Question

An insulated container containing monoatomic gas of molar mass m moving with a velocity v0. If the container is suddenly stopped. The change in temperature is

• A. $\frac{m\nu_{0}^{2}}{2R}$
• B. $\frac{m\nu_{0}^{2}}{3R}$
• C. $\frac{R}{m\nu_{0}^{2}}$
• D. $\frac{3m\nu_{0}^{2}}{2R}$

Answer 1

Answer: (B)

$\frac{m\nu_{0}^{2}}{3R}$

Answer 2

If the container is suddenly stopped loss in kinetic energy of gas $= \frac{1}{2}(mn)v_{0}^{2}$, where n is number of moles of gas

Let $\Delta T$is the fall in temperature of gas.

Then, $n\left( \frac{3}{2}R\Delta T \right) = \frac{1}{2}mv_{0}^{2}$

$\Delta T = \frac{mv_{0}^{2}}{3R}$