Question

An insulated container containing monatomic gas of molar mass m moving with a velocity $v_0$. If the container is suddenly stopped. The change in temperature is?

• A. $\frac{m{v}^2}{2R}$
• B. $\frac{m{v}^2}{3R}$
• C. $\frac{R}{m{v}_0^2}$
• D. $\frac{3m{v}_0^2}{2R}$

Answer 1

The correct option is B $\frac{m{v}^2}{3R}$

If the container is suddenly stopped loss in kinetic energy of gas $=\frac{1}{2}\left(mn\right)v_0^2$, where n is number of moles of gas.
Let $\Delta$T is the fall in temperature of gas,
Then, $n\left(\frac{3}{2}R\Delta T\right)=\frac{1}{2}mn{v}_0^2$
$\Delta T=\frac{m{v}_0^2}{3R}$