An air-conditioning system is used to maintain a house at 70^\circ{} ∘ F when the temperature outside is 100^\circ{} ∘ F. The house is gaining heat through the walls and the windows at a rate of 800 Btu/min, and the heat generation rate within the house from people, lights, and appliances amounts to 100 Btu/min. Determine the minimum power input required for this air-conditioning system. 1.20 hp

the minimum power input required for this air-conditioning system is 1.20 hp

Explanation:

Given the data in the question;

Temperature inside ( Sink ) T = 70°F = ( 70 + 460 )R = 530 R

temperature outside ( source )T = 100°F = ( 100 + 460 )R = 560 R

= 800 Btu/min

= 100  Btu/min

Now, from the equation of coefficient of performance of refrigerator;

= Desired output / Required input

= / --------- let this be equation 1

= ( ) /

where is the rate heat gained through the wall

is the heat generation from people and lights and appliances.

Now, lets consider the equation coefficient of performance of refrigerator in terms of temperatures;

= / ( - )

we substitute

= 530 / ( 560 - 530 )

= 530 / 30

= 17.667

so we substitute into equation 1;

= / ---------

= ( ) /

17.667 = ( 100 + 800 ) /

17.667 = 900 /

= 900 / 17.667

= 50.94 Btu/min

= ( 50.94 / 42.53 ) hp

= 1.198 hp ≈ 1.20 hp

Therefore, the minimum power input required for this air-conditioning system is 1.20 hp