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

AI Thread Summary
To prove thermodynamic equations for a Van der Waals gas, it's essential to start with the internal energy (U) as a function of temperature (T) and volume (V), and enthalpy (H) as a function of temperature (T) and pressure (P). The specific heat capacities, Cp and Cv, are critical for deriving the ratio gamma. The user suggests using the relationship k = (1/v)(dv/dt) but struggles to prove it, indicating the need for additional relevant equations. Reference to external resources, such as Wikipedia on Van der Waals gas, is recommended for further assistance. Understanding these relationships is key to solving the problem effectively.
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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.
 

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