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  1. Is the relation $ \Delta H = Q _P $ valid for both reversible and irreversible processes or only for reversible processes?

$Q_P$ is the heat exchanged at constant pressure.

  1. Specifically, is it valid for this case: saturated water (mass fraction = 1) is enclosed in one partition a box having two partitions of equal volume, the partition being evacuated. The partition is broken and the evacuated region gets filled with a mixture of water and steam. The temperature of the apparatus is maintained at $100^\circ\, \mathrm{C} $ (therefore the process will also be isobaric, from the phase diagram of water).
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I don't know if it is not true for every irreversible process, but it is certainly not true for the process you described in item 2. And it is not true for the case of a so-called constant pressure irreversible expansion or compression of a gas, where, during the deformation, the external pressure is held constant at a value different for the initial pressure of the gas.

In item 2, from the first law of thermodynamics, the heat added is equal to the change in internal energy of the water, not the change in enthalpy. The change in enthalpy of the water is greater than the change in internal energy (and thus greater than the amount of heat added).

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