Q 11-01-148JEE MainJEE Main 2023 (1 Feb, Shift 1)Medium
$\left(P+\dfrac{a}{V^2}\right)(V-b)=RT$ represents the equation of state of some gases, where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a$, $b$, $R$ are the constants. The physical quantity, which has dimensional formula as that of $\dfrac{b^2}{a}$, will be
Answer: (C) Compressibility
$[a]=[PV^2]$ and $[b]=[V]$, so $\left[\dfrac{b^2}{a}\right]=\left[\dfrac{V^2}{PV^2}\right]=\left[\dfrac1P\right]$. Compressibility ($1/$bulk modulus) has the dimensions of $1/$pressure.
Solution by Sreeraj P, M.Sc Physics