JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Units & Measurement

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

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 :

Answer: (C)

Solution

Only like quantities may be added, so

b

carries the dimension of volume,

[b] = L^{3}

, and

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

must have the dimension of pressure, giving

[a] = [P] [V^{2}] = (M L^{- 1} T^{- 2}) (L^{6}) = M L^{5} T^{- 2}

. Hence

[\frac{b ^{2}}{a}] = \frac{L ^{6}}{M L ^{5} T ^{- 2}} = M^{- 1} L T^{2} = [P]^{- 1} .

The reciprocal of pressure is the dimension of compressibility, which is the reciprocal of bulk modulus.

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Single correct option