Is defined as F = U - TS and it is the energy needed to create a system minus the heat it can get for free. But why is the heat that it can get for free given by: Q = TS I know the thermodynamic relation: S = Q/T So in that way I understand it. But how do you know, that the system will be in thermal equilibrium with surroundings, when it has received a total energy of Q = TS as heat? I mean, the point where heat stops interesting is when temperaturs are equal, i.e. when dS/dU is the same for both systems. How do you know that holds when a total of heat of Q=TS has entered?