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 20C on a day when the outside temperature is 35C. 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

Since COP=10, and W=5kW, using the expression Qa/W= COP {whereQa is the thermal load}

So, Qa/5=10

or, Qa= 50kW

Now, thermal load at steady state through the walls and windows at 30,000 kJ/h= 30000/3600 kJ/s= 8.33kW

thermal load from the computers, and lighting at 6,000 kJ/h= 6000/3600 kJ/s= 1.67kW

Now, since Qa= 50kW, the maximum number of people it can accommodate is n, then n*2kW per person +8.33+1.67= 50kW

Or, n*2= 40

or, n= 20 which is comparatively matching with the maximum number of people any a/c unit, operating under the same conditions and consuming the same amount of power, can accommodate

so, maximum 20 number of people it can accommodate.

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