Lattice models in teaching thermodynamics: Merging the configurational and translational entropies

The importance of connecting bulk thermodynamic properties with their microscopic origin is widely acknowledged by the teaching community. Due to their insightful simplicity, lattice models are therefore regarded by many as a useful tool for teaching statistical thermodynamics within a molecular context and thereby also classical thermodynamics. By invoking simple statistics, this microscopic approach produces well-known equations of state, such as the ideal gas law and the van der Waals equation of state. In this work, we strengthen the reach of lattice models and show that if the quantum volume (i.e., the cube of the thermal wavelength) is adopted as the volume of a lattice point, the configurational and translational entropies are merged. Furthermore, refined equations of state are obtained with little effort at a level suitable for undergraduate college students.