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Determine the cooling capacity required for the air conditioner in a classroom with the following conditions:

1. There are 26 people in the room, and each person dissipates heat at a rate of 360 kJ/h.
2. The room is lit with 15 light bulbs, each consuming 40 W.
3. A 200 W fan operates in the room, near a door to a computer closet. This fan pulls warm air into the classroom under the door at a rate of 200 kg/h.
4. The room gains 10 kJ in energy (enthalpy) for each kg of warm air entering.
5. The warm air enters at 10 m/s and leaves the room with negligible velocity through a large vent 3 m above the floor.
6. The room is otherwise well-sealed.
7. The room gains 5,000 kJ/h by heat transfer through the walls and windows.

Calculate the total cooling capacity required for the air conditioner to maintain a comfortable temperature in the classroom.

Answer :

Answer:

The capacity of refrigeration =5.35kw

Explanation:

Total people in classroom =26

One person dissipates =360kj/h

So 26 person will dissipates =360 × 26

=2.6kw

15 light bulb with 40w each

Total heat dissipates 15×40 =600

=0.6kw

Fan will dissipate =200w

=0.2kw

Room gain air at a rate of =200kg/h

Warm air enthalpy =10kj/kg

Total heat coming with warm air = 200×10

0.555kw

Heat coming from window walls =5000kj/h

=5000/3600= 1.388kw

Total heat coming in the room =2.6+0.6+0.2+0.55+1.388

=5.35kw

To maintain room at steady temperature

Heat should be removed at constant rate

Energy balance =energy in/energy out

Capacity of refrigeration =5.35kw

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Rewritten by : Barada

To find the heat transfer rate to warm air by 10.0°C, it's necessary to convert the volume of air to mass, then use the formula Q = mcΔT and find the power by dividing by time.

To determine the heat transfer rate needed to warm air by 10.0°C, you need to know the mass of air being warmed, the specific heat capacity of air, and the desired temperature change. First, you convert the volume of air brought into the room to its mass by using the density of air. Then, you can apply the heat transfer equation Q = mcΔT, where Q is the heat transfer, m is the mass of air, c is the specific heat capacity, and ΔT is the temperature change. The power, which is the rate of heat transfer, is then found by dividing the heat transfer by the time over which it occurs.

Given the volume flow rate of the air and the temperature change, one can calculate the necessary power in kilowatts (kW) to achieve the desired heating effect. Note that the specific heat capacity of air at constant pressure is approximately 1.005 kJ/kg·K.