1 out of 3 attempts As A classroom that normally contains 33 people is to be air
ID: 701475 • Letter: 1
Question
1 out of 3 attempts As A classroom that normally contains 33 people is to be air-conditioned with window air-conditioning units of 5.0-kW cooling capacity. A person at rest may be assumed to dissipate heat at a rate of about 410 kJ/h. There are 15 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 13,500 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 unitsExplanation / Answer
Answer is 2 units.
In this problem, we define the system to be the air in the room. We can assume that the air behaves as an ideal gas. If the temperature remains constant, there is no change in the internal energy of the air. Since the volume of the room remains constant, there is no work done. Thus the first law reduces to the equation that Q = 0. We account for the different heat sources in the total heat rate, Q, as follows. The heat input comes (a) from the 33 students, Qs = (33 people)(410 kJ/h•person)(kW•s /kJ)(h/3600 s) = 3.76 kW, (b) heat transfer through the wall, Qw = (13,500 kJ/h)(kW/kJ•s)(h/3600 s) =3.75 kW, and (c) heat added by the light bulbs, Qb = 15(100 W) = 1500 W = 1.5 kW. Thus the total heat input is 3.76 + 3.5 + 1.5 = 9.01 kW. The heat removal comes from the air conditioners which remove 5 kW each. Thus for the net Q to be zero we must have N air conditioners such that (5 kW)N = 9.01 kW. To satisfy this requirement, we must have two air conditioning units.
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