Working out the cp cv difference for van der waals equation

[imagemania]

Homework Statement

I've put all the information on the picture as i already created on there in an attempt to help brain storm some ideas that didn't work ...

http://dl.dropbox.com/u/48169762/Capture.PNG

Homework Equations

All on picture :)
http://dl.dropbox.com/u/48169762/Capture.PNG

The Attempt at a Solution

Working out $\frac{\partial V}{\partial T}$ via its inverse first - but it didn't work (extremly messy given pressure substitutions etc.) - as explainedd on the picture.

Any guidence is much appreciated!

 

[imagemania]

Ok, I've had another look at this problem and I'm still struggling, here's my idea:

[PLAIN]http://dl.dropbox.com/u/48169762/Capture3.PNG