Which of the following statement(s) (are) correct regarding the root mean square speed $\left({\mathrm{U}}_{\mathrm{r}\mathrm{m}\mathrm{s}}\right)$ and average translational kinetic energy $\left({\mathrm{\epsilon }}_{\mathrm{a}\mathrm{v}}\right)$ of a molecule in a gas at equilibrium?

• Correct answer
  A

  ${\mathrm{U}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$ is doubled when its temperature is increased four times
• Correct answer
  B

  ${\mathrm{\epsilon }}_{\mathrm{a}\mathrm{v}}$ at a given temperature does not depend on its molecular mass
• Correct answer
  C

  ${\mathrm{U}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$ is inversely proportional to the square root of its molecular mass
• D

  ${\mathrm{\epsilon }}_{\mathrm{a}\mathrm{v}}$ is doubled when its temperature is increased four times

Hence, the correct answer is options: 'A', 'B', 'C'.