Question

Which of the following statement(s) is(are) correct regarding the root mean square speed ($U_{rms}$) and average translational kinetic energy $\left({\epsilon }_{av}\right)$ of a molecule in a gas at equilibrium ?

• A. $U_{rns}$ is doubled when its temperature is increased four times
• B. ${\epsilon }_{av}$ is doubled when its temperature is increased four times
• C. ${\epsilon }_{av}$ at a given temperature does not depend on its molecular mass
• D. $U_{rns}$ is inversely proportional to the square root of its molecular mass

Answer 1

Answer: (A), (C), (D)

${\bar{E}}_K=\frac{3}{2}KT$ Average kinetic energy depends only on absolute temperature
K = Boltzmann constant
$U_{rms}=\sqrt{\frac{3RT}{M}}$
$U_{rms}\propto \sqrt{T}$
$U_{rms}\propto \frac{1}{\sqrt{M}}$
Using above formulae, correct statements are (A, C, D).