The Entropy and Thermodynamic Potentials of Real Gases and Mixtures of Real Gases and a Mass Action Law for Chemical Reaction Between Real Gases: III. Relations for Pure Gases, and the Equilibrium Pressure of a Gas in a Mixture

Thermodynamic relations.—Using the assumption that the pressure of a real gas approaches $\frac{\mathrm{nRT}}{V}$ as the volume approaches infinity, there are developed general thermodynamic equations for the energy, heat content, entropy, thermodynamic potentials $F_{V,T}$ and $F_{p,T}$, chemical potential and fugacity of a pure gas in terms of the appropriate independent variables $V$, $T$, $n$, or $p$, $T$, $n$. Each expression contains a definite integral which can be evaluated by use of an equation of state. The integrations are carried out by means of a new equation of state and all the thermodynamic quantities are expressed in terms of the variable $V$, $T$, $n$ and the constants of the equation of the state.