Specific volume: [tex]3.9 ft^3/mol = 0.109 m^3/mol[/tex]
Explanation:
We can solve this problem by applying the equation of state for ideal gases, which states that:
[tex]pV=nRT[/tex]
where
p is the gas pressure
V is the gas volume
n is the number of moles
R is the gas constant
T is the absolute temperature
The equation can be re-arranged as
[tex]V=\frac{nRT}{p}[/tex]
Here we want to find the specific volume, which is the volume of gas per number of moles, so we have to divide by n:
[tex]V_s=\frac{RT}{p}[/tex]
For the gas in this problem, we have:
[tex]p=25.5 psi[/tex] is the pressure
[tex]T=80F[/tex], converting to Kelvin:
[tex]T=(80-32)\cdot \frac{5}{9}+273.15=299.8 K[/tex]
[tex]R=0.3353 psi\cdot ft^3 /(lbmR)[/tex] is the gas constant
Solving for Vs,
[tex]V_s=\frac{(0.3353)(299.8)}{25.5}=3.9 ft^3[/tex]/mol
And since
1 feet = 0.3048 m
[tex](1 feet)^3 = (0.3048 m)^3 = 0.028 m^3[/tex]
Then the specific volume in SI units is
[tex]V_s = 3.9 ft^3 \cdot 0.028 = 0.109 m^3[/tex]/mol
Learn more about ideal gases:
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