Chapter 5, Problem 5.70QP

Interpretation Introduction

Interpretation:

Expression for the root-mean-square speed for a gas at temperature T has to be written. Each term in the equation has to be defined and the units are used in the calculations has to be shown.

Concept introduction:

Average kinetic energy: Average kinetic energy of the gas molecules is proportional to the temperature of the gas in kelvins.

• Average kinetic energy of a molecule is given by,

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

Where, m is the mas of molecule

u is the speed

C is proportionality constant

T is absolute temperature

According to the equation, the absolute temperature of a gas is a measure of the average kinetic energy of the molecules. Higher the temperature, the molecules are highly energetic. Thus, random molecular motion is referred to as thermal motion.