This physics problem is about energy and temperature Problem 11.32 - Enhanced -

Question

This physics problem is about energy and temperature

Problem 11.32 - Enhanced - with Feedback Part A Air conditioners are rated by their coefficient of performance at 69 F inside temperature and 91 What is the maximum possible coefficient of performance? Express your answer using two significant figures F outside temperature. An efficient but realistic air conditioner has a coefficient of performance of 3.2. You may want to review (-pages 336-337 CORmax = Submit My Answers Give Up Incorrect; Try Again Provide Feedback Continue

Explanation / Answer

Using the Second Law of Thermodynamics we have that

Qc/Tc - Qh/Th =< 0

notice the signs, heat going into the refrigerator is positive and heat leaving the refrigerator is negative, thus

Qc / Qh =< Tc / Th

or

Qh / Qc => Th / Tc

Solving for Qc/Qh in the equation for the first law we get

Qh/Qc = W/Qc + 1 >= Th/Tc

thus

W >= (Th/Tc - 1) * Qc

the COP is given by

Qc/W = COP <= 1/(Th/Tc - 1)

69 F = 293.706 K
91 F = 306.483 K

Thus, the max COP is

COP max = 1/(306.483/283.706-1) = 12.4

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