# 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 ${\displaystyle \phi =f/P\,}$ between fugacity ${\displaystyle f\,}$ and pressure ${\displaystyle P\,}$ is called the fugacity coefficient; therefore, ${\displaystyle \phi =1\,}$ for an ideal gas.

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

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

where ${\displaystyle G\,}$ is the Gibbs free energy, ${\displaystyle R\,}$ is the molar gas constant, and ${\displaystyle V\,}$ 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:

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