Installing AC Units
A classroom that normally contains 40 people is to be air-conditioned with window AC units that have a 5-kW cooling capacity. A person at rest may be assumed to dissipate heat at a rate of 360 kJ/h. There are 10 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 AC units required.
Expand Hint
Assuming there is no other heat dissipating equipment like computers, TVs, etc in the room, the total cooling load is determined from:
$$$\dot{Q}_{cooling}=\dot{Q}_{lights}+\dot{Q}_{people}+\dot{Q}_{heat\:gain}$$$
Hint 2
The number of air-conditioning units needed is:
$$$\frac{\dot{Q}_{cooling}}{cooling\:capacity}$$$
Assuming there is no other heat dissipating equipment like computers, TVs, etc in the room, the total cooling load is determined from:
$$$\dot{Q}_{cooling}=\dot{Q}_{lights}+\dot{Q}_{people}+\dot{Q}_{heat\:gain}$$$
where
$$$\dot{Q}_{lights}=10\times 100\:W=1\:kW$$$
$$$\dot{Q}_{people}=40\times 360\:kJ/h=4\:kW$$$
$$$\dot{Q}_{heat\:gain}=15,000\:kJ/h=4.17\:kW$$$
Substituting,
$$$\dot{Q}_{cooling}=1+4+4.17=9.17\:kW$$$
Thus, the number of air-conditioning units needed is:
$$$\frac{9.17\:kW}{5\:kW/unit}=1.83\rightarrow 2\:units$$$
2 units
Time Analysis
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