Question

A room has a width of 14.1 feet, a length of 15.5 feet, and a ceiling height of 12.0 ft. If the density of dry air is 1.28 kg/m³, then what is the mass of the air in the room that the air conditioning unit has to move?

Answer 1

The mass of the air in the room is approximately 95.14 kg, which is the amount of air the air conditioning unit must move.

Step-by-step explanation:

To calculate the mass of the air in the room, we need to first determine the volume of the room in cubic meters and then multiply that by the density of the air.

The room's dimensions are given in feet, so we must convert them to meters (1 foot = 0.3048 meters):

• Width: 14.1 feet * 0.3048 = 4.29888 meters
• Length: 15.5 feet * 0.3048 = 4.7244 meters
• Height: 12.0 feet * 0.3048 = 3.6576 meters

Now, we'll calculate the volume:

Volume = Width * Length * Height

= 4.29888 meters * 4.7244 meters * 3.6576 meters

= 74.331057152 cubic meters

Given the density of dry air is 1.28 kg/m³, the mass of the air in the room is:

Mass = Density * Volume

= 1.28 kg/m³ * 74.331057152 m³

= 95.14359315456 kilograms

The air conditioning unit would need to move approximately 95.14 kg of air.