Question

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.

Answer 1

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

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

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

$P_{in}=0.25\ Hp$