Respuesta :
Explanation:
Formula for compressibility factor is as follows.
z = [tex]\frac{P \times V_{m}}{R \times T}[/tex]
where, z = compressibility factor for helium = 1.0005
P = pressure
[tex]V_{m}[/tex] = molar volume
R = gas constant = 8.31 J/mol.K
T = temperature
So, calculate the molar volume as follows.
[tex]V_{m} = \frac{z \times R \times T}{P}[/tex]
= [tex]\frac{1.0005 \times 8.314 \times 10^{-3} m^{3}.kPa/mol K \times (60 + 273)K}{500 kPa}[/tex]
= 0.0056 [tex]m^{3}/mol[/tex]
As molar mass of helium is 4 g/mol. Hence, calculate specific volume of helium as follows.
[tex]V_{sp} = \frac{V_{m}}{M_{w}}[/tex]
= [tex]\frac{0.0056 m^{3}/mol}{4 g/mol}[/tex]
= 0.00139 [tex]m^{3}/g[/tex]
= 0.00139 [tex]m^{3}/g \times \frac{1 g}{10^{-3}kg}[/tex]
= 1.39 [tex]m^{3}/kg[/tex]
Thus, we can conclude that the specific volume of Helium in given conditions is 1.39 [tex]m^{3}/kg[/tex].
