The phase boundary between the superconducting and normal phases of a metal in the $H_e-T$ plane ( $H_e=$ magnitude of applied external field) is given by Fig. 1.43.
The relevant thermodynamic parameters are $T, p$, and $H_\epsilon$. Phase equilibrium requires the generalized Gibbs potential $G$ (including magnetic paramters) to be equal on either side of the curve. Consider state $A$ in the normal phase and $A^{\prime}$ in the superconducting phase; each lies on the phase boundary curve and has the same $T, p$ and $H_e$ but different entropies and magnetizations. Consider two other states $B$ and $B^{\prime}$ arbitrarily close to $A$ and $A^{\prime}$; as indicated by $p_A=p_B$.
(a) Use this information to derive a Clapeyron-Clausius relation (that is, a relation between the latent heat of transition and the slope $d H_e / d T$ of the curve). What is the latent heat at either end of the curve? (For a long rod-shaped superconducting sample with volume $V$ oriented parallel to the field, the induced magnetic moment is given by $M_H^{\prime}=-V H_e / 4 \pi$; in the normal state, set $M_H=0$.)
(b) What is the difference in specific heats at constant field and pressure ( $C_{p, H_e}$ ) for the two phases? What is the discontinuity in $C_{p, H_e}$ at $H_e=0, T=T_c$ ? At $T=0, H_e=H_c$ ?