Question

CALCULATING THE VOLUME AND WEIGHT OF THE AIR IN A ROOM

Data
1. Measure and record the length and width of a room that has a flat ceiling at three different locations. Estimate the ceiling height of the room without actually measuring it.
2. Make a guess of the weight of the air in the room and record your guess.
3. Find, using your textbook or an internet search, the density of air in units of kilograms per cubic meter.
4. Create the data table and enter your measurements.

Calculations
1. Calculate the volume of the room in cubic meters
2. Determine the best estimate of the error of this measurement
3. Convert the density of the air you found in kilograms per cubic meter to Newtons per cubic meter by multiplying by g, the acceleration due to gravity, i.e., 9.8 m/s². The density of air kilograms per cubic meter is called a mass density because it is mass divided by volume. The density of air in Newtons per cubic meter is called a weight density because it is weight divided by volume.
4. Calculate the weight of air in the room in Newtons by multiplying the weight density of air you calculated in #3 in Newtons per cubic meter) by the volume of air (in cubic meters) you calculated in #1.
5. Determine the best estimate of the error of this measurement and record the value on the data table.
6. Convert the weight of air in the room that you calculated in #4 from Newtons to pounds and record your result. Does the weight of the air in the room (in pounds) surprise you?

Answer 1

To estimate the volume and weight of air in a room, measure the dimensions, use the density of air (1.25 kg/m³ at sea level) to find the mass, then multiply by 9.8 m/s² to get the weight in Newtons, and convert to pounds.

Step-by-step explanation:

To calculate the volume and weight of air in a room, you must first measure the room's dimensions to determine the volume. Using the approximate density of air at sea level, which is 1.25 kg/m³, you can then estimate the mass by multiplying this density by the room's volume. Remember that the density of air decreases with altitude, so adjust your estimate if necessary.

Once you have the mass, you can calculate the weight by multiplying it by the acceleration due to gravity, 9.8 m/s². To convert the weight from Newtons to pounds, you can use the conversion factor 1 pound = 4.44822 Newtons. Thus, the weight of air in the room can be expressed in pounds.

If we consider a living room with dimensions of 5 m × 5 m × 3 m, using the density of 1.25 kg/m³, the mass of air inside this room would be 93.75 kg (volume of 75 m³ × density of 1.25 kg/m³). The weight of this air mass in Newtons would be approximately 918.75 N (mass of 93.75 kg × 9.8 m/s²), which is equal to about 207 pounds.