Q.A Carnot engine receives 2.0 kJ of heat from a reservoir at 500 K, does some work, and rejects some heat to a reservoir at 350 K.

The Carnot engine is a hypothetical, maximally-efficient heat engine proposed by the French engineer Sadi Carnot in 1824. Its cycle consists of exactly two reversible isothermal steps (heat exchange with the hot reservoir at $T_H$ and the cold reservoir at $T_C$) and two reversible adiabatic steps (work-only steps, with no heat exchange, connecting the two temperatures) — this specific combination is required because heat exchange can only be reversible if it happens isothermally, and work transfer can only be reversible if it happens adiabatically (with no heat crossing a temperature difference). Combining the isothermal and adiabatic work formulas gives the Carnot efficiency, $\eta = 1 - T_C/T_H$ — depending only on the two reservoir temperatures, and on nothing else about the engine's design or working substance. …