Rooms with floor areas of up to 15 m² are cooled adequately by window air conditioners whose cooling capacity is 5000 Btu/h. Assuming the COP (Coefficient of Performance) of the air conditioner is 3.5, determine the rate of heat gain of the room, in Btu/h, when the air conditioner is running continuously to maintain a constant room temperature.

Question

05-12-2024
Physics

High School

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Rooms with floor areas of up to 15 m² are cooled adequately by window air conditioners whose cooling capacity is 5000 Btu/h. Assuming the COP (Coefficient of Performance) of the air conditioner is 3.5, determine the rate of heat gain of the room, in Btu/h, when the air conditioner is running continuously to maintain a constant room temperature.

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nida00ira nida00ira · Answer 1 · 2023-10-19T02:45:24-04:00

The rate of heat gain of the room, when the air conditioner is running continuously, is approximately 3571.5 Btu/h, given a cooling capacity of 5000 Btu/h and COP of 3.5.

To determine the rate of heat gain of the room when the air conditioner is running continuously, we can use the concept of Coefficient of Performance (COP) and the formula:

[tex]\[ \text{Heat gain rate} = \text{Cooling capacity} \times \left(1 - \frac{1}{\text{COP}}\right) \][/tex]

Given:

- Cooling capacity of the air conditioner = 5000 Btu/h

- COP of the air conditioner = 3.5

Substitute the given values into the formula:

[tex]\[ \text{Heat gain rate} = 5000 \times \left(1 - \frac{1}{3.5}\right) \][/tex]

[tex]\[ \text{Heat gain rate} = 5000 \times \left(1 - 0.2857\right) \][/tex]

[tex]\[ \text{Heat gain rate} = 5000 \times 0.7143 \][/tex]

[tex]\[ \text{Heat gain rate} = 3571.5 \, \text{Btu/h} \][/tex]

Therefore, the rate of heat gain of the room, in Btu/h, when the air conditioner is running continuously to maintain a constant room temperature, is approximately 3571.5 Btu/h.