Cubic nature of van der Waals' gas equation


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> $V\_m^3-\dfrac{RT+bP}{P}V\_m^2+\dfrac{a}{P}V\_m-\dfrac{ab}{P}=0$
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So, At $T<T\_c$ the above equation has three real roots say $V\_1,V\_2,V\_3$, my doubt is what does this mean physically because for some particular pressure and temperature gas must have a fixed volume , so what does these three roots mean.




The van der Waals equation describes the isotherms of a gas with respect to pressure and volume. The first van der Waals root (the first solution of the cubic equation) will give you the dew point, which is the point where the first drop of liquid forms from the gas, the other root of the equation is the so-called bubble point, which is when the first liquid drop of the compound is formed. The intermediate root will always be found in a region where liquid and vapor coexist, but just as it is a region and not a point, that root itself has no physical meaning.


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