Question

You are adding a whole house fan to your home. You hope that it will reduce conditioning bills by allowing you to bring in cool outside air in the mornings. (It would also be valuable for ridding your home of unpleasant odors such as smoke, burned onions, or skunk.) You would like to be able to completely replace all the air in your house in 5 minutes. The first floor of your house measures 32' x 75' and has 9' ceilings. The second floor of your house measures 16' x 75' and has 8' ceilings. How much air, in cubic feet per minute, does your new fan need to move?

A) 22,500 cubic feet per minute
B) 45,000 cubic feet per minute
C) 67,500 cubic feet per minute
D) 90,000 cubic feet per minute

Answer 1

The new fan needs to move 6,240 cubic feet per minute to replace all the air in the house in 5 minutes, given the total volume of the house is 31,200 cubic feet.None of the options given (A, B, C or D) match this answer,

Step-by-step explanation:

To calculate how much air, in cubic feet per minute, the new fan needs to move, first determine the volume of the house. For the first floor, the volume can be calculated using the dimensions given: 32' x 75' x 9' ceilings. For the second floor: 16' x 75' x 8' ceilings.

Volume of first floor = 32' x 75' x 9' = 21,600 cubic feet.
Volume of second floor = 16' x 75' x 8' = 9,600 cubic feet.

Total volume of the house = 21,600 + 9,600 = 31,200 cubic feet.

To replace this air in 5 minutes, divide the total volume by 5 minutes:
31,200 cubic feet ÷ 5 minutes = 6,240 cubic feet per minute.

Therefore, the new fan needs to move 6,240 cubic feet per minute. None of the options given (A, B, C or D) match this answer, suggesting there may be a typo or incorrect options provided in the question.