Chapter 10, Problem 80QP

Interpretation Introduction

Interpretation:

It is to be proven that the average kinetic energy of two gas samples, ${\text{UF}}_{\text{6}}$ and $\text{He}$, is the same and isindependent of their different molecular masses.

Concept introduction:

From the kinetic molecular theory, the total kinetic energy of a mole of gas is equal to $\frac{3}{2}RT$. The average kinetic energy of one molecule is $\frac{1}{2}m\overline{u^2}$. Therefore,

$N_A\left(\frac{1}{2}m\overline{u^2}\right)=\frac{3}{2}RT$

Here, $N_{\text{A}}$ is Avogadro’s number, $R$ is thegas constant, and $\mu$ is the molecular mass.

So, the equation becomes:

$\begin{array}{l}\sqrt{\overline{u^2}}=\sqrt{\frac{3RT}{\mu }}\\ u_{rms}=\sqrt{\frac{3RT}{\mu }}\end{array}$

Thus, root mean square speed is as follows:

$\sqrt{\overline{u^2}}=u_{rms}$