Maxwell relation obtained from Helmholtz function is 

1
\({\left( {\frac{{\partial T}}{{\partial p}}} \right)_v} = {\left( {\frac{{\partial v}}{{\partial s}}} \right)_p}\;\)
2
\({\left( {\frac{{\partial p}}{{\partial T}}} \right)_v} = {\left( {\frac{{\partial s}}{{\partial v}}} \right)_T}\;\)
3
\({\left( {\frac{{\partial T}}{{\partial v}}} \right)_s} = {\left( {\frac{{\partial p}}{{\partial s}}} \right)_v}\)
4
\({\left( {\frac{{\partial v}}{{\partial T}}} \right)_p} = {\left( {\frac{{\partial s}}{{\partial p}}} \right)_T}\)
5
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