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 $\mathrm{P}, \mathrm{V}$ and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of $\frac{\mathrm{a}}{\mathrm{b}^{2}}$ is similar to that of :

JEE Main · 2024 · 27 Jan 2024 · Shift 2 · Units & Measurement

The equation of state of a real gas is given by

(P + \frac{a}{V ^{2}}) (V - b) = RT

, where

P, V

and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of

\frac{a}{b ^{2}}

is similar to that of :

Answer: (B)

(P + \frac{a}{V ^{2}}) (V - b) = R T

, every term added to or subtracted from a physical quantity must carry that quantity's dimensions. Since

\frac{a}{V ^{2}}

is added to pressure

P

[a] = [P] [V^{2}]

. Since

b

is subtracted from volume,

[b] = [V]

. Then

\frac{[ a ]}{[ b ] ^{2}} = \frac{[ P ] [ V ^{2} ]}{[ V ^{2} ]} = [P] .

The quantity

a / b^{2}

has the dimensions of pressure.

JEE Main · 2024 · 27 Jan 2024 · Shift 2 · Single correct option