Answer:
Explanation:
From the given information:
Water freezing temp. [tex]T_L = 32 ^0 \ F[/tex]
Heat rejected temp [tex]T_H = 72 ^0 \ F[/tex]
Recall that:
The coefficient of performance is:
[tex]COP_{ref} = \dfrac{T_L}{T_H - T_L} \\ \\ = \dfrac{32+460}{(72 +460) -(32+460)} \\ \\ =\dfrac{492}{532 -492} \\ \\ = \dfrac{492}{40} \\ \\ COP_{ref} = 12.3[/tex]
Again:
The efficiency given by COP can be represented by:
[tex]COP = \dfrac{Q_L}{W} \\ \\ W = \dfrac{Q_L}{COP} \\ \\ W = \dfrac{2000 \ lbm \times 144 \ Btu/lbm}{12.3} \\ \\ W = 23414.63 \ Btu[/tex]
Finally; the power input in an hour can be determined by using the formula:
[tex]Power= \dfrac{W}{t} \\ \\ Power = \dfrac{23414.63 \ Btu}{ 1 \ hr} \\ \\ Power = \dfrac{23414.634 \times 1055.056 \ J}{1 \times 3600} \\ \\ Power = 6.86 \ kW[/tex]
In hp; since 1 kW = 1.34102 hp
6.86kW will be = (6.86 × 1.34102) hp
= 9.199 hp
