Fugacity

In thermodynamics, the fugacity is a state function of any isothermal system. The fugacity, which has units of pressure, represents the tendency of a fluid to escape or expand isothermally. For gases at low pressures where the ideal gas law holds, fugacity is equal to pressure. The ratio $\phi =f/P\,$ between fugacity $f\,$ and pressure $P\,$ is called the fugacity coefficient; therefore, $\phi =1\,$ for an ideal gas.

The fugacity $f\,$ is defined at fixed temperature $T\,$ by the following differential relation:

$d\ln f={dG \over RT}={{VdP} \over RT}\,$

where $G\,$ is the Gibbs free energy, $R\,$ is the molar gas constant, and $V\,$ is the fluid's volume. For any two isothermal physical states, represented by subscripts 1 and 2, the ratio of the two fugacities is as follows:

$f_{2}/f_{1}=exp\left({1 \over RT}\int _{G_{1}}^{G_{2}}dG\right)=exp\left({1 \over RT}\int _{P_{1}}^{P_{2}}V\,dP\right)\,$