Suppose that a deep shaft were drilled in Earth’s crust near one of the poles, where the surface temperature is -40 C, to a depth where the temperature is 800 C. (a) What is the theoretical limit to the efficiency of an engine operating between these temperatures? (b) If all the energy released as heat into the lowtemperature reservoir were used to melt ice that was initially at -40 C, at what rate could liquid water at 0C be produced by a 100 MW power plant (treat it as an engine)? The specific heat of ice is 2220 J/kg K; water’s heat of fusion is 333 kJ/kg. (Note that the engine can operate only between 0C and 800C in this case. Energy exhausted at -40C cannot warm anything above -40C.)

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Suppose that a deep shaft were drilled in Earth’s crust near one of the poles, where the surface temperature is -40 C, to a
depth where the temperature is 800 C. (a) What is the theoretical
limit to the efficiency of an engine operating between these temperatures? (b) If all the energy released as heat into the lowtemperature
reservoir were used to melt ice that was initially at
-40 C, at what rate could liquid water at 0C be produced by a
100 MW power plant (treat it as an engine)? The specific heat of ice is 2220 J/kg K; water’s heat of fusion is 333 kJ/kg. (Note that the
engine can operate only between 0C and 800C in this case. Energy
exhausted at -40C cannot warm anything above -40C.)

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