Find thermal capacity of a Van der Waals gas

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Finding the thermal capacities \(C_P\) and \(C_V\) for a Van der Waals gas is challenging due to insufficient information about internal energy \(U\) or entropy \(S\). The equations provided in textbooks do not suffice to derive these capacities without additional details about the gas. It is suggested that \(C_V\) can be assumed to be the same as that of an ideal gas, as it does not depend on volume. To proceed, one can either derive relationships in terms of the compressibility factor \(\beta\), reference literature for internal energy, or postulate \(C_V\) based on ideal gas behavior. Ultimately, the problem remains incomplete without specific information about the gas's properties.
  • #31
MatinSAR said:
So for showing that ##[\frac {\partial C_V} {\partial V}]_T=0## I can use the link you've sahred ...
So do you see any other problem in my final answer?
Your argument goes like this:
  1. Assume (or prove) that ##C_V## does not depend on the volume
  2. Use the equation of state to derive the rhs of Mayer's relation
  3. Assume ##C_V=\frac32nR##
  4. Insert (3) in Mayer's relation
However step 1 was not needed.
 
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  • #32
pines-demon said:
Your argument goes like this:
  1. Assume (or prove) that ##C_V## does not depend on the volume
  2. Use the equation of state to derive the rhs of Mayer's relation
  3. Assume ##C_V=\frac32nR##
  4. Insert (3) in Mayer's relation
However step 1 was not needed.
Thanks again for your time @pines-demon ...
 
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