The rms velocity of a He molecule in helium gas with a temperature of 20°C is 1,352 m/s. What is the rms velocity of the molecule if the temperature of the gas is tripled?
A) 2,342 m/s
B) 3,640 m/s
C) 3,980 m/s
D) 4,056 m/s
E) 12,170 m/s

Question

Quizplus · Accepted Answer

The rms velocity of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant, $T$ is the temperature in Kelvin, and $m$ is the mass of the molecule. When the temperature is tripled, the new rms velocity becomes $v_{new} = \sqrt{\frac{3k(3T)}{m}} = \sqrt{3} \times v_{rms}$. Therefore, the new rms velocity is $\sqrt{3} \times 1352 \, \text{m/s} \approx 2342 \, \text{m/s}$.

The Rms Velocity of a He Molecule in Helium Gas