Estimate the temperature at which 40 kg of ethane stored in a 0.15 m3 vessel exerts a pressure of 20000 kPa.

Question

cpinder · Answer

So far, I've got calculated the volume like this. 

Vt=0.15m3=150000cm3 

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.

aaronq · Answer

Why not just use the ideal gas law?

cpinder · Answer

@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.

PV=ZRT=ZRTrTc
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

aaronq · Answer

Oh okay, you're into real gases now

aaronq · Answer

I can help you with this later, cuz i gotta go. Hopefully someone else capable comes before hand if you need this asap. I'll look back at this question later today

cpinder · Answer

@aaronq just realized I put this in chemistry and not in thermodynamics.