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Consider an office room that is being cooled by a 14,000 Btu/h window air conditioner. It is now decided to convert this room into a computer room by installing several computers, terminals, and printers with a total rated power of 8.5 kW. The facility has several 6,000 Btu/h air conditioners in storage that can be installed to meet the additional cooling requirements.

Assume:
- A usage factor of 0.5 (i.e., only 50% of the rated power will be consumed at any given time).
- Additional occupancy of eight people, each generating heat at a rate of 125 W.

Determine how many of these air conditioners need to be installed in the room.

(1 W = 3.412 Btu/h)

A) 2
B) 3
C) 4
D) 5

Answer :

After calculating the heat generated by the computers and occupancy and adding the existing cooling requirement, we find that 5 air conditioners of 6000 Btu/h are needed to cool the new computer room. Hence, option d) is correct.

To determine how many 6000 Btu/h air conditioners are needed to cool the new computer room, we need to calculate the total heat load generated by the computers, printers, and additional occupancy, and then divide that by the cooling capacity of each air conditioner available.

Firstly, for the computers and printers:
Power consumed = Total rated power times usage factor = 8.5 kW times 0.5 = 4.25 kW.
Converting this power to Btu/h using 1 W = 3.412 Btu/h:
Heat generated by computers = 4.25 kW times 1000 W/kW times 3.412 Btu/h/W = 14491 Btu/h.

Next, for the occupancy of eight people:
Heat generated = Number of people times Heat per person = 8 times 125 W/person = 1000 W.
Converting this to Btu/h:
Heat generated by people = 1000 W times 3.412 Btu/h/W = 3412 Btu/h.

Adding the existing cooling requirement (14,000 Btu/h), the computers and printers (14491 Btu/h), and the additional occupancy (3412 Btu/h), we get the total new cooling requirement:
Total cooling required = 14,000 Btu/h + 14491 Btu/h + 3412 Btu/h = 29903 Btu/h.

To find out how many 6000 Btu/h air conditioners are needed, we divide the total cooling requirement by the capacity of one air conditioner:
Number of air conditioners = Total cooling required / Capacity of each air conditioner = 29903 Btu/h / 6000 Btu/h ≈ 5.

Therefore, 5 air conditioners of 6000 Btu/h are needed to adequately cool the new computer room.

Hence, option d) is correct.

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