# Homework 1 (Due 4/6/16)

- Page ID
- 47367

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

## Q1.1

Describe what happens to the average kinetic energy of ideal gas molecules when the conditions are changed as follows:

- The pressure of the gas is increased by reducing the volume at constant temperature.
- The pressure of the gas is increased by increasing the temperature at constant volume.
- The average velocity of the molecules is increased by a factor of 2.

## Q1.2

What assumptions are made when applying the kinetic molecular theory to gases? Are all of these assumptions necessary? Why or why not?

## Q1.3

The root-mean-square speed of 6 particles is 2.47 ms^{-1}. The speed of 5 of the particles are 1.0, 2, 1.5, 3.0 and 2.5. Calculate the unknown speed of the 6^{th} particle. Find the average speed of the 6 particles.

## Q1.4

Consider the distribution of molecular velocities in a sample of helium. If the sample is cooled, will the distribution of velocities look more like that of H_{2} or of H_{2}O? Explain your answer.

## Q1.5

Find the \(v_{rms}\) of N_{2(g)} at 25ºC. What temperature must \(Cl_{2(g)}\) be to have the same \(v_{rms}\)?

## Q1.6

Use the Maxwell formula

\[f(v)=4\pi v^2 \left (\dfrac{m}{2\pi k_b T} \right)^{3/2}exp\left [\frac{-mv^2}{2k_bT}\right]\]

to derive an expression for \(c_{mp}\) of a gas.