1. Thermal Physics Topic 10.1 Ideal Gases

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

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

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

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

6. Charles’ Law w States that the volume of a fixed mass of gas is directly proportional to its absolute temperature at constant pressure w V  T or V/T = constant w When the conditions are changed w V 1 /T 1 = V 2 /T 2

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

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

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

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

11. The Pressure Law w States that the pressure of a fixed mass of gas is directly proportional to its absolute temperature at constant volume w P  T or P/T = constant w When the conditions are changed w P 1 /T 1 = P 2 /T 2

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

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

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

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

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

17. Combining the Laws w The gas laws can be combined to give a single equation w For a fixed mass of gas its pressure times its volume divided by its absolute temperature is a constant w PV/T = k w So that P 1 V 1 /T 1 = P 2 V 2 /T 2

18. The Ideal Gas Equation w PV = nRT w Where n is the number of moles w R is the universal gas constant 8.31 J mol -1 K -1

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

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

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

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

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

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

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

26. Pressure w Pressure can be explained by the collisions with the sides of the container w If the temperature increases, the average KE of the particles increases w 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 w Also the change in momentum is greater, therefore greater force

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

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

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