}$ and $F_{p,T}$ of a mixture of real gases, and the chemical potential and fugacity of a gas in a mixture are expressed as integrated functions of $V, T, n_1, n_2, \cdots$, and the constants of the equation of state of the pure gases composing the mixture. The expression for the thermodynamic potential $F_{V,T}$ is a fundamental equation in the Gibbs sense. A mass action law for reactions between real gases is given, the "mass action constant" $K_p$ being expressed in terms of the variables $V, T, x_1, x_2, \cdots$, ${\nu }_1, {\nu }_2, \cdots$, and the equation of state constants of the pure gases composing the equilibrium mixture. The determination of the values of the various integration constants are discussed for the following cases: (a) non-isothermal and (b) isothermal variations in the state of a system composed of gases which react chemically, (c) non-isothermal and (d) isothermal variations in the state of a system composed of nonreacting gases.