We can use the definition in eqn 3.1 to formulate an expression for the change in
entropy of the surroundings, ΔSsur. Consider an infinitesimal transfer of heat dqsur to
the surroundings. The surroundings consist of a reservoir of constant volume, so the
energy supplied to them by heating can be identified with the change in the internal
energy of the surroundings, dUsur.
2 The internal energy is a state function, and dUsur
is an exact differential. As we have seen, these properties imply that dUsur is independent
of how the change is brought about and in particular is independent of whether
the process is reversible or irreversible. The same remarks therefore apply to dqsur,
to which dUsur is equal. Therefore, we can adapt the definition in eqn 3.1, delete the
constraint ‘reversible’, and write