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JEE Main 2023 (1 Feb, Shift 1) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2023 (1 Feb, Shift 1)

Q29JEE Main 2023 · 1 FEB · SHIFT 1Medium

Applications of Dimensional Analysis

$\left(P + \frac{a}{V^2}\right)(V - b) = RT$ 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 $\frac{b^2}{a}$ , will be:

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Answer: (d)

$[a] = [PV^2]$ and $[b] = [V]$ .
$\left[\dfrac{b^2}{a}\right] = \dfrac{V^2}{PV^2} = \dfrac{1}{[P]}$ .
Compressibility $= \dfrac{1}{\text{bulk modulus}}$ has dimension $1/[P]$ .
So the answer is (d) compressibility.

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