Question

What are the characteristics of free energy $\left(G\right)$?

Answer 1

i) $G$ is defined as $H-TS$ where $H$ and $S$ are enthalpy and entropy of the system respectively $T=$ temperature. Since $H$ and $S$ are state functions, $G$ is a state function.
ii) $G$ is an extensive property while $\Delta G=G_2-G_1$ which is the free energy change between the initial and final states of the system.
iii) $G$ has a single value for the thermodynamic state of the system.
iv) $G$ and $\Delta G$ value correspond to the system only.
There are three cases of $\Delta G$ in predicting the nature of the process.
a) When $\Delta G<0$, (Negative), the process is spontaneous and feasible.
b) When $\Delta G=0$, the process is in equilibrium.
c) When $\Delta G>0$, (Positive), the process is non-spontaneous and not feasible.
v) $\Delta G=\Delta H-T\Delta S$ but according of $I$ law of thermodynamics.
$\Delta H=\Delta E+P\Delta V$ and $\Delta E=q-w$
$\therefore \Delta G=q-w+P\Delta V-T\Delta S$
but $\Delta S-q/T$ and $T\Delta S=q=$ heat involved in the process.
$\therefore \Delta G=q-w+P\Delta V-q=w+P\Delta V$
(or) $-\Delta G=w-P\Delta V=$ Network.
The decrease in free energy $-\Delta G$, accompanying a process taking place at constant temperature and pressure is equal to maximum obtainable work.
Network $=-\Delta G=w-P\Delta V$