# What is the difference between enthalpy and entropy?

Nov 24, 2015

Almost... everything. Letter, units... everything except that they're state functions and expressions of energy.

Enthalpy:

$\textcolor{b l u e}{\Delta H} = \Delta U + \Delta \left(P V\right)$

$= q + w + \Delta \left(P V\right)$

$= q \cancel{- P \Delta V + P \Delta V} + V \Delta P + \Delta P \Delta V$

$= \textcolor{b l u e}{q + V \Delta P + \Delta P \Delta V}$

where $U$ is internal energy, $q$ is heat flow, $w$ is expansion/compression work, and of course, $P$ is pressure and $V$ is volume.

The units for the generic enthalpy are usually in $\text{kJ}$.

This makes enthalpy the heat flow in a closed system, plus the amount of expansion/compression work done via a change in pressure.

Entropy:

$\textcolor{b l u e}{\Delta S \ge \frac{q}{T}}$

$\textcolor{b l u e}{\Delta S = \frac{{q}_{\text{rev}}}{T}}$

The units for the generic entropy are usually in $\text{J/K}$.

This makes entropy equal to the amount of reversible heat flow possible per unit temperature.