Question

An air conditioning system operating on reversed carnot cycle is required to remove heat from the house at a rate of 32kj/s to maintain its temperature constant at 20. if the temperature of the outside is 35 the power required to operate this air conditioning system is
(a) 0.58 kW
(b) 3.20 kW
(c) 1.56 kW
(d) 2.26 kW
(e) 1.64 kW

Answer 1

Answer:

(e) 1.64 kW

Explanation:

The Coefficient of Performance of the Reverse Carnot's Cycle is:

$COP = \frac{T_{L}}{T_{H}-T_{L}}$

$COP = \frac{293.15\,K}{308.15\,K-293.15\,K}$

$COP = 19.543$

Lastly, the power required to operate the air conditioning system is:

$\dot W = \frac{\dot Q_{L}}{COP}$

$\dot W = \frac{32\,kW}{19.543}$

$\dot W = 1.637\,kW$

Hence, the answer is E.