A mono-atomic gas of mass $4.0 u$ is kept in an insulated container. Container is moving with velocity $30 \mathrm{~m} / \mathrm{s}$. If container is suddenly stopped then change in temperature of the gas $\left(R=\right.$ gas constant) is $\frac{x}{3 R}$. Value of $x$ is

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Heat & Thermodynamics

A mono-atomic gas of mass

4.0 u

is kept in an insulated container. Container is moving with velocity

30 m / s

. If container is suddenly stopped then change in temperature of the gas

(R =

gas constant) is

\frac{x}{3 R}

. Value of

x

Answer: 3.6

Solution

Stopping the container destroys the ordered motion of the gas as a whole, and in an insulated container that energy goes entirely into the internal energy.

For one mole of molar mass

M = 4 \times 1 0^{- 3}

kg,

Δ U = \frac{1}{2} M v^{2} = \frac{1}{2} (4 \times 1 0^{- 3}) (30)^{2} = 1.8 J

A mono-atomic gas has

Δ U = \frac{3}{2} R Δ T

, so

Δ T = \frac{2 ( 1.8 )}{3 R} = \frac{3.6}{3 R}

Comparing with the given form

\frac{x}{3 R}

gives

x = 3.6

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Numerical answer

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