The Quantum-Volume and Bragg-Williams Equations of State

The quantum-volume (qv) and Bragg-Williams equations of state, as derived from a lattice gas model, are exploited. The qv equation of state includes a temperature-dependent excluded volume related to the thermal wavelength included in the translational contribution to the molecular partition function, but apart from this contribution intermolecular interactions are not included. The qv equation of state has the correct limiting behavior both in the limit of an ideal gas and in the packing-density limit. It also includes a nonclassical contribution to the internal energy and thereby a many-particle contribution to the kinetic energy, and it supports the view that it is both the position as well as the momentum of a system of particles that are distributed over the volume to maximize the multiplicity of the system. The qv equation of state is extended with intermolecular interactions through the Bragg-Williams mean-field approach, including also a hard-core contribution. For a one-component lattice gas, analytical expressions are presented for the pressure and the critical point as well as for the internal energy, the isochoric heat capacity, and the chemical potential, and results are presented for some simple systems. Given its relative simplicity, essentially on a textbook level, the model shows promising results, in particular for the temperature dependence of the isochoric heat capacity that shows a maximum close to the critical temperature. The presented model is supposed to serve as a foundation for further model extensions as well as for the development of interpretable analytical models in molecular thermodynamics for more complex systems and processes.