How Do You Prove Thermodynamic Equations for Van der Waals Gas?

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SUMMARY

The discussion focuses on proving thermodynamic equations for Van der Waals gas, specifically addressing the relationship between internal energy (U), enthalpy (H), heat capacities (Cp and Cv), and the adiabatic index (γ). Participants suggest using the equations U=f(T,V) and H=f(T,P) to derive the necessary relationships. The conversation emphasizes the need for relevant equations, directing users to resources such as the Wikipedia page on Van der Waals gas for additional information.

PREREQUISITES
  • Understanding of thermodynamic concepts such as internal energy and enthalpy
  • Familiarity with heat capacities Cp and Cv
  • Knowledge of the Van der Waals equation of state
  • Basic calculus for deriving relationships between variables
NEXT STEPS
  • Study the Van der Waals equation of state in detail
  • Learn how to derive heat capacities Cp and Cv for real gases
  • Explore the concept of the adiabatic index (γ) and its significance
  • Review thermodynamic identities and their applications in real gas behavior
USEFUL FOR

Students and researchers in thermodynamics, particularly those studying real gas behavior and the Van der Waals equation, as well as educators looking for resources to teach these concepts.

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Homework Statement


The question c) I have attached. Capture th.PNG (27.7 KB)
Capture th2.PNG (14.8 KB)

Homework Equations





The Attempt at a Solution


Use U=f(T,V) and H=f(T,P), then get Cp and Cv, so I can get gamma.
then k=(1/v)(dv/dt)
but I still can't prove it.
 

Attachments

  • Capture th.PNG
    Capture th.PNG
    13.7 KB · Views: 470
  • Capture th2.PNG
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