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In thermodynamics, the fugacity is a state function of any isothermal system. The fugacity, which has units of pressure, represents the tendancy of a fluid to escape or expand isothermally, and for gases at low pressures where the ideal gas law holds, fugacity is equal to pressure. The ratio <math> \phi = f/P \,<math> between fugacity <math>f\,<math> and pressure <math>P\,<math> is called the fugacity coefficient; therefore, <math> \phi = 1 \,<math> for an ideal gas.
The fugacity <math> f\,<math> is defined at fixed temperature <math> T\,<math> by the following differential relation:
- <math> d \ln f = {dG \over RT} = {{V dP} \over RT} \,<math>
where <math>G\,<math> is the Gibbs free energy, <math>R\,<math> is the molar gas constant, and <math>V\,<math> is the fluid's volume. Thus, for any two isothermal physical states, represented by subscripts 1 and 2, the ratio of the two fugacities is as follows:
- <math> 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>
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