2. THE KINETIC THEORY OF GASES

3. ASSUMPTIONS  A gas consists of a very LARGE number of identical molecules [ makes statistical calculations meaningful ]  Molecules are in rapid haphazard motion  There are no intermolecular forces between molecules  The volume of the molecules is negligible compared with the volume of their container  Collisions with the container and between molecules themselves are perfectly elastic

4. l l l x y z Cube of side length l contains n molecules each of mass m Consider one molecule with a velocity v v Cube of side l

5. Considering the x – direction only Let v x be the component of v in this direction vxvx m Initial momentum before collision is given by P 1 = m v x Momentum after collision P 2 = - m v x -v x m Change in Momentum P 1 - P 2 = m v x - (- m v x ) = 2 m v x

6. -v x m vxvx m The particle returns to the right hand wall after it has travelled a distance of 2 l l The time taken to travel this distance of 2 l = The average force exerted on the wall = change in momentum ÷ time

7. The force due to all n molecules will be Where is the mean value of the square of all of the velocities in the x - direction vZvZ vxvx R vyvy vyvy c

8. Using mean values But there are so many molecules, the mean x – velocity will equal the mean y – velocity which will also equal the mean z - velocity HENCE

9. SUBSTITUTE PRESSURE = FORCE ÷ AREA But l 3 = V, the volume of the box HENCE

10. But (nm)/V = mass of gas divided by its volume = its density  THIS IS THE ROOT MEAN SQUARE SPEED OF GAS MOLECULES

11. Consider three molecules with velocities 400, 500 and 600 ms -1 Their mean velocity = Their root mean square velocity =