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Two general relations for entropy change will be developed here. Both are expressed by using the specific heats. Which equation should we choose largely depends on the data available.

Relation 1:

Here we choose the entropy to be a function of temperature T and pressure p. That means this function can be stated as s = f(T,p).

We know that temperature and pressure are independent variables, therefore the total differential of specific entropy (entropy per unit mass): The first partial term on the r.h.s is replaced by using the Maxwell Relation:

The second partial term on the r.h.s is substituted by using the definition of the constant-pressure specific heat:

Then we obtain the total differential of specific entropy:

Relation 2:

Now we choose the entropy to be a function of temperature T and specific volume ν. That means this function can be stated as s = f(T, ν).

We know that temperature and specific volume are independent variables, therefore we also write down the total differential of specific entropy (entropy per unit mass):

Similarly the first partial term on the r.h.s is replaced by using the corresponding Maxwell Relation:

The second partial term on the r.h.s is substituted by using the definition of the constant-volume specific heat:

Then in this time we get the second expression of the total differential of specific entropy: