An air conditioning unit having a coefficient of performance of 10, maintains a

Question

An air conditioning unit having a coefficient of performance of 10, maintains a computer laboratory at 20'C on a day when the outside temperature is 35'C. The thermal load at steady state consists of energy entering through the walls and windows at a rate of 30,000 kJ/h, from the computers, and lighting at a rate of 6,000 kJ/h and from the occupants at the rate of 2kW per person. If the a/c unit consumes 5kW of power, determine the maximum number of people it can accommodate and compare this with the maximum number of people any a/c unit, operating under the same conditions and consuming the same amount of power, can accommodate.

Explanation / Answer

Let M is the number of people the machine can accomodate.

So the thermal load through wall etc. =30000kwlhr = 30000/3600 = 8.333 kw

Computer and lighting = 6000 = 6000/3600 = 1.667 kw

So total load = 2M +8.333+1.667 = 2M+10

Now AC consume 5 kw power

So AC delivered = CoF *power that AC consumed

                                = 5X10 = 50 kw of power

Hence 2M+10 = 50

Or, M = 20

This AC can accommodate maximum 20 no of people.

Usually the standard CoF of the AC machine is 5 to 8. So under the same condition the machine can accommodate 10 number of people.

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