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Enthalpy Change of Transition

The heat absorbed or released during a phase transition at a constant pressure, representing the energy difference between the phases.
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The statement of the theorem

Let S\mathcal{S} be a thermodynamic system undergoing a phase transition from an initial phase α\alpha to a final phase β\beta at constant pressure PP. Define the enthalpy HH as the thermodynamic potential H=U+PVH = U + PV, where UU is the internal energy. The enthalpy change of transition, ΔHα→β\Delta H_{\alpha \to \beta}, is defined by the path integral along the equilibrium coexistence curve Cα→β\mathcal{C}_{\alpha \to \beta} in the (T,P)(T, P) plane:\n\nΔHα→β=∫αβdH=∫T1T2Cp,α→β(dTT)⋅P⋅dTTor, more simply, using the definition of heat capacity at constant pressure:\Delta H_{\alpha \to \beta} = \int_{\alpha}^{\beta} dH = \int_{T_1}^{T_2} C_{p, \alpha \to \beta} \left( \frac{dT}{T} \right) \cdot P \cdot \frac{dT}{T} \quad \text{or, more simply, using the definition of heat capacity at constant pressure:} \n\nΔHα→β=∫TinitialTfinalCp(T,P)dTT⋅Pwhere Cp(T,P) is the specific heat capacity at constant pressure, and the integral is taken over the temperature range of the transition.\Delta H_{\alpha \to \beta} = \int_{T_{initial}}^{T_{final}} C_{p}(T, P) \frac{dT}{T} \cdot P \quad \text{where } C_{p}(T, P) \text{ is the specific heat capacity at constant pressure, and the integral is taken over the temperature range of the transition.} \n\nAlternatively, using the Clausius-Clapeyron relation for the coexistence curve P(T)P(T): \ndPdT=ΔSΔV=ΔHTΔV\frac{dP}{dT} = \frac{\Delta S}{\Delta V} = \frac{\Delta H}{T \Delta V} \nThis yields the rigorous statement for the latent heat (enthalpy change): \nΔH=∫P1P2TΔVVfinal−VinitialdP\Delta H = \int_{P_1}^{P_2} \frac{T \Delta V}{V_{final} - V_{initial}} dP
Source: Wikipedia