A Carnot engine extracts heat from a block of mass m and specific heat c initially at

Chapter 19, Problem 58

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

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