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.

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nuuk nuuk · Answer 1 · 2020-05-06T09:52:50+02:00

Answer:[tex]P_{in}=0.25\ Hp[/tex]

Explanation:

Given

Operating temperatures are

[tex]T_L=70^{\circ}F\approx 294.261\ K[/tex]

[tex]T_H=93^{\circ}F\approx 307\ K[/tex]

[tex]COP[/tex] is [tex]27\% [/tex] of Carnot refrigerator

[tex]COP_{carnot}=\dfrac{T_L}{T_H-T_L}[/tex]

[tex]COP_{carnot}=\dfrac{294.261}{307-294.261}[/tex]

[tex]COP_{carnot}=\dfrac{294.261}{12.74}[/tex]

[tex]COP_{carnot}=23.09\approx 23.1[/tex]

actual [tex]COP=0.27 \times COP_{carnot}[/tex]

[tex]COP_{actual}=6.237[/tex]

Also, [tex]COP=\dfrac{\text{Desired effect}}{\text{Power in}}[/tex]

[tex]6.237=\frac{4000}{P_{in}}[/tex]

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

[tex]P_{in}=0.25\ Hp[/tex]