The van der waal's equation for n=1 mole may be expressed as `V^(3)-(b+(RT)/(P))V^(2)+(aV)/(P)-(ab)/(P)=0`
Where V is the molar volume of the gas, which of the following is correct?

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

(d) 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 maybe real or one real and two imaginary.
At `T_(c)` there values of V become identical.