Chapter 10, Problem 148AP

Interpretation Introduction

Interpretation:

The root mean square speed, frequency, and the force are to be compared and the given statements are to be validated.

Concept introduction:

The root mean square speed for a molecules is calculated as

$u_{rms}=\sqrt{\frac{3RT}{M}}$

Here, $u_{rms}$ represents the root mean square speed of a molecule, $R$ represents the gas constant, $T$ represents the temperature, and $M$ represents its molar mass.

The most probable speed is calculated as

$u_{mp}=\sqrt{\frac{2RT}{M}}$

Here, $u_{mp}$ represents the most probable value of speed for the molecule, $R$ represents the gas constant, $T$ represents the temperature, and $M$ represents its molar mass.

The kinetic energy is calculated as

$E_k=\frac{1}{2}m\overline{u^2}$

Where, m is the mass and $\overline{u^2}$ is the mean square speed of the object.