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alexandr402 [8]
3 years ago
7

An air conditioner operating between 93°F and 70°F is rated at 4000 Btu/h cooling capacity. Its coefficient of performance is 27

% of that of a Carnot refrigerator operating between the same two temperatures. What horsepower is required of the air conditioner motor? (Halliday, 05/2018, p. 606) Halliday, D., Resnick, R., Walker, J. (05/2018). Fundamentals of Physics, 11th Edition [VitalSource Bookshelf version]. Retrieved from vbk://9781119306856 Always check citation for accuracy before use.
Physics
1 answer:
lana [24]3 years ago
6 0

Answer:P_{in}=0.25\ Hp

Explanation:

Given

Operating temperatures are

T_L=70^{\circ}F\approx 294.261\ K

T_H=93^{\circ}F\approx 307\ K

COP is 27\% of Carnot refrigerator

COP_{carnot}=\dfrac{T_L}{T_H-T_L}

COP_{carnot}=\dfrac{294.261}{307-294.261}

COP_{carnot}=\dfrac{294.261}{12.74}

COP_{carnot}=23.09\approx 23.1

actual COP=0.27 \times COP_{carnot}

COP_{actual}=6.237

Also, COP=\dfrac{\text{Desired effect}}{\text{Power in}}

6.237=\frac{4000}{P_{in}}

P_{in}=\frac{4000}{6.237}=641.33\ Btu/h

P_{in}=0.25\ Hp

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