Explanation Write the expression for the energy balance to the system. Q 1 + Q 2 = Q s + Q 0 (I) Here, the heat transfer from the outdoor to the heat pump is Q 0 , the heat transfer from the high temperature source is Q s , the heat transfer by the power cycle to the dwelling is Q 1 and the heat transfer by the heat pump to the dwelling is Q 2 . Rearrange the terms of the equation (I). Q 1 + Q 2 Q s = 1 + Q 0 Q s (II) Write the expression for second law for the heat engine. Q 1 Q s = T d T s Q 1 = T d T s Q s Here, the temperature at the dwelling is T d and the temperature of the source is T s . Write the expression for second law for the heat pump. Q 2 Q 0 = T d T 0 Q 2 = Q 0 T d T 0 Here, the outside temperature is T 0 . Substitute T d T s Q s for Q 1 and Q 0 T d T 0 for Q 2 in Equation (I). ( T d T s ) Q s + ( T d T 0 ) Q 0 = Q s + Q 0 ( T d T s − 1 ) Q s = ( 1 − T d T 0 ) Q 0 Q 0 Q s = T 0 T s × [ T d − T s ] [ T 0 − T d ] Substitute T 0 T s [ T d − T s ] [ T 0 − T d ] for Q 0 Q s in Equation (II)

Appendices to accompany Fundamentals of Engineering Thermodynamics, 8e

8th Edition

ISBN: 9781118957219

Author: Michael J. Moran, Howard N. Shapiro

Publisher: WILEY

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Chapter 5.11, Problem 14P

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The expression for the ratio total heating provided to the dwelling and the heat transfer from the high temperature source.

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Chapter 5.11, Problem 13P

Chapter 5.11, Problem 15P

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Appendices to accompany Fundamentals of Engineering Thermodynamics, 8e

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