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I was checking Castellan's Physical Chemistry. So, there's a passage that states:

Consider a liquid in equilibrium with its vapor under a pressure of 1 atm. The temperature is the equilibrium temperature, the normal boiling point of the liquid (Tb). Imagine that the system is confined in a cylinder by a floating piston carrying a mass equivalent to the 1 atm pressure. The cylinder is immersed in a temperature reservoir at the equilibrium temperature Tb . If the temperature of the reservoir is raised infinitesimally, a small quantity of heat flows from the reservoir to the system, some liquid vaporizes.

From this passage it comes that enter image description here

My question is, if enthalpy can be given by equation 1, and knowing dp is zero (constant pressure) and dT is zero (during physical state transformation the temperature is constant), how come the variation of enthalpy is not zero?

enter image description here

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The equation you wrote is for a single phase.. If there are two phases present, then the enthalpy per unit mass depends not only on the temperature and pressure but also on the mass fraction of each phase.

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