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  4. A monoatomic 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 ( x /3 R ) . Value of x is

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Q. A monoatomic 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
$\left( R =\right.$ gas constant) is $\frac{ x }{3 R } .$ Value of $x$ is___

JEE MainJEE Main 2021Kinetic Theory

Solution:

Given that mass of gas is $4 u$ hence its molar mass $M$ is $4 g / mol$
$\therefore \frac{1}{2} mv ^{2}= nC _{ v } \Delta T$
$\frac{1}{2} m \times(30)^{2}=\frac{ m }{ M } \times \frac{3 R }{2} \times \Delta T$
$\therefore \Delta T =\frac{3600}{3 R }$