JEE Advanced 2023 · Paper 2 · Physics Q4

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PhysicsSingle correct+3 / -1Question 21 of 51

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$ . The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $\mathrm v_n$ . At a fixed temperature and pressure, which of the following is the correct option?

\mathrm v_3 < \mathrm v_6

and

U_3 > U_6

\mathrm v_5 > \mathrm v_3

and

U_3 > U_5

\mathrm v_5 > \mathrm v_7

and

U_5 < U_7

\mathrm v_6 < \mathrm v_7

and

U_6 < U_7

Answer and worked solution

Official answer: C

Internal energy. By equipartition $U_n=\frac n2RT$ , which increases with $n$ .

Speed of sound. $\mathrm v_n=\sqrt{\gamma RT/M}$ with $\gamma=1+\frac2n$ . This decreases as $n$ increases.

Options.

(A) fails: $U_3<U_6$ .
(B) fails: $\mathrm v_5<\mathrm v_3$ .
(D) fails: $\mathrm v_6>\mathrm v_7$ .
(C) holds: $\mathrm v_5>\mathrm v_7$ and $U_5<U_7$ .

Topics:Degrees of freedom and equipartition Speed of waves Specific heats of gases

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