Question

A sample of an ideal gas is cooled from $450K$ to $225K$.
Which of the choices below BEST describes the effect on the average molecular kinetic energy, $\overline{KE}$, and the average molecular velocity, $\overline{v}$?

• A. Both $\overline{KE}$ and $\overline{v}$ are cut in half.
• B. Both $\overline{KE}$ and $\overline{v}$ are reduced by a factor of $\sqrt{2}$.
• C. $\overline{KE}$ is reduced by a factor of $\sqrt{2}$, while $\overline{v}$ is cut in half.
• D. $\overline{KE}$ is cut in half while $\overline{v}$ is reduced by a factor of $\sqrt{2}$.

Answer 1

Answer: (D)

$\overline{KE}$ is cut in half while $\overline{v}$ is reduced by a factor of $\sqrt{2}$.

T is reduced from 450K to 225K i.e half times

KE = $\frac{3}{2}KTKE\propto T\overrightarrow{V}\propto \frac{1}{\sqrt{T}}$

Ans : KE is also cut by half and $\overrightarrow{V}$ will be reduced by factor of $\sqrt{2}$