If I change the definition of *compressibility factor* of one mole of a real gas to \( \frac{pv}{RT}\) where

*p* designates the corrected pressure according to Van der waal's equation

*v* designates the corrected volume according to Van der waal's equation

So the question is what is the value of the new compressibility factor at critical conditions?

**Details and Assumptions**

The *compressibility factor* for one mole of a real gas at critical conditions is \( \frac{PV}{RT}\) is \( \frac{3}{8}\) .

If Pressure at *critical conditions* is \( \frac{a}{27b^{2}}\)

If Volume at *critical conditions* if 3b

If Temperature at *critical conditions* is \( \frac{8a}{27bR}\)

Here *R* is the gas constant and *a* and *b* are Van der waal's constants.

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