Equilibrium in systems in contact with a heat bath

We now consider the case in which the system is not isolated from the environment, but can exchange energy with it. We shall assume that the environment is represented by a very large system, a heat bath (Fig. ), meaning that its temperature remains constant and unaffected by the interactions with the system. We want to find the conditions that govern the exchange of energy between the system and the heat bath.

Figure: A system exchanging energy with a heat bath. Volume $V$ and number of particles $N$ are kept constant.