Solved: A Carnot engine extracts heat from a block of mass m and specific heat c

Chapter 19, Problem 62

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A Carnot engine extracts heat from a block of mass m and specific heat c initially at temperature Th0 but without a heat source to maintain that temperature. The engine rejects heat to a reservoir at constant temperature Tc. The engine is operated so its mechanical power output is proportional to the temperature difference Th - Tc: P = P0 Th - Tc Th0 - Tc where Th is the instantaneous temperature of the hot block and P0 is the initial power. (a) Find an expression for Th as a function of time, and (b) determine how long it takes for the engines power output to reach zero.