Solve Van der Waals Gas Homework: a) & b)

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Homework Help Overview

The discussion revolves around the thermodynamic properties of gases, specifically focusing on the relationship between heat capacities for ideal and Van der Waals gases. The original poster is tasked with demonstrating a relationship for an ideal gas and then deducing a similar relationship for a Van der Waals gas.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster describes their approach to part a) using the ideal gas equation and partial derivatives to arrive at the relationship Cpm - Cvm = R. They express uncertainty about how to approach part b) regarding the Van der Waals gas.
  • Some participants suggest evaluating the partial derivatives in the context of the Van der Waals equation and consider the implications of the triple product rule.
  • There is a question about whether the same method used for the ideal gas can be applied to the Van der Waals gas.

Discussion Status

The discussion is ongoing, with participants exploring different methods and interpretations. Some guidance has been provided regarding the evaluation of partial derivatives and the application of the Van der Waals equation, but no consensus or resolution has been reached yet.

Contextual Notes

The original poster has successfully completed part a) but is struggling with part b). There is an emphasis on including all parameters except for pressure in the final answer for part b), which may complicate the approach.

krootox217
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Homework Statement


Hi, I have the following task:
43921_adfda.JPG


Translated into English, that means:

" For Cpm and Cvm of gases the following relationship is true: (1)
a) Show with the relationship (1), that for an ideal gas Cpm - Cvm = R is valid
b) Deduce from equation (1) and the tripple product rule Cpm - Cvm for a Van der Waals gas (dependent on Vm, T and also R, a and b)"

I managed to solve a) but I don't know how to solve b)
Can someone help me?

Homework Equations


Tripple product rule: https://en.wikipedia.org/wiki/Triple_product_rule
Van der Waals equation: https://de.wikipedia.org/wiki/Van-der-Waals-Gleichung

The Attempt at a Solution


see above
 
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Show us what you did so far, please. That way we can better help you.

Chet
 
For a) I used p*Vm=RT

then I solved the equation once for p and once for Vm, and did the partial derivatives, which yielded T*(R/p)*(R/Vm) = Cpm- Cvm = (T*R2)/(p*Vm)

and then I said p*Vm=R*T and i reduced the fraction, which yielded Cpm- Cvm = R

But I don't understand how to start in the second task, could you help me?
 
I would start out by evaluating each of the partial derivatives in Eqn. 1 and see what I get. If that doesn't give me what I'm looking for, I would start thinking about ways in which the triple product rule might get me to where I want to be. Maybe you're going to have to "play with the math" at little.

Chet
 
Did I understand you correctly that I should do the same as in a), but this time not with the ideal gas equation, but with the van der waals equation?
 
krootox217 said:
Did I understand you correctly that I should do the same as in a), but this time not with the ideal gas equation, but with the van der waals equation?
Sure. The problem statement indicates that the final answer should include all the parameters except for P. To me, this means that the first partial derivative in Eqn. 1 might be troublesome. See how it all plays out. Start by evaluating the two partial derivatives in equation 1 based on the van der waals equation.
 
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Ok, thanks a lot! :)
 

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