The van der Waal's equation for a real gas may be rearranged to give , where is the molar volume of the gas. Indicate the correct statement(s) amongst the following:

Question

The van der Waal's equation for a real gas may be rearranged to give $V_m^3 - \left(b + \frac{RT}{P}\right)V_m^2 + \frac{a}{P}V_m - \frac{ab}{P} = 0$, where $V_m$ is the molar volume of the gas. Indicate the correct statement(s) amongst the following:

Prashant Kotian · Accepted Answer

Correct answer: A,B,C. The van der Waals equation is a cubic equation in . Above the critical temperature (), there is only one real root (gas phase) and two complex conjugate roots. Exactly at , the three roots converge into a single identical real root (). Below , the equation mathematically yields three distinct real roots corresponding to the liquid volume, gas volume, and an unstable intermediate state. Therefore, correct answer is A,B,C.

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