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A well-insulated room containing 1000 kg of air is initially at 50°C. An air conditioner with a COP (Coefficient of Performance) of 3 is turned on, and the room is cooled to 25°C in half an hour. Calculate the power consumed by the air conditioner. Assume constant specific heat for air at 300K.

Answer :

Final answer:

To calculate the power consumed by the A/C, use the formula Power = (mass of air) * (specific heat capacity of air) * (change in temperature) / (efficiency of A/C). Given the values provided, the power consumed by the A/C is 250,000 kW.

Explanation:

To calculate the power consumed by the A/C, we can use the formula:

Power = (mass of air) * (specific heat capacity of air) * (change in temperature) / (efficiency of A/C)

Given that the mass of air is 1000 kg, specific heat capacity of air is constant at 300K, and the change in temperature is 50°C - 25°C, we can substitute these values into the formula.

Therefore, the power consumed by the A/C is (1000 kg) * (300 K) * (25°C) / (3) = 250,000 kW.

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