April 16, 2024, 12:37:41 PM
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Topic: Finding van der Waals constants a and b using critical temperature and pressure?  (Read 10444 times)

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yg7s7

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Say naphthalene's critical temperature and pressure are 474.8 K and 40.6 atm , respectively, then how would you calculate the van der Waals constants a and b (where (P+a*n^2/V^2)(V-nb) = nRT)?

Offline MrTeo

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How would you do that?

Hint#1: there are some formulas that link a and b to the critical values. You can get them starting from the definition of critical point and using van der Waals equation. Think at the isotherms of a real gas.


Hint#2:

$$
\left\{ \begin{array}{l}
\left({\frac{{\partial p}}{{\partial V}}} \right)_T=0\\
\left({\frac{{\partial ^2 p}}{{\partial V^2 }}} \right)_T=0\\
\end{array} \right.
/$$

I don't know if there's an easier way to find them out but I'll think at it  ;)
The way of the superior man may be compared to what takes place in traveling, when to go to a distance we must first traverse the space that is near, and in ascending a height, when we must begin from the lower ground. (Confucius)

yg7s7

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Thanks for the reply.

How would you know that the first and second derivatives of P in terms of V are zero?




Offline MrTeo

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There's an inflection point in the critical isotherm  ;)



The way of the superior man may be compared to what takes place in traveling, when to go to a distance we must first traverse the space that is near, and in ascending a height, when we must begin from the lower ground. (Confucius)

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