Chapter 17, Problem 117A

Interpretation Introduction

Interpretation: The average kinetic energy of hydrogen gas at two different temperatures is to be evaluated.

Concept introduction: Average kinetic energy of gas particles is only a function of temperature. That means all gases at the same temperature will have the same average kinetic energies.

Average kinetic energy is calculated by the given formula

  $\text{K}\text{.E=}\frac{\text{3}}{\text{2}}\text{×k×T}$

where,

  $\text{k}$ = Boltzmann constant

  $\text{T}$ = Temperature in Kelvin

Answer to Problem 117A

Hydrogen gas at $\text{40 K}$ will have $\frac{2}{5}$ of an average kinetic energy for hydrogen gas at $\text{100 K}$

Explanation of Solution

Putting in the values, we get:

  $\begin{array}{l}\text{K}{\text{.E}}_{\text{100K}}\text{=}\frac{\text{3}}{\text{2}}\text{×k×100}\\ \text{K}{\text{.E}}_{\text{40K}}\text{=}\frac{\text{3}}{\text{2}}\text{×k×40}\\ \frac{\text{K}{\text{.E}}_{\text{40K}}}{\text{K}{\text{.E}}_{\text{100K}}}=\frac{\frac{\text{3}}{\text{2}}\text{×k×40}}{\frac{\text{3}}{\text{2}}\text{×k×100}}\\ \frac{\text{K}{\text{.E}}_{\text{40K}}}{\text{K}{\text{.E}}_{\text{100K}}}=\frac{2}{5}\\ \text{K}{\text{.E}}_{\text{40K}}=\frac{2}{5}\times \text{K}{\text{.E}}_{\text{100K}}\end{array}$