Enthalpy and Heat Capacity

Enthalpy, H, is a state function that combines a system's internal energy with pressure and volume.

The change in enthalpy equals the heat absorbed or released by the system at constant pressure.

Consider two cylinders, A and B, containing an ideal gas but under different conditions.

Cylinder A is sealed, so when it is heated, all the applied heat increases the system’s internal energy. Cylinder B, on the other hand, allows expansion upon heating and uses heat for both work and increasing the system's internal energy.

For cylinder A operating at constant volume, the internal energy increases with temperature. For cylinder B, maintained at constant pressure, the energy supplied equals the change in enthalpy, which also increases with temperature.

A plot of enthalpy versus temperature shows that a system’s enthalpy increases as its temperature rises at constant pressure. The slope of the tangent to this curve gives the heat capacity at constant pressure, C_p.

Likewise, a plot of internal energy versus temperature shows that internal energy increases at constant volume, and the slope of its tangent defines the heat capacity at constant volume, C_v.