High School

An air-conditioner is removing heat from a room at 22°C at a rate of 7000 kJ/h and rejecting the waste heat to the outdoors at 35°C. If the coefficient of performance of the air-conditioner is 2.9, what is the power consumed by the air-conditioner?

Answer :

The amount of power consumed by the air-conditioner during its performance is 40.22 kW.

A measure of power and efficiency compares the quantity of energy that is being wasted to the amount of energy that is being used productively.

Rate of energy ejected by the air-conditioner, R₁ = 7 x 10³ kJ/h

Coefficient of performance of the air-conditioner, η = 2.9

The expression for the coefficient of performance of the air-conditioner is given by,

η = Q₁/Q₂

So, the amount of heat energy consumed by the air-conditioner can be calculated as,

Q₂ = Q₁/η

Therefore, the power consumed by the air-conditioner is given by,

P = Q₂/t = (Q₁/t)/η

P = R₁/η

P = 7 x 10³/60 x 2.9

P = 40.22 kW

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