A reversible power cycle receives QH from a reservoir at TH and rejects QC to a reservoir at TC. The work developed by the power cycle is used to drive a reversible heat pump that removes Q'C from a reservoir at T'C and rejects Q'H to a reservoir at T'H.
a.) Develop an expression for the ratio Q'H / QH in terms of the temperatures of the four reservoirs.
b.) What must be the relationship of the temperatures TH, TC, T'C and T'H for Q'H / QH to exceed a value of 1.0 ?
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HINTS:
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* Be sure to check out the comments from Dr. B's course!
* Start with the careful application of the 1st Law to both the HE and HP. All of the W from the HE is used to drive the HP, and thus Wcycle>=W'cycle. The first law will then give you a relationship of the heat transfer rates of both cycles.
* Remember that the Kelvin principle is valid when the cycle is reversible (thus Q_H/Q_C = T_H/T_C). Use this Kelvin relationship somehow to derive your expression in part a.
* For Part b, recall that multiplying an inequality by (-1) switches the direction (e.g., greater than to less than).
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ANSWERS:
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b) T_C/T'_C = T_H/T'_H
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