The ones of these derived from the internal energy, enthalpy, Helmholtz function and Gibbs function are respectively (*) volume partial of temperature equals minus pressure partial of entropy, pressure partial of temperature equals entropy partial of volume, volume partial of entropy equals pressure partial of temperature and pressure partial of entropy equals minus temperature partial of volume.
For the class of functions to which these statements apply in n independent variables, there exist n squared minus n all over two generalized ones of these. The generalized form of these equations may be found by invoking Clairaut's theorem to equate mixed partial derivatives of a potential with respect to its natural variables. The ones of these derived from the internal energy, enthalpy, Helmholtz function and Gibbs function are respectively (*) volume partial of temperature equals minus pressure partial of entropy, pressure partial of temperature equals entropy partial of volume, volume partial of entropy equals pressure partial of temperature and pressure partial of entropy equals minus temperature partial of volume. For 10 points, name this set of four PDE's that give the relationships among different thermodynamic variables, named for a Scottish scientist known for his four laws of electromagnetism.
For the class of functions to which these statements apply in n independent variables, there exist n squared minus n all over two generalized ones of these.
the {Maxwell} relations