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When a man returns to his well-sealed house on a summer day, he finds that the house is at 35°C. He turns on the air conditioner, which cools the entire house to 20°C in 38 min. If the COP of the air-conditioning system is 2.8, determine the power drawn by the air conditioner. Assume the entire mass within the house is equivalent to 800 kg of air for which cv = 0.72 kJ/kg·°C and cp = 1.0 kJ/kg·°C.

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davidlcastiblanco

Answer:

[tex]W_a=1.35 kW[/tex]

Explanation:

Given:

[tex]COP=2.8[/tex]

[tex]C_v=0.72 kJ/kg*C[/tex]

[tex]m=800kg[/tex]

ΔT[tex]=35-20=15C[/tex]

[tex]t=38 minutes*\frac{60s}{1minute}=2280s[/tex]

So the power the air conditioner do first determine the heat that removed

[tex]Q_o=m*c_v*T'[/tex]

[tex]Q_o=800kg*0.72kJ/kg*C*15C=8640 kJ[/tex]

Now that heat in the time the air take to remove the heat

[tex]Q'_L=\frac{Q_o}{t}=\frac{8640 kJ}{2280s}=3.789 kW[/tex]

Finally that power drawn can be find by the power and the COP is knowing

[tex]W_a=\frac{Q_L}{COP}= \frac{3.78kW}{2.8}=1.35 kW[/tex]

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