# How does enthalpy relate to internal energy?

Nov 3, 2015

H = U + PV

#### Explanation:

H = U + PV

where H = enthalpy,
U = internal energy,
P = pressure,
and V = volume

Consider a process occurring at constant pressure and where the only work allowed is pressure-volume work (w = -PΔV):

The change on enthalpy is then given by:

$\Delta H = \Delta U + \Delta \left(P V\right) \implies \Delta H = \Delta U + P \Delta V$

and $\Delta U = {q}_{P} + w \implies \Delta U = {q}_{P} - P \Delta V$

Replacing $\Delta U$ by its expression in the expression of $\Delta H$
we get:

$\Delta H = {q}_{P}$ at constant pressure.