Question

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

• A. $\frac{m{v}_0^2}{2R}$
• B. $\frac{m{v}_0^2}{3R}$
• C. $\frac{3m{v}_0^2}{2R}$
• D. $\frac{1}{2}\frac{m{v}_0^2}{R}$

Answer 1

Answer: (B)

$\frac{m{v}_0^2}{3R}$

Here, m$=$molar mass of the gas $v_0=$ initial speed

Mass of gas $=$nm(n$=$ number of moles in the gas)

$\therefore$ Initial kinetic energy of the gas $=\frac{1}{2}\left(nm\right)v^2$

Final KE of gas $=0$

Change in kinetic energy, $\Delta K=\frac{1}{2}\left(nm\right)v^2$

Let change in temperature of gas $=\Delta T$

Change in internal energy of the gas

$\Delta U=n{C}_v\Delta T=n\left(\frac{3}{2}R\right)\Delta T$

As, $\Delta U=\Delta K$

$\Rightarrow \frac{3}{2}nR\Delta T=\frac{1}{2}mn{v}_0^2$

$\Rightarrow \Delta T=\frac{m{v}_0^2}{3R}$