Question

Why isothermal heat transfer is reversible heat transfer?

Answer 1

This heat transfer can only be reversible if there is no thermal gradient and so we assume that the entropy generation due to irreversible heat transfer is small compared to the amount of total heat transferred by forcing the step to be isothermal.

Answer 2

By discussing these inefficiencies, we eventually prove that we can never get more useful work out of a heat engine than when we exchange the heat at the same temperatures as the source and sink. ... For a reversible process and constant temperature, entropy change equals the reversible heat flow divided by temperature.