Thermodynamic Relationships for Perfectly Elastic Solids Undergoing Steady-State Heat Flow.

Available data on insulating, semiconducting, and metallic solids verify our new model that incorporates steady-state heat flow into a macroscopic, thermodynamic description of solids, with agreement being best for isotropic examples. Our model is based on: (1) mass and energy conservation; (2) Fourier's law; (3) Stefan-Boltzmann's law; and (4) rigidity, which is a large, yet heretofore neglected, energy reservoir with no counterpart in gases. To account for rigidity while neglecting dissipation, we consider the ideal, limiting case of a perfectly frictionless elastic solid (PFES) which does not generate heat from stress. Its equation-of-state is independent of the energetics, as in the historic model. We show that pressure-volume work () in a PFES arises from internal interatomic forces, which are linked to Young's modulus (Ξ) and a constant () accounting for cation coordination. Steady-state conditions are adiabatic since heat content () is constant. Because average temperature is also constant and the thermal gradient is fixed in space, conditions are simultaneously isothermal: Under these dual restrictions, thermal transport properties do not enter into our analysis. We find that adiabatic and isothermal bulk moduli () are equal. Moreover, / depends on temperature only. Distinguishing deformation from volume changes elucidates how solids thermally expand. These findings lead to simple descriptions of the two specific heats in solids: ∂ln()/∂ = -1/; = Ξ times thermal expansivity divided by density; = cΞ/. Implications of our validated formulae are briefly covered.