Difference between cp and cv - mathematical!

[ratio123]

have written out my question on a picture for you, the first gives the question - the second gives my rough intuition thoughts and why it doesn't work.
Any help will be appreciated! It is to do with thermal physics and the difference between cp and cv for the van der waals equation.
http://dl.dropbox.com/u/48169762/Capture.PNG
http://dl.dropbox.com/u/48169762/Capture3.PNG

Thanks !