Enthalpy

Enthalpy, H, is defined as

Enthalpy is a state function. Like internal energy, we can determine changes in the enthalpy,

Using the chain rule of calculus, we can rewrite the equation as

For a process in which the internal and external pressures are the same and remain constant (which is common in laboratory experiments), the V dP term is zero because dP is zero. Using the original definition of dU, the equation becomes

The integrated form of the last equation is

At constant pressure, to q = q_P, hence

Because constant-pressure processes are so common (almost any process exposed to the atmosphere can be considered constant-pressure), the equality of q and ΔH is common. Because of this, it is also common to use the words endothermic and exothermic to describe processes for which the ΔH is positive or negative, respectively. However, this is only strictly correct for constant-pressure processes. Hence the change in enthalpy for a process is usually easier to measure than the change in internal energy. As such, although the internal energy is the more fundamental quantity, the enthalpy is the more common.

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