# Entropy Changes

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: