Free Energy

Helmholtz Free Energy

Spontaneity ($\mathrm{\Delta }A<0$) at constant $T$ and $V$. Not particularly convenient unless you’re working in a bombe $$ \begin{align} A&=U-TS\ \Delta A&=\Delta U-T\Delta S\ \Delta A&=\Delta U-q_{rev}\ \Delta A&=w_{rev} \end{align} $$

Gibbs’ Free Energy

Spontaneity ($\mathrm{\Delta }G<0$) at constant $T$ and $P$ $$ \begin{align} G&=U-TS+PV\ G&=H-TS\ G&=A+PV\ \Delta G&=\delta w_{nonPV} \end{align} $$