# Is Gibbs free energy not zero always? [duplicate]

The heat q we provide is change in enthalpy. Also we measure entropy by the heat we provide with respect to Temperature(S=Q/T).

In gibbs equation, dG= dH-TdS dH is the energy we supply. Also TdS is also the energy we provide. This makes me think that dG=0. But why it is not?

## 2 Answers

If the system is in equilibrium you have $$dG = 0$$. In this event the pressure is constant and you have $$dq_P = dH$$, if you replace in the definition of $$dG$$ you have

dG = dq - TdS

so it is correct that dG = 0 since TdS = $$\delta q$$

Your equation for dG is incorrect. It should read $$dG=dH-TdS-SdT$$. When combined with the equation $$dH=TdS+VdP$$, you then get$$dG=VdP-SdT$$At constant temperature, this reduces to $$dG=VdP$$