The Temperature Equation

Abstract

In this chapter we carry out the classical procedure of thermodynamics of irreversible process [1],[2], to obtain the equation of the temperature in electrohydrodynamics. First, we review the thermodynamics of dielectric fluids at thermodynamic equilibrium [3],[4]. The internal electric energy of polar fluids depends on temperature through the permittivity. Given that temperature and internal energy are intimately connected, we split the internal electrical energy for polar fluids into two terms. The term that depends on temperature is added to the term for the internal energy of the fluid in the absence of the electric field to form the total internal energy. The remainder term, which is of the form (1/2)ε _np E ², where ε _np is the permittivity at frequencies above the microwave region but below the short infra red region, is ascribed to the macroscopic electrical energy. The permittivity ε _np only depends on the ionic and electronic molecular polarizabilities, and therefore it is independent of temperature.