Chapter 6, Problem 6.128QP

Interpretation Introduction

Interpretation: The root-mean-square speed of ${\text{CO}}_{\text{2}}$ molecules that have an average kinetic energy of $\text{4}\text{.2}\times {\text{10}}^{\text{-21}}\text{J}/\text{molecule}$ is to be calculated.

Concept introduction: According to kinetic theory of molecular gases, gases are hitting continuously against the walls of container when the temperature increases. Hence their total energy also increases. The kinetic energy for a single particle is given by the formula,

$\text{K}\text{.E}=\frac{1}{2}m{v}^2$

The root-mean-square speed of the gas is the speed of a molecule that is moving with a characteristic average kinetic energy.

$u_{rms}=\sqrt{\frac{3\text{R}T}{M}}$

To determine: The root-mean-square speed of ${\text{CO}}_{\text{2}}$ molecules that have an average kinetic energy of $\text{4}\text{.2}\times {\text{10}}^{\text{-21}}\text{J}/\text{molecule}$.