The Pressure-Temperature Relation for High Pressure Gases with Compressibility Factor Z1

Using equation of state and other fundamental formulae in canonical ensemble, we derive a partial differential equation satisfied by high-pressure gases. With this equation it is possible to obtain a new nonlinear differential equation, which gives the pressure-temperature relation for a gas with high pressure in the vicinity of (T0, p0). Following this way, we can avoid computing configuration integrals and improve the previous approach given in Ref.1. The mean error of our results is found to be less than 0.9% for |T|15 K in comparison with those calculated with Redlich-Kwong equation.