A reversible engine is used for only driving a reversible refrigerator. Engine is supplied 2000 kJ/s heat from a source at 1500 K and rejects some energy to a low temperature sink. Refrigerator is desired to maintain the temperature of 15ºC while rejecting heat to the same low temperature sink. Det

Question

A reversible engine is used for only driving a reversible refrigerator. Engine is supplied 2000 kJ/s heat from a source at 1500 K and rejects some energy to a low temperature sink. Refrigerator is desired to maintain the temperature of 15ºC while rejecting heat to the same low temperature sink. Determine the temperature of sink if total 3000 kJ/s heat is received by the sink.

Accepted Answer

[latex] ext{Let temperature of sink be T}_{sink} K.\ ext{Given:}\quad Q_{sink, HE} + Q_{sink, R} = 3000 kJ/s\ ext{Since complete work output from engine is used to run refrigerator so,}\\begin{aligned}2000 – Q_{sink, HE}&= Q_{sink, R} – Q_{R}\Q_{R}&= 3000 – 2000 = 1000 kJ/s\ ext{Also for engine,}&\\frac{2000}{1500}&= \frac{Q_{sink, HE}}{T_{sink}} ⇒ Q_{sink, HE} = \frac{4}{3} T_{sink,}\ ext{For refrigerator,}&\\frac{Q_{R}}{288}&= \frac{Q_{sink, R}}{T_{sink}} ⇒ Q_{sink, R} = \frac{1000 T_{sink}}{288}\end{aligned}\ ext{Substituting }Q_{sink, HE} ext{ and }Q_{sink, R} ext{ values.}\\begin{aligned}\frac{4}{3}T_{sink} + \frac{1000 T_{sink}}{288}&= 3000\⇒ \qquad \qquad T_{sink}&= 624.28 K\ ext{Temperature of sink}&= extbf{351.28ºC}\end{aligned}[/latex]

Question 4.14: A reversible engine is used for only driving a reversible re...

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