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`

Step-by-step 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)=(T_L)/(T_H-T_L)`

`COP_(carnot)=(294.261)/(307-294.261)`

`COP_(carnot)=(294.261)/(12.74)`

`COP_(carnot)=23.09\approx 23.1`

actual
`COP=0.27 * COP_(carnot)`

`COP_(actual)=6.237`

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

`6.237=(4000)/(P_(in))`

`P_(in)=(4000)/(6.237)=641.33\ Btu/h`

`P_(in)=0.25\ Hp`