Q. Which one, among the following, is the van der Waals’ equation, describing the behaviour of one mole of a real gas over wide ranges of temperature and pressure?
A) $\left( p + \frac{a}{V^{2}} \right)(V - b) = RT$
B) $\left( p - \frac{a}{V^{2}} \right)(V - b) = RT$
C) $\left( p + \frac{a}{V^{2}} \right)(V - b) = \frac{R}{T}$
D) $\left( p + \frac{a}{V^{2}} \right)(V + b) = RT$
Explanation
(a)
The van der Waals’ equation for $n$ moles of a gas is
$\ \ \ \ \ \ \left\lbrack p + \frac{n^{2}a}{V^{2}} \right\rbrack\ (V - nb) = nRT$
For one mole $(n = 1)$
$\ \ \ \ \ \ \ \ \ \ \ \left( p + \frac{a}{V^{2}} \right)(V - b) = RT$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.