Question

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

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

Answer 1

Answer: (A), (B), (D)

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

We know, $E_{av}=\frac{3}{2}{k}_{b}T$
$U_{rms}=\sqrt{\frac{3RT}{M}}$
Thus.
a) $E_{av}$ at a given temperature does not depend on molecular mass.
b) $U_{rms}$ is doubled when its temperature is increased four times.
c) $E_{av}$ increases four times when its temperature is increased four times.
d) $U_{rms}$ is inversely proportional to the square root of molecular mass



$E_{av}=\frac{3}{2}RT{U}_{rms}=\sqrt{\frac{3RT}{M}}$
$E_{av}$ does not depend on its molecular mass but depends upon absolute temperature.