I am a little worried that our classroom will be too hot lat

I am a little worried that our classroom will be too hot late in the spring and want to know now, so proper steps can be taken to make sure the room is comfortable. You can help by performing the energy balance of a full classroom. We have about 36 people in our class (including the instructor). The building is cooled by air conditioning units that provide 4 kw of colling capacity. Each person dissipates about 350 kJ/h. There are about 30 light bulbs in the room, each with a rating of about 40 W. The rate of heat transfer through the walls and windows to the room will probably be around 16,000 kJ/h on an average spring day. Determine the total number of air conditioning units needed to maintain the room at 22 degreeC

Solution

The heat released by the hot bodies in the room must be equal to the heat absorbed by the air conditioner , this is the condition for the room to stay at a constant temperatire is 22C

lets find the total heat released by all the hot bodies

heat released by 36 persons Q1 = 36 * 350 kJ / h

to find the heat relesed in second

                                    = 36 * 350 kJ / 60 *60 = 3.5 k W

heat emitted by 30 light bulbs Q2 = 30 * 40 W = 1200 W

heat transfer through wall and windows Q3 = 16000 kJ/ h       (1hour = 60*60 seconds)

to convert into kW                     = 16000 kJ / 60 *60    = 4.445 kW

total heat emission Qt = Q1 +Q2 +Q3 = 3500+ 1200+4445 = 9175 W

cooling capacity = 4000 W / AC

number of AC needed to keep the room at constant temperature N = total heat emission / 4000

                                           N = 9175 / 4000 = 2.293 > 2 ; 2 AC are not sufficinet even they work at full capacity

                                      hence minimum 3 air conditioners are needed on an average spring day.