Differential equations of thermodynamic properties, u, h, f and g can be given as function of p, T, v, s as below:

Above equations can be used for defining the functions u, h, f, g based upon analogy with,

From above four equations for properties to be exact differentials, we can write functions;

u = u(s, v)

h = h(s, p)

f = f(v, T)

g = g(p, T)

For differential of function ‘u’ to be exact;

Above four conditions for exact differentials of thermodynamic properties result into “Maxwell relations”.

Thus, “Maxwell relations” are :

Maxwell relations have large significance as these relations help in estimating the changes in entropy, internal energy and enthalpy by knowing p, v and T.