Solution Found!
Prove that if you had a heat engine whose efficiency was
Chapter 4, Problem 16P(choose chapter or problem)
Prove that if you had a heat engine whose efficiency was better than the ideal value (4.5), you could hook it up to an ordinary Carnot refrigerator to make a refrigerator that requires no work input.
Questions & Answers
(1 Reviews)
QUESTION:
Prove that if you had a heat engine whose efficiency was better than the ideal value (4.5), you could hook it up to an ordinary Carnot refrigerator to make a refrigerator that requires no work input.
ANSWER:
Step 1 of 3
A heat engine has a maximum efficiency of:
\(e=1-\frac{T_{c}}{T_{h}}\)
where \(T_{h}\) is the temperature of the hot reservoir from which heat \(Q_{h}\) is extracted and \(T_{c}\) is the temperature of the cold reservoir to which heat \(Q_{c}=Q_{h}-W\) is expelled after work \(W\) is extracted. From the second law of thermodynamics, the heat and temperature ratios satisfy (at the optimum efficiency):
\(\begin{array}{c} \frac{Q_{c}}{Q_{h}}=\frac{T_{c}}{T_{h}} \\ Q_{c}=Q_{h} \frac{T_{c}}{T_{h}} \end{array}\)
Thus the work done by an optimal heat engine is:
\(\begin{array}{c} W=Q_{h}-Q_{c}=Q_{h}-Q_{h} \frac{T_{c}}{T_{h}} \\ W=Q_{h}\left(1-\frac{T_{c}}{T_{h}}\right) \end{array}\)
...(1)
Reviews
Review this written solution for 22675) viewed: 379 isbn: 9780201380279 | An Introduction To Thermal Physics - 1 Edition - Chapter 4 - Problem 16p
Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.
No thanks, I don't want to help other students