1. Thermal Physics
Topic 10.1 Ideal Gases

2. Boyle’s Law
States that the pressure of a fixed mass of gas is inversely proportional to its volume at constant temperature
P  1/V or PV = constant
When the conditions are changed
P1V1 = P2V2

3. The Experiment oil Bourdon Pressure gauge Volume of dry air Air from
foot pump
oil

4. What to do A column of trapped dry air in a sealed tube by the oil
The pressure on this volume of air can be varied by pumping air in or out of the oil reservoir to obtain different pressures
Wait to allow the temperature to return to room temperature

5. The Results P V P
1/ V PV P

6. Charles’ Law
States that the volume of a fixed mass of gas is directly proportional to its absolute temperature at constant pressure
V  T or V/T = constant
When the conditions are changed
V1/T1 = V2/T2

7. The Experiment Tap 1 Fixed mass of gas Mercury in U tube
Tap 2 Tap 3
Water reservoir
Fixed mass
of gas
Mercury in U tube

8. What to do
Fill the mercury column with mercury using the right hand tube (tap 1 open, tap 2 closed)
With tap 1 open drain some mercury using tap 2, then close tap 1 and 2. To trap a fixed mass of gas
Fill the jacket with water (make sure tap 3 is closed)

9. and then
Change the temperature of the water by draining some water from tap 3 and adding hot water
Equalise the pressure by leveling the columns using tap 2
Read the volume from the scale

10. The Results V
T oC
A value for
absolute zero V
T K

11. The Pressure Law
States that the pressure of a fixed mass of gas is directly proportional to its absolute temperature at constant volume
P  T or P/T = constant
When the conditions are changed
P1/T1 = P2/T2

12. The Experiment
Bourdon gauge
Ice
Water
Fixed
Mass of
gas
Heat

13. What to do Change the temperature of the water by heating it
Record the pressure of the gas

14. The Results P
T oC
A value for
absolute zero P
T K

15. Absolute Zero and the Kelvin Scale
Charles’ Law and the Pressure Law suggest that there is a lowest possible temperature that substances can go
This is called Absolute Zero
The Kelvin scale starts at this point and increases at the same scale as the Celsius Scale

16. Therefore -273oC is equivalent to 0 K
∆1oC is the same as ∆1 K
To change oC to K, add 273
To change K to oC, subtract 273

17. Combining the Laws
The gas laws can be combined to give a single equation
For a fixed mass of gas its pressure times its volume divided by its absolute temperature is a constant
PV/T = k
So that P1V1/T1 = P2V2/T2

18. The Ideal Gas Equation PV = nRT Where n is the number of moles
R is the universal gas constant J mol-1 K-1

19. An Ideal Gas Is a theoretical gas that obeys the gas laws
And thus fit the ideal gas equation exactly

20. Real Gases
Real gases conform to the gas laws under certain limited conditions
But they condense to liquids and then solidify if the temperature is lowered
Furthermore, there are relatively small forces of attraction between particles of a real gas
This is not the case for an ideal gas

21. The Kinetic Theory of Gases
When the moving particle theory is applied to gases it is generally called the kinetic theory
The kinetic theory relates the macroscopic behaviour of an ideal gas to the microscopic behaviour of its molecules or atoms

22. The Postulates
Gases consist of tiny particles called atoms or molecules
The total number of particles in a sample is very large
The particles are in constant random motion
The range of the intermolecular forces is small compared to the average separation

23. The Postulates continued
The size of the particles is relatively small compared with the distance between them
Collisions of a short duration occur between particles and the walls of the container
Collisions are perfectly elastic

24. The Postulates continued
No forces act between the particles except when they collide
Between collisions the particles move in straight lines
And obey Newton’s Laws of motion

25. Macroscopic Behaviour
The large number of particles ensures that the number of particles moving in all directions is constant at any time

26. Pressure
Pressure can be explained by the collisions with the sides of the container
If the temperature increases, the average KE of the particles increases
The increase in velocity of the particles leads to a greater rate of collisions and hence the pressure of the gas increases as the collisions with the side have increased
Also the change in momentum is greater, therefore greater force

27. Pressure continued
When a force is applied to a piston in a cylinder containing a volume of gas
The particles take up a smaller volume
Smaller area to collide with
And hence collisions are more frequent with the sides leading to an increase in pressure

28. Also, as the piston is being moved in
It gives the particles colliding with it more velocity
Therefore they have more KE
Therefore the temperature of the gas rises.

29. Collisions Because the collisions are perfectly elastic
There is no loss of KE as a result of the collisions