Answer to Question #144454 in Molecular Physics | Thermodynamics for Aqib Abdullah

Question

A room designed to house around 54 individuals at once needs a cooling system. The cooling units available in the market have a capacity of 3 kilowatts. Assume that one individual radiates heat at roughly 350 kilojoules per hour. The room also has twelve 100 W bulbs. The room is to be maintained at 20 degree celsius but at this temperature Some 13500 kJ/h amount of heat also enters through the wall. Find the

a. The net heat transfer rate for the room in kW

b. The number of cooling units required

Hint: Some rounding off might be necessary

Answer 1

Number of individuals = 54

1 Individual heat rate = 350kj/hr

54 individuals heat rate = 54(350) = 18900kj/hr

1 bulb = 100W = 360kj/hr

12 bulbs = 12(360) = 4320kj/hr

Amount of heat that enters = 13500kj/hr

Total heat absorbed in the room at 20°C = 18900 + 4320 + 13500 = 36,720kj/hr

a) Net heat transfer rate = 36,720/3600 = 10.2kW

b) 1 cooling unit = 3kW

Number of cooling units needed = 10.2/3 = 3.4 cooling units

$\therefore$ 4kW of cooling units should be bought for the temperature in the room to be around 20°C or a little bit lesser, but 3 cooling units will make the temperature of the room much higher than 20°C since the cooling units won't be enough to keep the temperature low.