Q 11-01-106JEE MainJEE Main 2024 (27 Jan, Shift 2)Easy
The equation of state of a real gas is given by $\left(P + \dfrac{a}{V^2}\right)(V - b) = RT$, where $P$, $V$ and $T$ are pressure, volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\dfrac{a}{b^2}$ is similar to that of:
Answer: (B) $P$
Only like quantities can be added, so $\dfrac{a}{V^2}$ has the dimensions of $P$, giving $[a] = [PV^2]$. Similarly $[b] = [V]$.
$$\left[\frac{a}{b^2}\right] = \frac{[PV^2]}{[V^2]} = [P]$$
Solution by Sreeraj P, M.Sc Physics