Departure Functions with Temperature, Molar Volume and Composition as the Independent Variables

1 Departure Functions with Temperature, Molar Volume and Composition as the Independent Variables 

The following equality can be derived for the departure function of a general thermodynamic M T, V, ri)  

Applying conventional thermodynamic manipulations on eq 2.46, the following relations can be obtained  

If the reference volume F, is replaced by the actual volume V of the system, then the corresponding residual functions are recovered (and are listed in Table 2.3). The thermodynamic properties for the reference state are defined by the following relations  

From eqs 2.52 through 2.56, the mixture properties for ideal gases are obtained as follows  

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