Q 11-01-239JEE MainJEE Main 2025 (2 Apr, Shift 1)Easy
The equation for a real gas is given by $\left(P + \dfrac{a}{V^2}\right)(V - b) = RT$, where $P, V, T$ and $R$ are the pressure, volume, temperature and gas constant, respectively. The dimension of $ab^{-2}$ is equivalent to that of:
Answer: (D) Energy density
Only like quantities can be added, so $a/V^2$ has the dimensions of pressure and $b$ has the dimensions of volume:
$$[a] = [P][V^2] = ML^{-1}T^{-2}\cdot L^6 = ML^5T^{-2},\qquad [b] = L^3$$
$$[ab^{-2}] = \frac{ML^5T^{-2}}{L^6} = ML^{-1}T^{-2}$$
This is the dimension of pressure, which is the same as energy per unit volume, i.e. **energy density**.
Solution by Sreeraj P, M.Sc Physics