• The equations that relate the partial derivatives of properties P, v, T, and s of a simple compressible system to each other are called the Maxwell relations.

• They are obtained from the four Gibbs equations by exploiting the exactness of the differentials of thermodynamic properties.

• The Maxwell relations are as follows:

$$(\frac{dT}{dv})_s = -(\frac{∂P}{∂s})_v$$ $$(\frac{dT}{dP})_s = (\frac{∂v}{∂s})_P$$ $$(\frac{∂s}{∂v})_T = (\frac{∂P}{∂T})_v$$ $$(\frac{∂s}{∂P})_T = -(\frac{∂v}{∂T})_P$$

• They are extremely valuable in thermodynamics because they provide a means of determining the change in entropy, which cannot be measured directly, by simply measuring the changes in properties P, v, and T.