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Enthalpy, denoted by H, is a convenient energy concept defined from properties of a system:


where U is internal energy, p is pressure and V is volume, and is thus also a property of the system. The term U + d(pV) appears often in equations resulting from the First Law of Thermodynamics. Internal energy, and hence enthalpy, can only be quantified relative to an arbitrary reference value. In most applications, however, it is the changes in enthalpy that are important, so the values of the reference state chancel out. The convenience of enthalpy as a thermodynamic concept is illustrated by the definitions of the molar heat capacities of a closed system of constant volume, , and constant pressure, , in a reversible process:


where h, u and v are the molar enthalpy, molar internal energy and molar volume, respectively.

For solids and liquids, enthalpy change resulting from a change in pressure and temperature can be calculated from


Enthalpy and other thermodynamic properties of gases and vapors are usually expressed in terms of their deviation from ideal behavior. Residual enthalpy, , is defined as the difference between the actual enthalpy and the ideal enthalpy. For an isothermal process,


Accurate experimental data should be used in evaluating this expression, but approximate values (±2%) can be obtained by using the Compressibility Factor , which is plotted in compressibility charts as a function of reduced temperature and pressure. Residual enthalpy can be expressed in terms of the compressibility factor for a change at constant temperature and composition:


It follows from the definition of enthalpy and the First Law of Thermodynamics that the change in enthalpy in a closed system at constant pressure in a reversible process is equal to the heat input. The change in enthalpy in a chemical reaction at constant pressure is then the heat of reaction , which in most reactions result mainly from changes in bond strength over the course of a reaction. As enthalpy is a state function, the change in enthalpy is independent of the path of change, so that , for any reaction can be calculated from a suitable combination of values for standard reference reactions.

The heat of formation of a chemical compound is a special case of the heat of reaction, where the compound is the only product from reactants comprising its component elements. The heat of combustion is the enthalpy change when a substance is oxidized with molecular oxygen. Enthalpy change associated with a phase change in a pure substance, known as latent heat, is calculated from the Clapeyron Equation:


where p* is the saturation pressure and is the change in molar volume between the two phases. In the special case of vaporization (or sublimation), where the vapor behaves as an ideal gas and the volume of liquid (or solid) is small compared to that of the vapor,


Enthalpy changes associated with changes in concentration, such as the heat of dilution, mixing or crystallization, can be evaluated from enthalpy concentration charts.

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