alleryThe root-mean-square (rms) speed of gas molecules is given by:
A$v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}}$
B$v_{\text{rms}} = \sqrt{\dfrac{RT}{M}}$
C$v_{\text{rms}} = \sqrt{\dfrac{2RT}{M}}$
D$v_{\text{rms}} = \sqrt{\dfrac{8RT}{\pi M}}$
Answer & Solution
Correct answer: A. $v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}}$
From kinetic theory, the average translational kinetic energy of a molecule is $\dfrac{1}{2} m \overline{v^2} = \dfrac{3}{2} kT$
giving $\overline{v^2} = \dfrac{3kT}{m} = \dfrac{3RT}{M}$, where $M$ is molar mass.
The **rms** speed is the square root: $v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}}$.
Other useful speeds: most probable speed $v_p = \sqrt{\dfrac{2RT}{M}}$ (option C)
average speed $\langle v\rangle = \sqrt{\dfrac{8RT}{\pi M}}$ (option D). Order: $v_p < \langle v\rangle < v_{\text{rms}}$.
Keep practising Unit 4B: Conservation of Linear Momentum & Collisions
Browse all Unit 4B: Conservation of Linear Momentum & Collisions questions for AP Physics 1, or explore more Physics topics.
Related questions
Average translational kinetic energy of a gas molecule at temperature $T$ is:The **rms speed** of gas molecules at absolute temperature $T$ is:The pressure of an ideal gas in kinetic theory is given by:The relation between universal gas constant $R$, Avogadro number $N_A$, and Boltzmann consThe ideal gas equation is:The SI unit of pressure is:Force per unit area acting perpendicular to a surface is called:If the absolute temperature of an ideal gas is doubled, the rms speed of its molecules: