Van der Waals Equation, Virial Expansion

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unscientific
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Homework Statement



Taken from Concepts in thermal Physics:

Textbook page showing the van der Waals equation (p + a/V_m^2)(V_m - b) = RT as equation 26.10, the virial expansion pV_m/RT = 1 + B/V_m + C/V_m^2 + ... as 26.40, and Example 26.2 with derivation steps through equations 26.41 to 26.43 defining B(T) = b - a/RT.

Homework Equations


The Attempt at a Solution



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

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

[tex]p = \frac{RT}{V_m -b} - \frac{a}{V_m^2}[/tex]

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:

Textbook page showing the van der Waals equation (p + a/V_m^2)(V_m - b) = RT (26.10), the virial expansion pV_m/RT = 1 + B/V_m + C/V_m^2 + ... (26.40), and Example 26.2 with derivation steps (26.41) to (26.43) giving B(T) = b - a/RT.



Homework Equations





The Attempt at a Solution



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

[tex]p = \frac{RT}{V_m -b} - \frac{a}{V_m^2}[/tex]
[tex]pV_m = \frac{VRT}{V_m -b} - \frac{a}{V_m}[/tex]

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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  • Equation rearranging the van der Waals equation: pV = RT/(V - b) - a/V^2 = RT/V (1 - b/V)^(-1) - a/V^2, with the pV on the left and the minus sign and the plus sign boxed in red.
    van.png
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