The Effective ``Gamma'' for Isentropic Expansions of Real Gases

In an isentropic expansion of a real gas, the relationship pvγ = C (γ, C constant) is not exact. A development is given for an accurate exponent ᾱ (the effective ``gamma''), related to the ratio of specific heats, which permits the use of the relationship p0v0ᾱ = p1v1ᾱ for an isentropic expansion between any two pressures. The exponent may be computed from the initial conditions of the gas, the expansion ratio, equation of state data, and data on the variation of specific heat with temperature.