Two Carnot engines work in series: the first between 800 K and an intermediate temperature T, the second between T and 200 K. If both engines have equal efficiency, T equals:

The Carnot cycle alternates two isothermal steps (heat absorbed at T_H, released at T_C) with two adiabatic steps (no heat exchange); the enclosed loop area equals the net work output, and η = 1−T_C/T_H is the maximum possible efficiency between those two temperatures.