Solve Peng–Robinson equation of state for Variable Vm

[cenaluc]

I do not find a method to solve this equation for Vm.
Is anybody able to help me? Any guideline/idea would be great!

Thanks!!

Ref:
- See image
- https://en.wikipedia.org/wiki/Cubic_equations_of_state

 

[blamocur]

3 steps:

1. Convert it to a canonic cubic equation
2. Convert from the canonic form to "depressed cubic".
3. Use https://en.wikipedia.org/wiki/Cubic_equation#Cardano's_formula] Cardano's formula [/url].

 

[cenaluc]

3 steps:

1. Convert it to a canonic cubic equation
2. Convert from the canonic form to "depressed cubic".
3. Use https://en.wikipedia.org/wiki/Cubic_equation#Cardano's_formula] Cardano's formula [/url].

Wow thanks for the answer!!!
Basically I shall find the only real solution of "t" and then recalculate the original "x" right??

Something like the image attached

 

[blamocur]

I haven't checked every line, but overall it looks like the right direction. Once you go through the steps you can then plug in the found solution into the equation and see if it holds.
Good luck.

 

[cenaluc]

Thanks a lot, help really appreciated!!