Randall D. Knight — Heat Engines and Refrigerators: Problem 54

Suppose the hot side of a Carnot engine is attached not to a large energy reservoir but to an object with mass \( M \), specific heat \( c \), and initial temperature \( T_H \). Each small amount of heat energy drawn from the object to run the engine slightly decreases the object’s temperature. The engine will continue running, with lower and lower efficiency, until the object’s temperature is reduced to \( T_C \), the temperature of the cold reservoir, which we assume is a true energy reservoir. Find an expression for the total work done by the engine.