Chapter 13.1, Problem 8LC

Interpretation Introduction

Interpretation:

The factor by which the average kinetic energy decreases when oxygen gas is cooled from $300\text{ K}$ to $150\text{ K}$ .

Concept Introduction :

The kinetic theory of gases is a theoretical model, to characterize the molecular makeup of the gas. It is a theory that describes the states of matter and is based on the idea that all matter is made up of small particles that are constantly moving.

Answer to Problem 8LC

The average kinetic energy is directly proportional to the Kinetic temperature.

Explanation of Solution

The expression for average kinetic energy is as follows:

  $E=\frac{3}{2}kT$

Here, $k$ is Boltzmann constant and $T$ is temperature. Temperature is always taken in Kelvin scale.

Now, calculate the average kinetic energy at $300\text{ K}$ as shown,

  $E_1=\frac{3}{2}k\times 300$

Now, calculate the average kinetic energy at $150\text{ K}$ as shown,

  $E_2=\frac{3}{2}k\times 150$

Now, calculate the difference in average kinetic energy,

  $\begin{array}{c}{E}_1-E_2=\frac{3}{2}k\times 300-\frac{3}{2}k\times 150\\ =\frac{3}{2}k\times 150\end{array}$

Now, calculate the factor by which the average kinetic energy decreases as follows:

  $\begin{array}{c}\text{Decrease in kinetic energy}=\frac{\frac{3}{2}k\times 150}{\frac{3}{2}k\times 300}\\ =0.5\end{array}$

Thus, the average kinetic energy become half of the initial average kinetic energy.