Factor a in Van der Waals equation of state off by a factor of 0.1?

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SUMMARY

The forum discussion focuses on the discrepancy in the calculation of the Van der Waals (VdW) parameter 'a' for nitrogen and carbon dioxide, where the calculated value is consistently off by a factor of 0.1. The user correctly computes the parameter 'b' using the critical temperature and pressure, but encounters an error with 'a', which should be 3.60 x 10-1 Pa m6 mol-2 instead of 3.60 Pa m6 mol-2. The user references critical properties from Wikipedia and calculations from Zemansky and Dittman, confirming that the values for 'a' and 'b' are accurate according to established sources.

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  • Understanding of the Van der Waals equation of state
  • Knowledge of critical temperature and pressure concepts
  • Familiarity with unit conversions (e.g., atm to Pa)
  • Basic thermodynamics principles related to the Joule-Thomson effect
NEXT STEPS
  • Review the derivation of the Van der Waals equation parameters 'a' and 'b'
  • Study the critical properties of gases, focusing on nitrogen and carbon dioxide
  • Learn about the Joule-Thomson effect and its implications in thermodynamics
  • Explore common pitfalls in unit conversions in thermodynamic equations
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Students and professionals in thermodynamics, particularly those studying gas behavior and the Van der Waals equation, as well as anyone preparing for lab exams related to the Joule-Thomson effect.

dingo_d
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Hello

So I have a lab exam in Joule-Thomson effect and I have given values for a and b for VdW equation of state for nitrogen and carbon dioxide. When I take the critical temp. and pressure and put it in the equations:

a=\frac{27(T_c R)^2}{64 p_c} and
b=\frac{T_c}{8p_c}

b gives correct value, but a is off by a factor of 0.1.

E.g. For CO_2, given in the table (the experiments and the Phywe can't be wrong) a=3.60 Pa\ m^6\ mol^{-2}, and if I put the values from the http://en.wikipedia.org/wiki/Critical_properties" on wikipedia, I get: a=3.60\times 10^{-1}\ Pa\ m^6\ mol^{-2}. Not only for carbon dioxide, but for nitrogen too...

What is even weirder is that b is correct for the same temps and pressure!

So can someone find where this comes from? I calculated from Zemansky and Dittman the coefficients a and b and they are fine (the same as in wikipedia).

I converted all the necessary values (atm in Pa, used temp in K)...
 
Last edited by a moderator:
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The 0.36 is correct and the 3.6 is incorrect.
 

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