Question

A monatomic gas of mass $4.0\text{u}$ is kept in an insulated container. Container is moving with a velocity of $30\text{m/s}$. If the container is suddenly stopped, then the change in temperature of the gas is $\frac{x}{3R}$ $(R=$ gas constant$)$. Value of $x$ is _____.

Answer 1

We know that,
$\Delta KE=\Delta U$

For adiabatic process $($as container is insulated$)$,
$\Delta U=n{C}_v\Delta T$

$\Rightarrow \Delta KE=n{C}_v\Delta T$

$\Rightarrow \frac{1}{2}m{v}^2=\frac{3}{2}\times \frac{m}{M}\times R\Delta T$

$\Rightarrow \Delta T=\frac{M{v}^2}{3R}$

$\Rightarrow \Delta T=\frac{4\times {30}^2}{3R}=\frac{1200}{R}=\frac{x}{3R}$

$\Rightarrow x=3600$