On thermodynamic potentials in linear thermoelasticity

The four thermodynamic potentials, the internal energy u 1⁄4 uð ij; sÞ, the Helmholtz free energy f 1⁄4 f ð ij; T Þ, the Gibbs energy g 1⁄4 gðrij; T Þ and the enthalpy h 1⁄4 hðrij; sÞ are derived, independently of each other, by using the Duhamel–Neumann extension of Hooke’s law and an assumed linear dependence of the specific heat on temperature. A systematic procedure is then presented to express all thermodynamic potentials in terms of four possible pairs of independent state variables. This procedure circumvents a tedious transition from one potential to another, based on the formal change of variables, and inversions of the stress–strain and entropy–temperature relations. The general results are applied to uniaxial loading paths under isothermal, adiabatic, constant stress, and constant strain conditions. An interplay of adiabatic and isothermal elastic constants in the expressions for exchanged heat along certain thermodynamic paths is indicated. 2004 Elsevier Ltd. All rights reserved.