Problem 3 (20 points) - A Curious Suggestion While walking through the library, you stumble upon a few students discussing an idea to improve the efficiency of a reversible thermal energy conversion process. The fundamental idea is to improve the efficiency of the reversible heat engine by using a reversible heat pump to increase the temperature of the high temperature energy source of the heat engine, from TH TH. The two schematics below show i. the original system, with the heat engine operating between an energy source and sink at T and TL, respectively, and ii. the modified system with the heat pump operating between T and TH, respectively, and the heat engine operating between T and TL, respectively. Note that for this discussion to make any sense, the high temperature energy source for the heat engine in the second orientation must be finite (i.e., not a reservoir). If it were a thermal reservoir, it would be impossible to alter its temperature. For clarity, you may consider the finite thermal source to be an incompressible substance. i) TH QH Rev. HE QL T ii) Wout TL TH Ti Rev. HE Rev. HP Qi QH QL Wout Win Please answer the following questions: a) Why is the rate of heat transfer out of the heat pump equal in magnitude to the rate of heat transfer into the heat engine in orientation (ii)? Remember that the temperature of the finite temperature source remains constant, and that the temperature source is an incompressible substance. b) Show that the combined system of orientation (ii) has a thermal efficiency n = 1- T TE c) Explain how the above expression must always be less than the efficiency of the original orientation, assuming the heat pump is truly a heat pump. Page 4 of 6