The van der Waals' equation for one mole may be expressed as
`V_(M)^(3)-(b+(RT)/(P))V_(m)^(2)+(aV_(m))/(P)-(ab)/(P)=0`
where `V_(m)` is the molar volume of the gas. Which of the followning is incorrect?

Options

A. For a temperature less than `T_(c)` V has three real roots
B. For a temperature more than `T_(c)`, V has one real and two imaginary roots
C. For a temperature equal to `T_(c)` all three roots of V are real and identical
D. All of these

Answer

D

Explanation

The given equation is cubic equation in the variable V and, therefore, for a single value of P and T, there should be three values of V, all of which may be real or one real and two imaginary.
At `T_(c)` there values of V become identical.