High-Temperature Equation of State

An equation of state is obtained in closed form for a gas composed of molecules with a Lennard-Jones (n, 6) potential. It is derived by expanding the partition function in powers of n−1 and expanding the attractive part of the potential in powers of T−1. The resulting equation is of the form P/ρkT=A+B/T+ClogT where A, B, and C can be simply expressed in terms of known hard-sphere quantities such as the compressibility factor and the radial distribution function as functions of density. The equation contains no adjustable parameters and reliably reproduces PVT data up to densities of 40 mole/liter and reduced temperatures as low as 3.