Answer :
To determine the specific weight of the gas, we need to know the relationship between density and specific weight. Specific weight (also known as weight density) is defined as the weight of a substance per unit volume.
The formula for specific weight, [tex]\gamma[/tex], is:
[tex]\gamma = \rho \cdot g[/tex]
where:
- [tex]\gamma[/tex] is the specific weight,
- [tex]\rho[/tex] is the density of the substance,
- [tex]g[/tex] is the acceleration due to gravity.
In this problem, the density [tex]\rho[/tex] is given as [tex]0.003[/tex] slugs per cubic foot, and the standard acceleration due to gravity [tex]g[/tex] is [tex]32.2[/tex] feet per second squared (ft/s²).
First, we convert the density from slugs per cubic foot to kilograms per cubic meter (kg/m³) because specific weight is often preferred in SI units:
- 1 slug = 14.5939 kg
- 1 cubic foot = 0.0283168 cubic meters
Converted density [tex]\rho[/tex] in kg/m³:
[tex]\rho = 0.003 \text{ slugs/ft}^3 \times \frac{14.5939 \text{ kg}}{1 \text{ slug}} \times \frac{1 \text{ ft}^3}{0.0283168 \text{ m}^3} \approx 1.554 \text{ kg/m}^3[/tex]
Now, calculate specific weight in newtons per cubic meter (N/m³) using SI units for [tex]g[/tex]:
[tex]g = 9.81 \text{ m/s}^2[/tex]
[tex]\gamma = 1.554 \text{ kg/m}^3 \times 9.81 \text{ m/s}^2 \approx 15.25 \text{ N/m}^3[/tex]
Thus, the specific weight of the gas is approximately [tex]15.2 \text{ N/m}^3[/tex], which corresponds to option B.
Therefore, the correct answer is:
[tex]\text{B. } 15.2 \text{ N/cu. m.}[/tex]
