Question

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

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

Answer 1

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

The correct options are
A $U_{rms}$ is inversely proportional to the square root of its molecular mass
C $U_{rms}$ is doubled when its temperature is increased four times
D $E_{av}$ at a given temperature does not depend on its molecular mass

We know that,
$U_{rms}=\sqrt{\frac{3RT}{M}}$
Hence,
$U_{rms}$ is doubled when its temperature is increased four times and $U_{rms}$ is inversely proportional to the square root of its molecular mass.

$E_{av}=\frac{3}{2}RT$
$E_{av}$ at a given temperature does not depend on its molecular mass