Suppose that a deep shaft were drilled in Earth's crust near one of the poles, where the surface temperature is – 40^oC, to a depth where the temperature is 800^oC. 

(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^oC, at what rate could liquid water at 0^oC be produced by a 100 MW power plant (treat it as an engine)? The specific heat of ice ts 2220 J/kg ∙ K; water's heat of fusion is 333kJ/kg. (Note that the engine can operate only between 0^oC and 800^oC in this case. Energy exhausted at – 40^oC cannot warm anything above –40^oC.)