Helmholtz Free Energy from the CS Approximation

There are several forms similar to Eq. (275) which could be used to arrive at a Helmholtz free energy. The CS form, however, is presently the most widely used. In the following the internal contributions, vibrational electronic, etc., are not considered. The molar Helmholtz free energy. A, is related to the pressure of the fluid at constant temperature whether ideal or not by 

Integration of Eq. (278) yields the Helmholtz free energy of the ideal gas with the question of what the integration constant is. This, however, is known from quantum statistical thermodynamics, i.e. 

The second term of Eq. (275) may be integrated keeping in mind that the ideal gas is applicable as the volume approaches infinity and so the total CS Helmholtz free energy, is 

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