# How does pressure affect enthalpy?

May 26, 2015

Enthalpy is the heat content of a system as a function of entropy and pressure.

As the pressure increases ($\Delta P > 0$), so does enthalpy, and vice versa. Thus, more compressed molecules such as solids have greater intermolecular forces than less compressed molecules such as liquids or gases; their interactions are harder to separate.

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

$= q + w + P \Delta V + V \Delta P + \Delta P \Delta V$

$= T \Delta S - P \Delta V + P \Delta V + V \Delta P + \Delta P \Delta V$

$= T \Delta S + V \Delta P + \Delta P \Delta V$

Enthalpy can still exist even at constant pressure; that describes the enthalpy of vaporization or fusion.

Notice how the equation changes at constant pressure ($\Delta P = 0$):

$\Delta H = T \Delta S + {\cancel{V \Delta P + \Delta P \Delta V}}^{0}$

Thus:

$\frac{\Delta {H}_{v a p}}{{T}_{v a p}} = {q}_{r e v , P} / {T}_{v a p} = \Delta {S}_{v a p}$

$\frac{\Delta {H}_{f u s}}{{T}_{f u s}} = {q}_{r e v , P} / {T}_{f u s} = \Delta {S}_{f u s}$

where ${q}_{P}$ is heat flow at a constant pressure.