# Homework 1 (Due 4/6/16)

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:

1. The pressure of the gas is increased by reducing the volume at constant temperature.
2. The pressure of the gas is increased by increasing the temperature at constant volume.
3. 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 6th 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 H2 or of H2O? 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.