EXERCISE 2.6. Consider a system which has the capacity to do work, AW-YaX+dW'. Assume that processes take place spontaneously so that ds = (1/T)4Q+d;S, where d;S is a differential element of entropy due to the spontaneity of the process. Given the fundamental equation for the Gibbs free energy, G=U-XY - TS, show that -(dG)yr=W' + Td;S. Therefore, at fixed Y and T, all the Gibbs free energy is available to do work for reversible processes. However, for spontaneous processes, the amount of work that can be done is diminished because part of the Gibbs free energy is used to produce entropy. This result is the starting point of nonequilibrium thermodynamics.