Question

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.

Answer 1

`W_a=1.35 kW`

Step-by-step explanation:

Given:

`COP=2.8`

`C_v=0.72 kJ/kg*C`

`m=800kg`

ΔT
`=35-20=15C`

`t=38 minutes*(60s)/(1minute)=2280s`

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

`Q_o=m*c_v*T'`

`Q_o=800kg*0.72kJ/kg*C*15C=8640 kJ`

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

`Q'_L=(Q_o)/(t)=(8640 kJ)/(2280s)=3.789 kW`

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

`W_a=(Q_L)/(COP)= (3.78kW)/(2.8)=1.35 kW`