Q88 / 100 · BITSAT 2022 · Physics

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

  • A
    $m v^2 / 4 R$
  • B
    $m v^2 / 2 R$
  • C
    $m v^2 / R$
  • Correct answer
    D
    $m v^2 / 3 R$

Solution

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, $$ \begin{aligned} \Delta Q & =\Delta E_K \\ \frac{3}{2} n R \Delta T & =\frac{1}{2} m n v^2 \\ \Rightarrow \quad \Delta T & =\frac{m v^2}{3 R} \end{aligned} $$

Hence, the correct answer is option: 'D'.

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