  We derive the work cost of using generalized thermal baths from the physical
equivalence of quantum mechanics under unitary transformations. We demonstrate
our method by considering a qubit extracting work from a single bath to amplify
a cavity field. There, we find that only half of the work investment is
converted into useful output, the rest being wasted as heat. These findings
establish the method as a promising tool for studying quantum resources within
the framework of classical thermodynamics.
