A monoatomic gas of mass 4.0 u is kept in an insulated container.

Question:

A monoatomic gas of mass $4.0 \mathrm{u}$ 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

$(R=$ gas constant $)$ is $\frac{x}{3 R} .$ Value of $x$ is_______.

Solution:

Given that mass of gas is $4 u$ hence its molar mass $M$ is $4 \mathrm{~g} / \mathrm{mol}$

$\therefore \frac{1}{2} \mathrm{mv}^{2}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}$

$\frac{1}{2} \mathrm{~m} \times(30)^{2}=\frac{\mathrm{m}}{\mathrm{M}} \times \frac{3 \mathrm{R}}{2} \times \Delta \mathrm{T}$

$\therefore \Delta \mathrm{T}=\frac{3600}{3 \mathrm{R}}$

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