Question

A room has dimensions of 15 ft by 15 ft by 20 ft contains air with a density of 0.0724 pounds-mass per cubic feet. The weight of air in the room in pounds-force is

Answer 1

the weight of the air in pound-force (lb-f) is 325.8 lbf

Step-by-step explanation:

Given;

dimension of the room, = 15 ft by 15 ft by 20 ft

density of air in the room, ρ = 0.0724 lbm/ft³

The volume of air in the room is calculated as;

Volume = 15 ft x 15 ft x 20 ft = 4,500 ft³

The mass of the air is calculated as;

mass = density x volume

mass = 0.0724 lbm/ft³ x 4,500 ft³

mass = 325.8 lb-m

The weight of the air is calculated as;

Weight = mass x gravity

Weight = 325.8 lb-m x 32.174 ft/s²

Weight = 10482.29 lbm.ft/s²

The weight of the air in pound-force (lb-f) is calculated as;

1 lbf = 32.174 lbm.ft/s²

`Weight =10,482.29\ lbm.ft/s^2* (1 \ lbf)/(32.174 \ lbm.ft/s^2) \\\\Weight = 325.8 \ lbf`

Therefore, the weight of the air in pound-force (lb-f) is 325.8 lbf