perturbative treatment of statistical mechanics. or alternatively where A, B, C, A′, B′, and C′ are temperature dependent constants. Peng–Robinson model Peng–Robinson equation of state (named after D.-Y. Peng and D. B. Robinson) has the interesting property being useful in modeling some liquids as well as real gases. Wohl model The Wohl equation (named after A. Wohl) is formulated in terms of critical values, making it useful when real gas constants are not available, but it cannot be used for high densities, as for example the critical isotherm shows a drastic decrease of pressure when the volume is contracted beyond the critical volume. or: or, alternatively: where with , where are (respectively) the molar volume, the pressure and the temperature at the critical point. And with the reduced properties one can write the first equation in the reduced form: Beattie–Bridgeman model This equation is based on five experimentally determined constants. It is expressed as where This equation is known to be reasonably accurate for densities up to about 0.8 ρcr, where ρcr is the density of the substance at its critical point. The constants appearing in the above equation are available in the following table when p is in kPa, v is in , T is in K and R = 8.314 Benedict–Webb–Rubin model The BWR equation, sometimes referred to as the BWRS equation, where d is the molar density and where a, b, c, A, B, C, α, and γ are empirical constants. Note that the γ constant is a derivative of constant α and therefore almost identical to 1. Thermodynamic expansion work The expansion work of the real gas is different than that of the ideal gas by the quantity . See also Compressibility factor Equation of state Ideal gas law: Boyle's law and Gay-Lussac's law References Further reading External links http://www.ccl.net/cca/documents/dyoung/topics-orig/eq_state.html Gases