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

Area of Science:

• Thermodynamics
• Solid-state physics
• Materials science

Background:

• Existing models for heat flow in solids often neglect the role of rigidity.
• A comprehensive thermodynamic description requires accounting for all significant energy reservoirs.

Purpose of the Study:

• To develop and validate a new macroscopic, thermodynamic model for steady-state heat flow in solids.
• To incorporate the energy reservoir of rigidity into the thermodynamic description of solids.

Main Methods:

• The model is based on mass and energy conservation, Fourier's law, Stefan-Boltzmann's law, and the concept of rigidity.
• It considers the ideal case of a perfectly frictionless elastic solid (PFES) to analyze rigidity without dissipation.
• Analysis focuses on steady-state, adiabatic, and isothermal conditions.

Main Results:

• The model successfully describes insulating, semiconducting, and metallic solids, with best agreement for isotropic materials.
• Adiabatic and isothermal bulk moduli (B) are found to be equal.
• Formulas for the two specific heats in solids were derived, relating them to bulk modulus, Young's modulus (Ξ), and cation coordination (n).

Conclusions:

• The validated model provides a more complete thermodynamic description of solids by including rigidity.
• The findings simplify the understanding of thermal expansion and specific heats in solids.
• The model's implications extend to various solid materials, particularly isotropic ones.