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 [math]\displaystyle{ \phi = f/P \, }[/math] between fugacity [math]\displaystyle{ f\, }[/math] and pressure [math]\displaystyle{ P\, }[/math] is called the fugacity coefficient; therefore, [math]\displaystyle{ \phi = 1 \, }[/math] for an ideal gas.
The fugacity [math]\displaystyle{ f\, }[/math] is defined at fixed temperature [math]\displaystyle{ T\, }[/math] by the following differential relation:
- [math]\displaystyle{ d \ln f = {dG \over RT} = {{V dP} \over RT} \, }[/math]
where [math]\displaystyle{ G\, }[/math] is the Gibbs free energy, [math]\displaystyle{ R\, }[/math] is the molar gas constant, and [math]\displaystyle{ V\, }[/math] 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:
- [math]\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) \, }[/math]