Question

3.. Show that equilibrium is defined by an extremum of the Gibbs free energy (i.e., dG = 0) and that the extremum is a minimum (d²G > 0).

Answer 1

we know

when ,that is no change in Gibbs free energy,

that is the change in total heat content of the sytem will be equal to the entropy change at that particular temperature. The degree of randomness become equal to total heat content of the system. No more heat is going to absorb or release, if did like that entropy will also change, so they are in equilibrium state.

if , means positive value of change in Gibbs energy, so to get a positive value should be negative. ie the work is non spontaneous one. if it will be spontaneous work , without any external supply of energy that reaction will occur. So we can say the condition of equilibrium only if it is a non spontaneous one. so either > or should be negative.