An equation of state of gases at high temperatures and densities

An equation of state is obtained in closed form for a gas composed of molecules with Lennard-Jones (n,1/2n) potentials. It is useful at temperatures above about 12 (ε/k), where -ε is the minimum energy of interaction and at all densities at which the equilibrium state is a fluid. It is derived by summing over all the cluster integrals of the virial expansion that occur in the approximation for the pair distribution function proposed by Percus and Yevick. Each cluster integral is represented correctly to terms of the order of n -1.The equation agrees well with machine calculations of the pressure of dense gases for n = ∞ and n = 12, with static measurements of the compression of gases at high reduced temperatures, and with some preliminary measurements of the density of argon compressed by shockwaves to pressures in the range 100-200 kb.