Working out the cp cv difference for van der waals equation

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SUMMARY

The discussion focuses on calculating the difference between the heat capacities at constant pressure (cp) and constant volume (cv) in the context of the van der Waals equation. The user attempts to derive the partial derivative of volume with respect to temperature, \(\frac{\partial V}{\partial T}\), but encounters difficulties due to complex pressure substitutions. The user seeks guidance on resolving these issues and clarifying the relationship between cp and cv in non-ideal gas scenarios.

PREREQUISITES
  • Understanding of the van der Waals equation of state
  • Familiarity with thermodynamic concepts of heat capacity
  • Knowledge of partial derivatives in calculus
  • Ability to interpret graphical representations of equations
NEXT STEPS
  • Study the derivation of the van der Waals equation and its implications for real gases
  • Learn about the relationship between cp and cv for non-ideal gases
  • Explore methods for calculating partial derivatives in thermodynamic contexts
  • Review examples of heat capacity calculations in thermodynamics
USEFUL FOR

Students and professionals in thermodynamics, particularly those studying real gas behavior and heat capacity differences, will benefit from this discussion.

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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!
 
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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
 
Last edited by a moderator:

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