Thermodynamics Compressibility Factor

[Logan McEntire]

Homework Statement

Please consider ethylene at 152^oF and 126 atm. Please determine the molar volume (ft³/lbmole) if Z is determined by Corresponding States Theory.

Homework Equations

Z=PV_m/R_mT
V_m= Molar volume
R=R_m/M
M= molecular weight
R_m=1545(ft*lbf)/(lbmol*^oR)
Z_c=(P_cv_c)/(R*T_c)
T_c=283 K
P_c=51.2 Bar
M=28.05 Kg/Kmol
P_R=P/P_c

The Attempt at a Solution

I can find V_c but that's not 152 ^oF and 126 atm.
I don't know Z at these conditions either so I can't use the other equation.

 

[Chestermiller]

What is the reduced temperature and the reduced pressure? Do you have a copy of the graph of z as a function of reduced pressure and reduced temperature?

 

[John Park]

I'd imagine that if they say "Z is determined by Corresponding States Theory", that implies it's constant.

 

[Chestermiller]

I'd imagine that if they say "Z is determined by Corresponding States Theory", that implies it's constant.

What does this mean? Actually, z is a function of reduced pressure and reduced temperature. Do you know the definition of these quantities?

 

[John Park]

For an ideal gas (admittedly a long way from the critical point) z is constant as a function of pressure. Closer to the critical point in general it varies with pressure, but that doesn't seem to rule out the possibility that it takes its critical value here. How would you use the statement about Corresponding States Theory?