Van der Waals Equation, Virial Expansion

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Homework Help Overview

The discussion revolves around the Van der Waals equation and its representation in the context of thermal physics. Participants are examining the correctness of the equation and its algebraic formulation.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the accuracy of the Van der Waals equation as presented in the source material, specifically regarding the signs and dimensional correctness of the terms involved. There is a focus on identifying potential algebraic mistakes in the equations provided.

Discussion Status

Several participants have pointed out what they perceive to be errors in the algebraic formulation of the Van der Waals equation. There is an ongoing examination of the equations, with some participants agreeing on the presence of mistakes while others are analyzing specific terms for correctness.

Contextual Notes

Participants are working from a specific textbook reference, which may impose constraints on their interpretations and the equations they are discussing. The discussion reflects a collaborative effort to clarify the mathematical representation of the Van der Waals equation.

unscientific
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Homework Statement



Taken from Concepts in thermal Physics:

depeu8.png

Homework Equations


The Attempt at a Solution



Shouldn't the van der waal's equation be:

p = \frac{RT}{V_m -b} - \frac{a}{V_m^2}
pV_m = \frac{VRT}{V_m -b} - \frac{a}{V_m}
 
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unscientific said:
Shouldn't the van der waal's equation be:

p = \frac{RT}{V_m -b} - \frac{a}{V_m^2}

Yes. So (26.41) has a wrong sign. But it looks like they got it right in (26.42) and (26.43).
 
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unscientific said:

Homework Statement



Taken from Concepts in thermal Physics:

depeu8.png



Homework Equations





The Attempt at a Solution



Shouldn't the van der waal's equation be:

p = \frac{RT}{V_m -b} - \frac{a}{V_m^2}
pV_m = \frac{VRT}{V_m -b} - \frac{a}{V_m}

You're right. It sure looks like they made a slew of algebra mistakes. The first term on the right hand side of 26.41 isn't even dimensionally correct.

Chet
 
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Chestermiller said:
You're right. It sure looks like they made a slew of algebra mistakes. The first term on the right hand side of 26.41 isn't even dimensionally correct.

Chet


Right. I didn't notice that they should not have had the factor of V on the left side of equation 26.41.
 

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