Question

Calculate the specific volume of Helium using the compressibility factor. 500 kPa, 60 degrees Celsius

Answer 1

Step-by-step explanation:

Formula for compressibility factor is as follows.

z =
`(P * V_(m))/(R * T)`

where, z = compressibility factor for helium = 1.0005

P = pressure

`V_(m)` = molar volume

R = gas constant = 8.31 J/mol.K

T = temperature

So, calculate the molar volume as follows.

`V_(m) = (z * R * T)/(P)`

=
`(1.0005 * 8.314 * 10^(-3) m^(3).kPa/mol K * (60 + 273)K)/(500 kPa)`

= 0.0056
`m^(3)/mol`

As molar mass of helium is 4 g/mol. Hence, calculate specific volume of helium as follows.

`V_(sp) = (V_(m))/(M_(w))`

=
`(0.0056 m^(3)/mol)/(4 g/mol)`

= 0.00139
`m^(3)/g`

= 0.00139
`m^(3)/g * (1 g)/(10^(-3)kg)`

= 1.39
`m^(3)/kg`

Thus, we can conclude that the specific volume of Helium in given conditions is 1.39
`m^(3)/kg`.