A classroom that normally contains 40 people is to be air-conditioned with window airconditioning units of 5-kW cooling capacity. A person at rest may be assumed to dissipate heat at a rate of about 360 kJ/h. There are 11 lightbulbs in the room, each with a rating of 100 W. The rate of heat transfer to the classroom through the walls and the windows is estimated to be 15,000 kJ/h. If the room air is to be maintained at a constant temperature of 21∘C, determine the number of window air-conditioning units required.

2 window air-conditioning units are required.

Explanation:

Rate of heat transfer by a person at rest = 360 kJ/h = 360 kJ/h × 1 h/3600 s = 0.1 kW

Assuming the 40 people in the classroom are at rest.

Rate of heat transfer of 40 people at rest = 40×0.1 = 4 kW

Rate of heat transfer by 1 lightbulb = 100 W = 100/1000 = 0.1 kW

Rate of heat transfer by 11 lightbulbs = 11×0.1 = 1.1 kW

Rate of heat transfer to the classroom through the walls and windows = 15000 kJ/h = 15000 kJ/h × 1 h/3600 s = 4.167 kW

Total heat transfer = 4 + 1.1 + 4.167 = 9.267 kW

Cooling capacity of a window air-conditioning unit = 5 kW

Number of air-conditioning units required = 9.267/5 = 2 (to the nearest integer)

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