Thermodynamic Description of Elastic Solids

Part 1

Inconsistencies in the current thermodynamic description of elastic solids

Part 2

Limits on the thermo-elastic coupling

Part 3

The work function

Part 4

Heat capacity

Part 5

Internal energy and other state funcitons

Contemporary thermodynamics assumes that with the introduction of the volume coefficient of expansion and the bulk modulus the thermodynamic description of the solid* phase is completed. It is also assumed that the rest of the thermodynamic equations describing gas phase can be used for solids without modification. The author/s disagrees with these assumptions and suggests that the thermodynamic description of solids is incomplete and additional modifications are necessary.

In part one it is demonstrated that using the conventional thermodynamic equations of solids leads to erroneous results.

In the second part the complete thermo-elastic coupling of solids is challenged. Using rigorous mathematics it is shown that neither the pressure not the temperature correlates to the volume but rather to the compressed and expanded volume respectively. These volume changes are not interchangeable and have to be treated separately (Fig. 1). It is concluded that thermoelastic coupling in solid phase exist only at constant volume and that the relationship between the temperature and pressure is irreversible.

In part three by making distinction between the different volume changes the proper work functions for each of the thermodynamic conditions have been derived. It is shown that a self consistent thermodynamic description of a system requires a homogeneous model thus both the system and the surrounding have the same phase.

In part four the description of the solid phase heat capacities is given. The values of the constant pressure and volume heat capacities are differ by the mechanical work done on the surrounding at one degree of temperature increase. Modifying the work functions for elastic solids resulting that the heat capacities has to be adjusted to accommodate the modifications of the work function. The characteristic behavior of the molar work heat capacities is shown as function of pressure and temperature in Fig. 2.

In the last part the internal energy and other state functions are discussed for solids.

* The word of solid in this text refers to homogeneous, isotropic, non-viscous solids which have linear elasticity. It is assumed in the investigations that the stresses are isotropic; therefore, the principal stresses can be identified as the pressure.

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