The density of air is 1.12 x 10-3 g/cm3.
a) what volume of air in cubic meters will have a mess of 1.00kg
b)express this density as lb/ft3.
(a) mass = density*volume, so
1.00 g = 1.12*10^-3 v
v = 0.8928g * 10^3 cm^3 * 1kg/1000g * (1m/100cm)^3
= 0.8928 * 10^-6 m^3
(b) 1.12 * 10^-3 g/cm^3 * 1lb/453.592g * (1ft/30.48cm)^3 = 8.72 * 10^-11 lb/ft^3
Express the density as lb/ft3.
a) To find the volume of air in cubic meters that will have a mass of 1.00 kg, we can use the formula:
Density = Mass / Volume
Given:
Density of air = 1.12 x 10^(-3) g/cm3 (Remember to convert to kg/m3)
Mass = 1.00 kg
First, let's convert the density from grams per cubic centimeter (g/cm3) to kilograms per cubic meter (kg/m3):
1 g/cm3 = 1000 kg/m3 (Since there are 1000 grams in a kilogram and 1 cm3 = (0.01 m)3 = 0.000001 m3)
So, the density of air is 1.12 x 10^(-3) * 1000 = 1.12 kg/m3
Now, let's rearrange the formula to solve for volume:
Volume = Mass / Density
Volume = 1.00 kg / 1.12 kg/m3
Volume = 0.89285714 m3 (rounded to 8 decimal places)
Therefore, the volume of air in cubic meters that will have a mass of 1.00 kg is approximately 0.8929 m3.
b) To express the density as pounds per cubic foot (lb/ft3), we need to convert the units again.
1 kg/m3 = 0.06242796 lb/ft3 (approximately)
So, the density of air in lb/ft3 is approximately:
1.12 kg/m3 * 0.06242796 lb/ft3 = 0.069976 lb/ft3 (rounded to 6 decimal places)
Therefore, the density of air is approximately 0.069976 lb/ft3.
To find the volume of air that has a mass of 1.00 kg, we can use the formula:
Density = Mass / Volume
a) Volume of air with a mass of 1.00 kg in cubic meters:
Rearranging the formula, we have:
Volume = Mass / Density
Given mass = 1.00 kg and density = 1.12 x 10^-3 g/cm^3, we need to convert the density to kg/m^3 before calculation:
1.12 x 10^-3 g/cm^3 = 1.12 x 10^-6 kg/cm^3
Now we can calculate the volume:
Volume = 1.00 kg / (1.12 x 10^-6 kg/cm^3)
To convert cm^3 to m^3, we need to divide by 10^6:
Volume = (1.00 kg / (1.12 x 10^-6 kg/cm^3)) / 10^6
Simplifying the expression:
Volume = 1.00 x 10^6 cm^3 / 1.12
Finally, converting cm^3 to m^3:
Volume = (1.00 x 10^6) / (1.12 x 10^6) m^3
Cancelling out the common factor of 10^6:
Volume = 0.8929 m^3
Therefore, the volume of air with a mass of 1.00 kg is approximately 0.8929 cubic meters.
b) Expressing this density as lb/ft^3:
To convert the density from kg/m^3 to lb/ft^3, we need to apply the following conversion factors:
1 kg = 2.20462 lb
1 m = 3.28084 ft
First, convert the density from kg/m^3 to lb/m^3 by multiplying by the conversion factor:
Density_lb/m^3 = Density_kg/m^3 * (2.20462 lb / 1 kg)
Density_lb/m^3 = 1.12 x 10^-3 g/cm^3 * (2.20462 lb / 1 kg)
Next, convert the density from lb/m^3 to lb/ft^3 by dividing by the conversion factor of the cubic feet:
Density_lb/ft^3 = Density_lb/m^3 / (3.28084 ft)^3
Density_lb/ft^3 = (1.12 x 10^-3 g/cm^3 * (2.20462 lb / 1 kg)) / (3.28084 ft)^3
Simplifying the expression:
Density_lb/ft^3 = 0.0807 lb/ft^3
Therefore, the density of air can be expressed as approximately 0.0807 lb/ft^3.