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Maxwell Relations Maxwell relations are links between the independent variables. We require focus on the independent variables and the directions of the arrows only. From figure 32.1 we can write

Since both the arrow are in the same direction (upward), there is no change in sign. For the next Maxwell relation, we require. To rotate the Mnemonic diagram by 900 (Figure)

For next relation, we require to rotate it by 900 again (Figure)

Similarly for the other relation we require to rotate another 900 (Figure 32.4)

And the relation is

Equations (32.30) - (32.33) can be re-written as

All four relations can be summarized as or

Other measurable quantities, such as Coefficient of volume expansion,

Compressibility

Specific heat at constant pressure

Specific heat at constant volume

Therfore

Examples: Thermodynamics Relations involving Entropy The entropy of a substance can be expressed in terms of independent variable (T,P) or (T,v) and these relations are quite useful in estimating the entropy change when the system changes its state from to (a) Entropy as a function of T and P

or

Maxwell relation and

or

(b) Entropy a as function of T and v

using

or