# Why does gibbs free energy decrease with temperature?

##### 1 Answer
May 22, 2014

Free Energy (G) can either increase or decrease for a reaction when the temperature increases. It depends on the entropy (S) change.

The change in a quantity is represented by the Greek letter delta. But let me use "d" for delta since I cannot type the Greek letter. The equation for the change in free energy is dG = dH - TdS. Where H is the enthalpy, S is the entropy and T is the Kelvin temperature. Since the change in G depends on minus T times the change in S, if the entropy decreases (that means dS is negative) then -TdS is positive. Hence, when the temperature increases the numeric value of the free energy becomes larger.

Just the opposite is true if the entropy increases. In this case dS will be positive and -TdS becomes more negative when the temperature goes up. So the numeric value of the free energy becomes smaller.

You have to be careful with the terminology. A reaction with a delta G of -2000 kJ gives more free energy than one with a delta G of -1000kJ, but -1000 is a larger number than -2000!