Estimate the temperature at which 40 kg of ethane stored in a 0.15 m3 vessel exerts a pressure of 20000 kPa.
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So far, I've got calculated the volume like this.
V=V/MW=150000cm3/(40kg*30mol/kg) = 112500 cm3/mol
And I've calculated Pr like so.
Pr=P/Pc= (20000 kPa*.01 bar/kPa) / 48.72 bar = 4.105
I'm lost from here.
Why not just use the ideal gas law?
@aaronq we can't use the ideal gas law because this is a non ideal gas. It has a compressibility factor of z, which we don't know.
I'm looking at the solution manual right now and this is what it says.
Tr=alpha/Z where alpha=PVR/Tc alpha=29.548mol/kg (Tried to get this but I couldn't)
whence Tr=0.889/Z at Pr=P/Pc (I've calculated Pr already)
This equation giving Tr as a function of Z and eq (3.57) in conjunction with tables E3 and E4 are two relations in the same variables which must be satisfied at the given reduced pressure. The intersection of these two relations can be found by one means or another to occur at about:
Tr=1.283 and Z=0.693
From there, T=TrTc=391.7K or 118.5C