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A thermodynamic state function H defined as
where U is the internal energy, p is pressure, and V is volume.

Specific enthalpy of a homogeneous system, h, is its enthalpy divided by its mass, m, defined by
where u is specific internal energy and v is specific volume. With aid of the gas laws, the specific enthalpy of an ideal gas may also be written as
where T is temperature and cp is the specific heat at constant pressure. The specific enthalpy of a liquid, hl;t7, is
where cl is the liquid's specific heat, which is nearly independent of pressure and specific volume. For a system consisting of a mixture of components, the total enthalpy is the mass-weighted sum of the enthalpies of each component. Thus, the total enthalpy of a system consisting of a mixture of dry air, water vapor, and liquid water is
where md, mv, and mw are the masses of dry air, water vapor, and liquid water, respectively; cpd and cpv the specific heats of dry air and water vapor; and cw is the specific heat of liquid water. This quantity is commonly called moist enthalpy, with specific moist enthalpy given by h = H/(md + mv + mw). With the aid of the definition of the latent heat of vaporization (
see latent heat), moist enthalpy may also be written as
where mt is the mass of vapor plus liquid and Lv is the latent heat of vaporization. Similar relations can be written to include the effects of ice. In an adiabatic, reversible process, enthalpy and specific enthalpy are conserved, although the component specific enthalpies may not be, due to the exchange of enthalpy between components in phase changes.

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