Thermal Physics (Kinetic Theory) A Level Slide

Thermal Physics A Level Physics Slide

1. Thermal Physics A level Physics 2024 - 2025

2. Phet – States of matter

3. Temperature The Kinetic-molecular Theory All Matter Is Made Up Of Tiny Particles That Are Always In Motion Absolute Temperature is a measure of the Average Kinetic Energy of individual particles.

4. Measurement of Temperature A thermometer is any device that is used to measure temperature Each type of thermometer uses a physical property of a material that varies with temperature - examples of such properties include: The density of a liquid The volume of a gas at constant pressure Resistance of a metal e.m.f. of a thermocouple In each case, the thermometer must be calibrated at two or more known temperatures (commonly the boiling and melting points of water, 0 o C and 100 o C respectively) and the scale divided into equal divisions.

5. The Density of a Liquid A liquid-in-glass thermometer depends on the density change of a liquid (commonly mercury) It consists of a thin glass capillary tube containing a liquid that expands with temperature A scale along the side of the tube allows the temperature to be measured based on the length of liquid within the tube

6. Volume of a Gas at Constant Pressure The volume of an ideal gas is directly proportional to its temperature when at constant pressure (Charles’s law) V ∝ T As the temperature of the gas increases, its volume increases and vice versa A gas thermometer must be calibrated - by knowing the temperature of the gas at a certain volume, a temperature scale can be determined depending on how quickly the gas expands with temperature

7. Resistance of a Metal Recall that electrical resistance changes with temperature e.g. the resistance of a filament lamp increases when current increases through it For metals: resistance increases with temperature at a steady rate For thermistors: resistance changes rapidly over a narrow range of temperatures As a thermistor gets hotter, its resistance decreases. This means a thermometer based on a thermistor can be used to measure a range of temperatures The relationship between the resistance and temperature is non-linear. This means the graph of temperature against resistance will be a curved line and the thermistor will have to be calibrated

8. E.M.F. of a Thermocouple A thermocouple is an electrical device used as the sensor of a thermometer It consists of two wires of different, or dissimilar, metals attached to each other, producing a junction on one end. The opposite ends are connected to a voltmeter When this junction is heated, an e.m.f. is produced between the two wires which is measured on the voltmeter The greater the difference in temperature between the wires, the greater the e.m.f However, a thermocouple requires calibration since the e.m.f. does not vary linearly with temperature The graph against e.m.f. and temperature is a positive, curved line

9. Absolute Zero (0K) Absolute zero is the lowest possible temperature where particles have the lowest possible energy. William Kelvin, b. 1824, Belfast

10. Absolute Zero (0K)

11. The Absolute scale 14 Converting between scales A change of one degree celsius is the same as a change of one kelvin . Therefore: o C = K - 273 OR K = o C + 273

12. Complete (use 273K = 0 o C): Situation Celsius ( o C) Absolute (K) Boiling water 100 Vostok Antarctica 1983 - 89 Average Earth surface 288 Gas flame 1500 Sun surface 6000 15

13. Answers: Situation Celsius ( o C) Absolute (K) Boiling water 100 373 Vostok Antarctica 1983 - 89 184 Average Earth surface 15 288 Gas flame 1500 1773 Sun surface 5727 6000 16

14. Lowest laboratory T ~ 10 -7 K That’s 0.00000001 K At Cern’s RHIC (Relativistic Heavy Ion Collider), T ~ 10 13 K That’s 10000000000000 K The Big Bang, T ~ 10 40 K or more That’s 10000000000000000000000000000000000000000K Some Temperatures

15. Thermal E nergy 18 Thermal energy is the internal energy of an object (J). It is equal to the sum of the randomly distributed kinetic and potential energies of all of the object’s molecules. Molecular kinetic energy increases with temperature. Electrostatic potential energy increases if an object changes state from solid to liquid or liquid to gas . Electrostatic potential energy for a liquid/solid is negative since energy has to be supplied to break bonds. Think, Pair Share: Why is the internal energy of gas almost entirely kinetic?

