At normal temperature and pressure, air has
a density of 0.001184 g/mL. What is the mass
of air in a room that is 3.71 m by 3.60 m by
2.51 m?
Answer in units of kg
I would change the dimensions to cm, find the volume (371 x 360 x 251) in cubic centimeters, use density to convert to grams, then convert to kg. Remember cubic centimeters (cc) = mL.
To find the mass of air in the room, we can multiply the volume of the room by the density of air.
First, let's calculate the volume of the room. We have the dimensions of length (L), width (W), and height (H) given in meters (m). Using the formula for the volume of a rectangular prism, we have:
Volume = L * W * H
Substituting the given values, we get:
Volume = 3.71 m * 3.60 m * 2.51 m
Calculate the volume:
Volume = 33.48216 m^3
Next, we multiply the volume by the density of air to find the mass:
Mass = Volume * Density
Given that the density of air is 0.001184 g/mL, we need to convert the density to the appropriate units. Since the volume is in cubic meters (m^3), we need to convert the density to grams per cubic meter (g/m^3).
Density in g/m^3 = Density in g/mL * 1000
Density in g/m^3 = 0.001184 g/mL * 1000
Now, we can multiply the volume by the converted density:
Mass = 33.48216 m^3 * 0.001184 g/m^3
Calculate the mass:
Mass = 0.03958514864 kg
Therefore, the mass of air in the room is approximately 0.04 kg.