Deriving linear isotherms for solids

In this paper, we have derived two equations of state, one for the metallic and ionic solids and the other for the remaining solids on the basis of the concept of the average effective pair potential (AEPP). According to the former EOS, (Z−1)υ2 is linear with respect to 1/ρ, where Z is the compressibility factor and υ = 1/ρ is the molar volume for each isotherm. On the basis of the latter EOS, (Z−1)υ2 is a linear function in terms of ρ2 for each isotherm. As these EOSs suggest, the temperature dependencies of the internal energy is separable from its density dependencies. Hence, the heat capacity of a solid is independent of its density, interaction potential parameters and non-ideal thermal pressure. However, unlike the heat capacity, the isothermal compressibility and isobaric thermal expansivity both depend on all of them. The linear parameters of the EOSs are related to the average interaction coefficients at zero temperature and also vibrational energy. Since the temperature dependencies of the parameters of both equations are simple, they may, successfully, be applied to the study of the pVT behavior of solids at high temperatures. Using only two parameters which are physically interpretable as well as being able to predict at least two regularities in solids are the merits of the new equations of state. In short, these EOSs can open a new window to investigate the EOSs in solids just like the LIR EOS in fluids.