Complete equation of state based on specific heat

Abstract

In thermodynamics, the complete equation of state (EOS) for closed system is a functional relation defined by two independent state variables, and all other thermodynamic relations can be deduced by it. For example, Helmholtz free energy F as a function of specific volume v and temperature T of the system is a complete EOS. Unfortunately, the concrete expressions of these complete EOSs are unavailable. Here we establish a practical form of the complete EOS based on the pressure function pT(v) and constant-volume specific heat function Cv(v，T) This complete EOS is mathematically equivalent to the Helmholtz free energy F. Here pT(v) is determined by the measurement and Cv(v，T) can be expressed by two parts. One part is the lattice contribution based on the Debye model and the other part is electronic contribution obtained from the free electron model. Using this complete EOS we calculate the isothermal equation for six metals from the Hugoniot data. Good agreement between the isothermal equation and the experimental data verifies the reliability of the complete EOS. Through this complete EOS we can derive the concrete expression of physical parameters, and these physical parameters including the volume expansion coefficient, the volume speed of sound, the adiabatic modulus, and W-J coefficient are calculated by using the experimental data of Cu. Analyzing their variation trends we can timely adjust parameter in the calculation of the EOS. This kind of complete EOS is useful in the field of high temperature and high pressure physics.