Thermodynamics of a dia- or paramagnetic substance

The same method used in Section 14.12 can be applied here to obtain a differential expression for the energy of the substance. In order to do so we subtract from the magnetic induction of the total system, B, the magnetic induction of the empty solenoid when the current is the same as that of the filled solenoid. Thus, 

We define M = Ksm, where M is the total magnetic moment. Then Equation (14.97) becomes 

We can obtain expressions for the differentials of the enthalpy and the Gibbs and Helmholtz energies from the usual definitions. In such expressions M is an independent variable. Because it is more convenient to use H as an independent variable, the new functions (H — /j0HM), (A — /i0HM), and (G — /i0HM) are used. The differential expressions for these functions are 

the condition of exactness may be applied to such equations. Particularly, from Equation (14.102) we have 

An expression of particular interest is obtained from Equation (14.100). We have 

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