Entropy and free energy

Abstract

As we have seen, the equation giving a system’s change in internal energy when undergoing a reversible process is dE=dQ-dW, (3.1) where dQ is the heat absorbed by the system and dW the work done by the system. We also have (see (2.4)) dQ=TdS. (3.2) Hence dE=TdS-dW, (3.3) or dW=-(dE-TdS)=-dF, (3.4) where F=E-TS (3.5) is called the Helmholtz free energy of the system. This form of the equation in effect combines the first two laws of thermodynamics, asserting that the work done by the system is not merely at the expense of some of its internal energy but at the expense of the internal energy less the heat. Thus the greatest useful work that a system can do is equal to (the loss of) its free energy.