To find the volume of air with a mass of 1.00 kg using the given density, we can use the formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Rearranging this gives us:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
(a) First, we need to convert the density from \( g/cm^3 \) to \( kg/m^3 \).
Given the density of dry air: \[ 1.12 \times 10^{-3} , g/cm^3 \]
We know:
- \( 1 , g/cm^3 = 1000 , kg/m^3 \)
So, \[ 1.12 \times 10^{-3} , g/cm^3 = 1.12 \times 10^{-3} \times 1000 , kg/m^3 = 1.12 , kg/m^3 \]
Now we can calculate the volume for a mass of 1.00 kg:
\[ \text{Volume} = \frac{1.00 , kg}{1.12 , kg/m^3} \approx 0.892857 , m^3 \]
Thus, the volume of air that will have a mass of 1.00 kg is approximately:
\[ \boxed{0.8929 , m^3} \]
(b) Now let's convert the density from \( kg/m^3 \) to \( lb/ft^3 \).
We know the following conversions:
- \( 1 , kg \approx 2.20462 , lb \)
- \( 1 , m^3 = 35.3147 , ft^3 \)
Using the density \( 1.12 , kg/m^3 \):
First, convert kilograms to pounds: \[ 1.12 , kg/m^3 \times 2.20462 , lb/kg \approx 2.464 , lb/m^3 \]
Next, convert from \( m^3 \) to \( ft^3 \): \[ \text{Density in } lb/ft^3 = \frac{2.464 , lb/m^3}{35.3147 , ft^3/m^3} \approx 0.0698 , lb/ft^3 \]
Therefore, the density in \( lb/ft^3 \) is approximately:
\[ \boxed{0.0698 , lb/ft^3} \]