Maxwell Relations are commonly known as a set of four partial differential equations between four thermodynamic quantities or potentials: pressure (P), volume (V), temperature (T), and entropy (S). So for example the expression (∂T/∂V) |_S  means the partial derivative of T with respect to V while keeping S constant.

• • (∂T/∂V) |_S = -(∂P/∂S) |_V
  • (∂P/∂T) |_V = (∂S/∂V) |_T
  • -(∂S/∂P) |_T = (∂V/∂T) |_P
  • (∂V/∂S) |_P = (∂T/∂P) |_S

In my diagram above, the expressions that are equal are on either side of the common leg of adjacent isosceles right triangles.

Further Reading:

https://en.wikipedia.org/wiki/Maxwell_relations

Maxwell’s Relations (Part 1)

Maxwell’s Relations (Part 2)

Maxwell’s Relations (Part 3)

https://en.wikipedia.org/wiki/Thermodynamic_potential

Thermodynamics and the Four Thermodynamic Potentials

[*12.194, *12.195]

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