JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Heat & Thermodynamics

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas in

n

. The internal energy of one mole of the gas is

U_{n}

and the speed of sound in the gas is

v_{n}

. At a fixed temperature and pressure, which of the following is the correct option ?

Answer: (C)

Solution

For an ideal gas:

Internal energy: $U = \frac{f}{2} n R T$ , where $f$ is degrees of freedom. So $U$ increases with $f$ .
Speed of sound: $v_{sound} = \frac{γ R T}{M} = (\frac{2}{f} + 1) \frac{R T}{M}$

Since

γ = 1 + \frac{2}{f}

, as

f

increases,

γ

decreases, and hence

v

decreases.

Therefore:

Option (C) is correct.

JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Single correct option