Answer:
the minimum power input required for this air-conditioning system is 1.20 hp
Step-by-step 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