# Why does a system expand isothermally?

Considering the first step of the Carnot process, heat is transferred from a bath to the system with both at the same temperature. But how does this process start? Why should the system spontaneously absorb heat and expand as a result. And even if I pull on the piston an infinitesimal bit, why should the process continue and do not stay at the new equilibrium state?

Since you are pulling very slowly, it will also stay in thermal equilibrium with the bath. So temperature keeps constant over the process. Should the internal energy $U$ depend on temperature only, as is the case for an ideal gas, we have $dU=0$.
But because energy leaves the system as work, it must be compensated for by a heat flow into the system, since $dU = \delta Q + \delta W$. That heat is absorbed from the bath, although they are at the same temperature.