Enthalpy and Heat Capacity

Enthalpy (H) is a state function combining a system's internal energy with the product of pressure and volume, expressed as H = U + pV. Since internal energy, pressure, and volume are state functions, enthalpy is also a state function. However, only changes in enthalpy (ΔH) can be measured, not absolute values for specific substances.

At constant pressure, the change in enthalpy (ΔH) equals the heat (q) absorbed or released by the system. When a system loses heat to surroundings, like burning wood, ΔH is negative and the process is exothermic. When a system gains heat, like a cold pack, ΔH is positive and the process is endothermic.

In a sealed cylinder at constant volume, all applied heat increases internal energy. In an open cylinder at constant pressure, heat is distributed between work done during expansion and increasing internal energy. This difference explains why heat capacity varies between constant volume (Cv) and constant pressure (Cp) conditions.

The slope of the tangent to an enthalpy versus temperature plot at constant pressure gives the heat capacity at constant pressure (Cp). Similarly, the slope of an internal energy versus temperature plot at constant volume defines the heat capacity at constant volume (Cv). These slopes quantify how much heat is needed to raise temperature.

Heat capacity (C) is the amount of heat required to raise a substance's temperature by one degree Celsius and depends on the amount of substance, making it an extensive property. Molar heat capacity is heat capacity divided by moles, making it an intensive property independent of substance amount.

A system's enthalpy increases as its temperature rises at constant pressure. This relationship is linear and can be visualized on an enthalpy-temperature plot, where the positive slope indicates that higher temperatures correspond to higher enthalpy values. The rate of this increase is quantified by heat capacity at constant pressure.

Absolute enthalpy values cannot be measured because enthalpy depends on internal energy, pressure, and volume—all of which have arbitrary reference points. Only changes in enthalpy (ΔH) between two states can be determined experimentally, making it a practical measure for thermodynamic calculations and applications.