16. Heat 19 Heat is the flow of thermal energy from a high temperature object to a lower temperature object (represented by Δ Q) When something absorbs heat its internal energy increases ( Δ Q is +) When something releases heat its internal energy decreases ( Δ Q is -) What two changes to a substance could occur when it absorbs or releases heat energy? The temperature of the substance may change. Some or all of the substance may change state.

17. Heat and Temperature 21 If two objects are in thermal contact heat will flow from the higher temperature substance to the lower. This process continues until the objects reach thermal equilibrium. Two objects are said to be in thermal equilibrium with each other if there is not net transfer of heat energy between them. This will only occur if both objects are at the same temperature.

18. Heat and temperature When the air temperature is 20 C we feel fairly warm. If we jump into 20 C water we feel cold. Why?

19. Recap Define: Thermal energy Absolute Temperature Thermal equilibrium State as many differences as you can between: A solid and a liquid A solid and a gas

20. Recap questions What is the internal energy of an object? What is heat? What is temperature? Define thermal equilibrium? State and explain whether heating an object will always increase it’s temperature. What is absolute zero? How do you convert from Celsius to Kelvin?

21. SPECIFIC HEAT CAPACITY A bulk property that depends on the substance and its state. The amount of heat energy (J) required to raise the temperature of 1kg of a substance through 1K. SPECIFIC HEAT CAPACITY Per unit mass i.e. kg -1 A flow of internal energy (J) How much energy the material contains per unit temperature (K -1 )

22. Δ Q = heat energy supplied in Joules m = mass in kilograms c = specific heat capacity units: J kg - 1 K - 1 Δθ = temperature change in Kelvin or Celsius (T 2 -T 1 ) SPECIFIC HEAT CAPACITY The amount of heat energy required to raise the temperature of 1kg of a substance through 1K. Applies to situations where a substance changes temperature but not state. E θ

23. Worked Example A bucket containing 11.5 litres of cold water at 10°C is taken into a house at a warmer temperature and left inside until it has reached thermal equilibrium with it new surroundings. If 504 kJ of energy is absorbed from the surroundings to heat the water, what is the temperature of the room?

24. Worked Example A bucket containing 11.5 litres of cold water at 10°C is taken into a house at a warmer temperature and left inside until it has reached thermal equilibrium with it new surroundings. If 504 kJ of energy is absorbed from the surroundings to heat the water, what is the temperature of the room ? ∆Q =504 k J M =11.5 kg c = 4200 J kg -1 °K -1 ∆ θ = ? Using ∆ θ = 504,000 J / (11.5kg × 4200 J K -1 °C -1 ) = 10.4 °C (to 3 s.f. ) So temperature of the water = 10°C + 10.4 °C = 20.4 °C Temperature of the room = T of water in thermal eqm . = 20.4 °C

25. Complete Substance Mass SHC (Jkg -1 K -1 ) Temperature change Energy (J) water 4 kg 4 200 50 o C gold 4 kg 129 25 800 air 4 kg 50 K 200 000 glass 700 40 o C 84 000 hydrogen 5 mg 14 300 400 K brass 400 g 370 50 o C to ___ K 14 800

26. Answers Substance Mass SHC (Jkg -1 K -1 ) Temperature change Energy (J) water 4 kg 4 200 50 o C 840 000 gold 4 kg 129 50 o C 25 800 air 4 kg 1 000 50 K 200 000 glass 3 kg 700 40 o C 84 000 hydrogen 5 mg 14 300 400 K 28.6 brass 400 g 370 50 o C to 423 K 14 800

27. Examples of SHC Substance SHC (Jkg -1 K -1 ) Substance SHC (Jkg -1 K -1 ) water 4 200 helium 5240 ice or steam 2 100 glass 700 air 1 000 brick 840 hydrogen 14 300 wood 420 gold 129 concrete 880 copper 385 rubber 1600 aluminium 900 brass 370 mercury 140 paraffin 2130 31

