Why is the enthelpy of a phase transition different from 0?

[ricard.py]

Hello,
Wikipedia states: Phase changes, such as melting or evaporation, are also isothermal processes.
I am interested in calculating the enthalpy of a given phase transition.

If the process is isothermal, I would immediately say that H is 0, according to the following equation:

dH=CpdT

But I know that this is not true, why?

 

[WannabeNewton]

$(\frac{\partial H}{\partial T})_p = C_p$ is only true at constant pressure. During a phase transition neither the volume nor pressure of a substance need be constant.

 

[Chestermiller]

Hello,
Wikipedia states: Phase changes, such as melting or evaporation, are also isothermal processes.
I am interested in calculating the enthalpy of a given phase transition.

If the process is isothermal, I would immediately say that H is 0, according to the following equation:

dH=CpdT

But I know that this is not true, why?

The equation you wrote applies to only a single phase at constant pressure. If you want to extend it to calculate the change in enthalpy for a phase transition, you need to include latent heat of melting or evaporation. During the phase transition at constant pressure, the temperature remains constant until the phase transition is complete. One way of integrating the above equation over the phase transition is to express the heat capacity in terms of the Dirac delta function δ(T), assuming you are familiar with this function. This gives:
ΔH=\int_{T_v^-}^{T_v^+}{Lδ(T-T_v)dT}
where L is the latent heat of vaporization, and T_v is the heat of vaporization. In this way, the heat capacity at the transition is Lδ(T-T_v).

Chet