JEE Main 2025 Apr 4 Shift 1, Physics Q7: Law of Equipartition of Energy

JEE Main2025Apr 4, Shift 1Physics

Consider the sound wave travelling in ideal gases of He, CH $_{4}$ , and CO $_{2}$ . All the gases have the same ratio $\frac{P}{ρ}$ , where $P$ is the pressure and $ρ$ is the density. The ratio of the speed of sound through the gases $v_{H e} : v_{C H_{4}} : v_{C O_{2}}$ is given by

A
$\frac{7}{5} : \frac{5}{3} : \frac{4}{3}$
B
$\frac{5}{3} : \frac{4}{3} : \frac{7}{5}$
C
$\frac{5}{3} : \frac{4}{3} : \frac{4}{3}$
D
$\frac{4}{3} : \frac{5}{3} : \frac{7}{5}$

Solution

Speed of sound in an ideal gas is $v = \frac{γ P}{ρ}$ . Since $P / ρ$ is the same for all three gases, the ratio reduces to $γ_{H e} : γ_{C H_{4}} : γ_{C O_{2}}$ .

Adiabatic indices:

Gas	Type	$γ$
He	monoatomic	$5/3$
CH $_{4}$	polyatomic	$\approx 4/3$
CO $_{2}$	polyatomic (linear, treated similarly)	$\approx 4/3$

So the required ratio is $5/3 : 4/3 : 4/3$ .

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JEE Main 2025 Apr 4 Shift 1, Physics Q7: Law of Equipartition of Energy

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