Question

Suppose your dorm room is 11 ft wide by 12 ft long by 8.5 ft high and has an air conditioner that 

exchanges air at a rate of 1200 L/min. How long would it take the air conditioner to exchange

the air in your room once?

Answer 1

Dimensions of door room is

$12 \;ft \times 11 \; ft \times 8.5 \;ft$

Length of the door room is 12 ft.

Width of the door room is 11 ft.

Height of the door room is 8.5 ft.

Expression for the volume is as follows:

$Volume = Length \times Width \times Height$

Substitute the values of length, width, and height volume of the room in the 1st expression to calculate the volume of the room.

$Volume = Length \times Width \times Height \\ = 12 \;ft \times 111 \times ft \times 8.5 \;ft \\ = 1122 \;ft^3 \\ = 1.122 \times 10^3 \;ft^3 \times (\frac{12 \;in}{1 \;ft})^3 \times (\frac{2.54 \;cm}{1 \;in})^3 \\ = 3.177 \times 10^7 \;cm^3 \\ ≈3.2 \times 10^7 \;cm^3$

Therefore, volume of thedoor room is $3.2 \times 10^7 \;cm^3.$

Since air occupies the volume available to it, volume air will be the volume of the room.

Volume of the air is $3.2 \times 10^7 \;cm^3.$

Relationship between the cubic centimeters and liters is as follows:

1 L= 1000 cm³

Multiply the volume of air in cubic centimeters with the conversion factor

$(\frac{1 \;L}{1000 \;cm^3})$

obtained from the equality statement to calculate the volume of air in liters.

$3.2 \times 10^7 \;cm^3 \times \frac{1 \;L}{1000 \;cm^3} = 3.2 \times 10^4 \;L$

Therefore, the volume of air in liters is $3.2 \times 10^4 \;L.$

Volume of air available in the room is $3.2 \times 10^4 \;L.$

Rate at which the air condition exchanges the air is 1200 L/min.

Equality statement obtained from the rate of exchange of air is as follows:

1 min = 1200 L

Multiply the volume of air available in the room with the conversion factor

$(\frac{1 \;min}{1200 \;L})$

obtained from the rate at which the air condition exchanges the air to calculate the time taken by air conditioner to exchange the air available in the room.

$3.2 \times 10^4 \;L \times \frac{1 \;min}{1200 \;L} = 26.7 \;min ≈ 27 \;min$

Therefore, the time took by the air conditioner to exchange the air available in the room is 27 min.