Respuesta :
Explanation:
It is known that equation for ideal gas is as follows.
PV = nRT
The given data is as follows.
Pressure, P = 1500 psia, Temperature, T = [tex]104^{o}F[/tex] = 104 + 460 = 564 R
Volume, V = 2.4 cubic ft, R = 10.73 [tex]psia ft^{3}/lb mol R[/tex]
Also, we know that number of moles is equal to mass divided by molar mass of the gas.
n = [tex]\frac{mass}{\text{molar mass}}[/tex]
m = [tex]n \times W[/tex]
= [tex]0.594 \times 16.04[/tex]
= 9.54 lb
Hence, molecular weight of the gas is 9.54 lb.
- We will calculate the density as follows.
d = [tex]\frac{PM}{RT}[/tex]
= [tex]\frac{1500 \times 16.04}{10.73 \times 564}[/tex]
= 3.975 [tex]lb/ft^{3}[/tex]
- Now, calculate the specific gravity of the gas as follows.
Specific gravity relative to air = [tex]\frac{\text{density of methane}}{\text{density of air}}[/tex]
= [tex]\frac{3.975 lb/ft^{3}}{0.0765 lb/ft^{3}}[/tex]
= 51.96
