# Are van der Waals coefficients independent of temperature?

In the van der Waals equation for real gases, the coefficients $$a$$ and $$b$$ are used as respective correction terms for pressure and volume in the ideal gas equation.

I want to know whether the van der Waals coefficients are independent of absolute temperature or not.

• The "formal" constants are just that - constants. However one could certainly have a table of $a$ and $b$ values for different ranges of temperature and pressure. See wikipedia article real gas for other equations. en.wikipedia.org/wiki/Real_gas
– MaxW
Oct 10, 2016 at 20:11

## 2 Answers

The van der waals constant can be directly obtained from the critical temperature and pressure. We have,

$${a = \frac{27 R^2 T_c^2} {64 P_c}}$$

$${b = \frac{R T_c }{ 8 P_c}}$$

Since, $$T_c$$ and $$P_c$$ are constants, we can conclude that the van der waals constants are really "constants."

The constants a and b in the Van der Waals equation are supposed to be independent of temperature. But it is important to remember that, even though the Van der Waals equation does a better job of approximating the behavior of real gases than the ideal gas law (over a larger range of parameter values), it too is just approximation that applies only over a limited range of values for the parameters.