# How to determine a temperature on which process is spontaneous by using function of Gibbs free energy?

## Seems like this question can't be solved, maybe I just need any correlation between temperature and gibbs free energy?

Jul 11, 2018

If $\Delta S > 0$
$\frac{\Delta H}{\Delta S} < T$
If $\Delta S < 0$
$\frac{\Delta H}{\Delta S} > T$

#### Explanation:

$\Delta G = \Delta H - T \Delta S$
G is gibbs free energy
H is enthalpy
S is entropy
$\Delta G = - T \Delta {S}_{\text{net}}$
If $\Delta {S}_{\text{net}} < 0$
$\Delta G = - T \Delta {S}_{\text{net}} < 0 \left(\because T > 0 K\right)$, the process is spontaneous.

If $\Delta H$ and $\Delta S$ is given,
$\Delta H - T \Delta S < 0$
$\Delta H < T \Delta S$
If $\Delta S > 0$
$\frac{\Delta H}{\Delta S} < T$
If $\Delta S < 0$
$\frac{\Delta H}{\Delta S} > T$