Answer: Refrigeration and Heat Pump Cycle ApplicationsAn

Chapter 5, Problem 53P

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QUESTION:

An inventor claims to have devised a refrigeration cycle operating between hot and cold reservoirs at 300 K and 250 K, respectively, that removes an amount of energy \(Q_{\mathrm{C}}\) by heat transfer from the cold reservoir that is a multiple of the net work input—that is, \(Q_{\mathrm{C}}=\mathrm{N} W_{\text {cycle }}\), where all quantities are positive. Determine the maximum theoretical value of the number N for any such cycle.

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QUESTION:

An inventor claims to have devised a refrigeration cycle operating between hot and cold reservoirs at 300 K and 250 K, respectively, that removes an amount of energy \(Q_{\mathrm{C}}\) by heat transfer from the cold reservoir that is a multiple of the net work input—that is, \(Q_{\mathrm{C}}=\mathrm{N} W_{\text {cycle }}\), where all quantities are positive. Determine the maximum theoretical value of the number N for any such cycle.

ANSWER:

Solution 53P

Step 1 of 5

Here our aim is to determine the maximum theoretical value of the number N for the refrigerator developed by the inventor for the given parameters.

For this, we need to find the coefficient of performance of the refrigerator he developed, and the maximum theoretical coefficient for a reversible refrigeration cycle for the given parameters and then determine the maximum value of  N.

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