Enthalpy

Remarks

From $dU = T \, dS - p \, dV$ one gets $dH = T \, dS + V \, dp$, where $T$ is the temperature and $S$ the entropy. So the natural variables of $H$ are $S$ and $p$, and $T = (\partial H / \partial S)_p$, $V = (\partial H / \partial p)_S$. In a process at constant pressure in which only expansion work is done, the heat taken in is $Q = \Delta H$. Example: for $n$ moles of a monatomic ideal gas, $U = \frac{3}{2} nRT$ and $pV = nRT$, so $H = \frac{5}{2} nRT$, where $R$ is the gas constant. Non-example: $U - pV$ is not the enthalpy; the sign of the term $pV$ matters, and $U - pV$ has differential $T \, dS - 2p \, dV - V \, dp$, with no simple meaning.