1. Thermal Physics Topic 3.2 Modelling Gases Courtesy to Greengates school in mexico

2. Understandings: w Pressure w Equation of state for an ideal gas w Kinetic model of an ideal gas w Mole, molar mass and the Avogadro constant w Differences between real and ideal gases Applications and skills: w Solving problems using the equation of state for an ideal gas and gas laws w Sketching and interpreting changes of state of an ideal gas on pressure–volume, pressure–temperature and volume– temperature diagrams

3. The Mole w The mole is the amount of substance which contains the same number of elementary entities as there are in 12 grams of carbon-12 w Experiments show that this is 6.02 x 10 23 particles w A value denoted by N A and called the Avogadro Constant (units mol -1 )

4. Molar Mass w Molar mass is the mass of one mole of the substance w SI units are kg mol -1

5. Example w Molar mass of Oxygen gas is 32 x10 -3 kg mol -1 w If I have 20g of Oxygen, how many moles do I have and how many molecules? w 20 x 10 -3 kg / 32 x10 -3 kg mol -1 w  0.625 mol w  0.625 mol x 6.02 x 10 23 molecules w  3.7625 x 10 23 molecules

6. Thermal Properties of Gases w Investigations involved the measurement of Pressure Volume Temperature w These experiments used these macroscopic properties of a gas to formulate a number of gas laws

7. Units w Temperature is always measured in K w Volume is usually in m 3 w Pressure can be different units as long as you are consistent w But 1 atm = 1.01 x 10 5 Nm -2 = 101.3 kPa = 760 mmHg

8. 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

9. 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

10. 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.

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

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

13. 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

14. 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

15. 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

16. 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

17. 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

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

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

20. The Experiment

21. Boyle’s law You-tubes w Marshmallow in vacuum http://www.youtube.com/watch?feature=endscr een&v=OHY9fFQhX68&NR=1http://www.youtube.com/watch?feature=endscr een&v=OHY9fFQhX68&NR=1 w Shaving cream in vacuum http://www.youtube.com/watch?v=RPlCO3AIT V4&feature=relatedhttp://www.youtube.com/watch?v=RPlCO3AIT V4&feature=related w Balloon in vacuum http://www.youtube.com/watch?v=J_I8Y-i4Axc

22. The Results P V P 1/ V

23. 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

24. The Experiment

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

27. 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

28. The Experiment w The Pepsi can http://www.youtube.com/watch?v=PeHIN- HMwM4http://www.youtube.com/watch?v=PeHIN- HMwM4

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

30. Apply your knowledge!

31. 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 This is called Absolute Zero w The Kelvin scale starts at this point and increases at the same scale as the Celsius Scale Therefore -273 o C is equivalent to 0 K ∆1 o C is the same as ∆1 K To change o C to K, add 273 To change K to o C, subtract 273

32. 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 w 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

33. Be a Thinker!

35. Ideal Gas versus real gas w An ideal gas is a theoretical gas that obeys the gas laws and thus fit the ideal gas equation exactly w Real gases conform to the gas laws at low pressures and large volumes. w they condense to liquids and then solidify if the temperature is lowered w there are relatively small forces of attraction between particles of a real gas This is not the case for an ideal gas

36. Apply your knowledge!

37. Applying the ideal gas equation

38. Be a thinker!