When the temperature of both the heat source and the heat sink of a heat engine is the same, the entropy change (ΔS) will be zero. According to the second law of thermodynamics, the entropy of an isolated system can only increase or remain constant; it cannot decrease.
In the case of a heat engine, which operates between a high-temperature source and a low-temperature sink, the ideal reversible efficiency is given by the Carnot efficiency:
η = 1 - (Tc/Th)
where η represents the efficiency, Tc is the temperature of the cold sink, and Th is the temperature of the hot source.
When Tc and Th are equal, meaning the temperatures of both the source and the sink are the same, the denominator of the equation becomes zero. In this situation, the Carnot efficiency becomes undefined or approaches infinity.
Practically, for an ideal reversible heat engine operating between two equal temperature reservoirs, no net work is done, and there is no change in entropy. The engine would operate in a reversible cycle where all the heat absorbed from the source is rejected to the sink, resulting in no net change in entropy.