What is the effect of the temperature on the van-der-Waals constants $a$ and $b$?

I have checked on the effect of pressure and volume on the van-der-Waals constants, but I've not been able to get the effect of temperature.


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    $\begingroup$ See, they are constants; they are assumed not to depend on anything. $\endgroup$ – Ivan Neretin Jan 7 at 14:51

$a$ and $b$ are supposed to be constants. But, they in fact aren't, so your question is in principle valid.

vdW is not a very good model to describe $V_m(p,T)$ of any actual non-ideal gas over a larger pressure or temperature range, and if you take a really good model (those have 6 or 8 parameters), you can just mathematically derive $a(p,T)$ and $b(p,T)$.

However I doubt there is a general trend for a and b with increasing temperature or pressure. I'm sure you could find one for similar (e.g. mono- or diatomic, elementar) gases.

vdW is useful (just like virial coefficents and other models with only two or three parameters) to accurately model $p,V,T$ in a limited range without a large computational effort, e.g. for process control.

(The value of the vdW theory is imo an educational one: It gives a convincing reason why real gases are non-ideal, and correctly describes the trends.)


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