The internal energy of the electromagnetic field is distinct from that of the matter exposed to the field. The choice of field variable is determined by physical considerations concerning the electric, displacement, magnetic and induction fields. Legendre transform are worked out in order to define electric and magnetic enthalpies and free enthalpies. Spatial derivatives of the enthalpies yield the force densities that dielectrics and magnets experience in inhomogeneous electric and magnetic induction fields. Either internal energy or electric enthalpy must be used to analyse the force on a dielectric inserted in a capacitor, depending on the constraint (constant charge or constant field). Likewise, internal energy or magnetic enthalpy must be considered to analyse the force on a paramagnetic material inserted in a coil or in between the poles of a magnet. A complete analysis of adiabatic demagnetisation offers an example of application of Mayer’s relation to specific heat at constant induction field or constant magnetisation. The effect is predicted for the case of a paramagnetic material with a magnetisation that obeys Curie’s law.