Observations About the Differential Relationships

The relationships summarized in Table 3.1 can be used to solve many problems, as we will illustrate. But before we do so. it is useful to make three general observations about Table 3.1. First, we note that the relationships for U and A are simpler when V and T are chosen as the independent variables. Whenever possible, we will choose V and T as the independent variables for calculating AU and A A. For H and G. the relationships are simpler when p and T are the independent variables, and these are the ones we will generally choose to 

The second observation is that the equations we have derived for extensive variables Z can be applied to the difference AZ. For example  

The third observation is that the equations apply as well when the extensive properties are replaced by the corresponding intensive molar properties.0 For 

The substitutions can be made because the extensive thermodynamic variables in the equations are homogeneous of degree one.d Thus, dividing the equation by n converts the extensive variable to the corresponding molar intensive variable. For example, to prove that equation (3.48) follows from equation 

Since n is constant in the equations we have derived, we can write equation (3.49) as 

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