The density of dry air is 1.12 X 10-3 g/cm3.
(a) What volume of air in cubic meters will have a mass of 1.00kg?
(b) Express this density as lb/ft3.
there are (10^2 )^3 = 10^6 cm^3 / m^3
there are 10^3 g / kg
so
m = 1 kg = V m^3 * 1.12 X 10-3 g/cm3 * 10^-3 kg/g * 10^6 cm^3/m^3
1 = V * 1.12
V = 0.89 m^3
or
1.12 * 10^3 g / m^3 = 1.12 kg/m^3
Now you do the pounds and feet
Do b for me.
To solve part (a) of the question, we need to find the volume of air in cubic meters that will have a mass of 1.00 kg. We're given the density of dry air, which is 1.12 x 10^-3 g/cm^3.
To find the volume, we can use the formula:
density = mass / volume
First, we need to convert the mass from kilograms to grams, because the density is given in grams per cubic centimeter.
1.00 kg = 1000 grams
Now let's rearrange the formula to solve for volume:
volume = mass / density
Substituting the values into the formula:
volume = 1000 grams / 1.12 x 10^-3 g/cm^3
To cancel out the units, we divide the mass in grams by the density:
volume = (1000 grams) / (1.12 x 10^-3 g/cm^3)
Now we can simplify:
volume ≈ 892,857 cm^3
But the question asks for the volume in cubic meters, not cubic centimeters. To convert, we need to remember that 1 cm^3 is equal to 10^-6 m^3.
volume = 892,857 cm^3 x (1 m^3 / 10^6 cm^3)
Simplifying further:
volume ≈ 0.892857 m^3
Thus, the volume of air in cubic meters that will have a mass of 1.00 kg is approximately 0.892857 m^3.
Now let's move on to part (b), where we need to express the density of air as lb/ft^3.
To convert the density from g/cm^3 to lb/ft^3, we'll need to use conversion factors. Here are the steps:
First, let's convert grams to pounds. There are 453.592 grams in a pound.
density in lb/ft^3 = density in g/cm^3 x (1 lb / 453.592 g) x (1 m^3 / 35.3147 ft^3) x (100 cm / 1 m)^3
Substituting the given density value:
density in lb/ft^3 ≈ 1.12 x 10^-3 g/cm^3 x (1 lb / 453.592 g) x (1 m^3 / 35.3147 ft^3) x (100 cm / 1 m)^3
Simplifying:
density in lb/ft^3 ≈ 0.07649 lb/ft^3
Therefore, the density of dry air is approximately 0.07649 lb/ft^3.