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A monoatomic gas of molar mass $m$ is kept in a insulated container. Container is moving with velocity $v$. If the container is suddenly stopped, then the change in the temperature of the gas is
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Verified Answer
The correct answer is:
$m v^2 / 3 R$
$m v^2 / 3 R$
Let the insulated container has $n$ moles of the monoatomic gas. The loss of kinetic energy of the gas,
$$
\Delta E_K=\frac{1}{2}(m n) v^2
$$
If the change in temperature of the gas is $\Delta T$, then heat gained by the gas is,
$$
\Delta Q=\frac{3}{2} n R \Delta T
$$
Now, according to question,
$$
\begin{aligned}
\Delta Q & =\Delta E_K \\
\frac{3}{2} n R \Delta T & =\frac{1}{2} m n v^2 \\
\Rightarrow \quad \Delta T & =\frac{m v^2}{3 R}
\end{aligned}
$$
$$
\Delta E_K=\frac{1}{2}(m n) v^2
$$
If the change in temperature of the gas is $\Delta T$, then heat gained by the gas is,
$$
\Delta Q=\frac{3}{2} n R \Delta T
$$
Now, according to question,
$$
\begin{aligned}
\Delta Q & =\Delta E_K \\
\frac{3}{2} n R \Delta T & =\frac{1}{2} m n v^2 \\
\Rightarrow \quad \Delta T & =\frac{m v^2}{3 R}
\end{aligned}
$$
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