Chapter 20, Problem 53P

GO 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 low- temperature reservoir were used to melt ice that was initially at –40°C, at what rate could liquid water at 0°C 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 0°C and 800°C in this case. Energy exhausted at –40°C cannot warm anything above –40°C.)