The equation of state of a real gas is given by (P + a/V²)(V - b) = RT, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of a/b² is similar to that of: (a) P (b) RT (c) PV (d) R

Answer: (a). Only like quantities add: a/V² has dimension of P, so [a] = [PV²]. b is subtracted from V, so [b] = [V]. [a/b²] = (PV²)/(V²) = [P]. So the answer is (a) P.

The equation of state of a real gas is given by (P + a/V²)(V - b) =… | JEE Main 2024 (27 Jan, Shift 2)

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Applications of Dimensional Analysis

The equation of state of a real gas is given by $\left(\mathrm{P} + \frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V} - \mathrm{b}) = \mathrm{RT}$ , where $\mathrm{P, V}$ and $\mathrm{T}$ are pressure, volume and temperature respectively and $\mathrm{R}$ is the universal gas constant. The dimensions of $\frac{\mathrm{a}}{\mathrm{b}^2}$ is similar to that of:

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Answer: (a)

Only like quantities add: $\dfrac{a}{V^2}$ has dimension of $P$ , so $[a] = [PV^2]$ .
$b$ is subtracted from $V$ , so $[b] = [V]$ .
$\left[\dfrac{a}{b^2}\right] = \dfrac{PV^2}{V^2} = [P]$ .
So the answer is (a) P.

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