JEE Main 2022 — Physics Thermodynamics

2022mcqmedium

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $1.4$ . Vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :

( $R=$ universal gas constant)

Official previous-year question

Held on 26 Jun 2022 · Verified 6 Jul 2026.

Options

A
$\frac{M{v}^{2}}{7R}$
B
$\frac{M{v}^{2}}{5R}$
C
$2\frac{M{v}^{2}}{7R}$
D
$7\frac{M{v}^{2}}{5R}$

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Solution

KE of the vessel $=\frac{1}{2}m{v}^{2}$

When the vessel is suddenly stopped, the ordered motion of the gas molecules is converted into disordered motion of the molecules increasing thereby the internal energy of the gas. Thus,

$\Delta U=n{C}_{v}\Delta T=\frac{1}{2}m{v}^{2}=\frac{1}{2}(nM){v}^{2}$

Where $n$ is number of moles of the gas in the vessel and $M$ is molecular weight of the gas.

$\therefore \Delta T=\frac{M{v}^{2}}{2{C}_{v}}$

As ${C}_{v}=\frac{R}{\gamma -1}$

$\therefore \Delta T=\frac{M{v}^{2}(\gamma -1)}{2R}=\frac{M{v}^{2}(1.4-1)}{2R}=\frac{M{v}^{2}}{5R}$

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Solution

KE of the vessel $=\frac{1}{2}m{v}^{2}$

When the vessel is suddenly stopped, the ordered motion of the gas molecules is converted into disordered motion of the molecules increasing thereby the internal energy of the gas. Thus,

$\Delta U=n{C}_{v}\Delta T=\frac{1}{2}m{v}^{2}=\frac{1}{2}(nM){v}^{2}$

Where $n$ is number of moles of the gas in the vessel and $M$ is molecular weight of the gas.

$\therefore \Delta T=\frac{M{v}^{2}}{2{C}_{v}}$

As ${C}_{v}=\frac{R}{\gamma -1}$

$\therefore \Delta T=\frac{M{v}^{2}(\gamma -1)}{2R}=\frac{M{v}^{2}(1.4-1)}{2R}=\frac{M{v}^{2}}{5R}$

JEE Main 2022 — Physics Thermodynamics

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Solution

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JEE Main 2022 — Physics Thermodynamics

Options

Did you get this right?

Solution

Your note

JEE Main Thermodynamics in other years

More JEE Main Thermodynamics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Optics

Waves & Oscillations

Keep practicing Thermodynamics