A New Concise Equation of State for Gases Incorporating Thermodynamic Laws, Entropy and Partition Function

Abstract

Thermodynamic functions and laws were developed over the years to “bridge” the gap between the equations of state and thermal properties of matter. Here the author has incorporated the thermodynamic properties into the equation of state thereby forming one simple composite equation. The heat capacity difference is introduced in place of the gas constant in her earlier concise equation of state for gases, PVf =RT based on free volume and molecular association/dissociation. This work provides a new and simple relation between the P,V,T properties, internal energy (E), enthalpy (H), Gibbs (G) and Helmholtz (A) free energies, heat energy (Q), entropy (S), partition function (f) and the thermodynamic laws. As a proper definition of “heat” is essential for the discussion of the second law, Q for a gas at the given P,V,T,S is defined here as TS = PVflnW, where W is the thermodynamic probability related to f. The latter is expressed here as the ratio Vf/VdB where VdB is the volume corresponding to the de Broglie wave length. Also, for the first time experimental heat capacities at various P, V and T are correlated with the extent of molecular association. The available data for nitrogen have been used to demonstrate the validity of the new equation of state.