How to Compute Work Using Peng Robinson EOS for Mercury Compression?

[HoopsNut 4L]

Homework Statement

Vapor mercury is to be adiabatically and reversibly compressed from 0.1 MPa to 10 MPa in a
continuous process. Compute the work required in Joules per mole.

Properties of Mercury

Tc =1735 K, Pc =161 MPa.

ω=-0.1644, CP/R =2.5

Homework Equations

The Peng Robinson Equation of State...(see attached file)

work=delta(H)

H=Cp*delta(T)

(Cp/R)*R= Cp

R=8.314

The Attempt at a Solution

I'm having trouble getting started. I think I need to solve PREOS for the T to find the change in T. But that can't be all because I still don't know the density. So that's one equation and twp unknown. On top of that, I have Pc, Tc rather than T and P. If I don't have Tr I can't find those.

It must be rather apparent that I need some serious help. If anyone can help get me on the right track I would appreciate it very much.

Thanks in advance.

 

[Valkarie]

Peng Robinson Equation of StateP=RT/V-a*(1-Tr^0.5)/(V^2)+ b*(1-Tr^0.5)/V^3wherea= 0.45724*R^2*Tc^2.5/Pcb= 0.07780*R*Tc^1.5/Pc