28. Consequences of the high specific heat capacity of water

29. Consequences of the high specific heat capacity of water

30. Consequences of the high specific heat capacity of water

31. Consequences of the high specific heat capacity of water

32. Problem Solving Σ Q gained = Σ Q lost A 0.200 kg Sample Of Water At 80.0 o C Is Mixed With 0.200 kg of Water At 10.0 o C. Assume No Heat Loss To The Surroundings. What Is The Final Temperature Of The Mixture? m = 0.200 kg at T = 80.0 o C m = 0.200 kg at T = 10.0 o C c = 4180 J/ kg K θ f = m 1 c 1 T 1i + m 2 c 2 T 2i m 1 c 1 + m 2 c 2 θ f = (0.200*4180*80.0) + (0.200*4180*10.0) (0.200*4180) + (0.200*4180) θ f = 45.0 o C

33. States of Matter Solid Liquid Gas Shape Particle motion Internal Energy Separation of particles

34. Specific Latent Heat Per unit mass i.e. kg -1 Concealed/ hidden Internal energy (J)

35. Latent heat This is the energy required to change the state of one kilogram of a substance e.g. melting or boiling. 39

36. Latent Heat of Fusion A certain amount of heat is required to melt or freeze a substance: ◦ melting: thermal energy is added ◦ freezing: thermal energy is removed (released) The amount of energy required depends on the mass of the substance and on the latent heat of fusion: Q = m L f

37. Latent Heat of Vaporization A certain amount of heat is also required in order to vaporize or condense a substance ◦ remember, to vaporize refers to a liquid changing into the gas phase at its boiling point! ◦ Vaporizing: heat flows into the substance in order to overcome bonds. ◦ condensing: heat flows out of the substance as bonds are formed. The amount of energy required depends on the mass of the substance and on the latent heat of vaporization: Q = m L v

38. Measuring Specific Latent Heat

39. If you have a large bucket with a mixture of ice and water in it you can expect it to remain at 0 C regardless of the outside temperature, as long as there remains significant amount of ice in the bucket. Only after all the ice has melted will the temperature of the drink begin to rise. Think, pair share: Why is this?

40. Substance S.L.H. of Fusion kJ/kg S.L.H. of Vaporization kJ/kg Water 334 2264.705 Ammonia 332.17 1369 Carbon dioxide 184 574 Hydrogen 58 455 Nitrogen 25.7 200 Oxygen 13.9 213 Toluene 72.1 351

41. The Ice trade

42. By Peter Rinker - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=33444154

43. Heating H 2 O at a constant rate Ice Q = mc D T Ice + Water Melting Q = mL f Water Q = mc D T Water + Water Vapor (steam) Boiling Q = m L v Water Vapor (steam) Q = mc D T AB: The energy added increases the KE thus increasing the temperature. CD: The energy added increases the KE thus increasing the temperature. EF: The energy added increases the KE thus increasing the temperature. BC: The energy added increases the PE thus increasing the separation between molecules (phase change).

44. 48 Why do solids expand when they get hotter? Atoms vibrate with respect to each other. Hotter atoms vibrate more. Asymmetric potential means average separation increases x Low T Thermal excitation U(x) x Potential energy between two atoms Average separation High T

45. Boiling vs. Evaporation Boiling Occurs throughout liquid Temperature of liquid remains constant from an external heat source Evaporation Occurs only at the surface of the liquid Increase Evaporation Increase surface area Increase temperature Decrease humidity Fan! Leads to cooling

46. Identify what is happening at each stage Task The diagram shows the uptake of heat by 1 kg of water, as it passes from ice at -50 ºC to steam at temperatures above 100 ºC

47. 52 A: Rise in temperature as ice absorbs heat. B: Absorption of latent heat of fusion. C: Rise in temperature as liquid water absorbs heat. D: Water boils and absorbs latent heat of vaporization. E: Steam absorbs heat and thus increases its temperature. Answer

48. Complete Substance Change SLH (Jkg -1 ) Mass Energy (J) water melting 336 000 4 kg water freezing 336 000 200 g water boiling 2.25 M 9 M water condensing 2.25 M 600 mg CO 2 subliming 570 k 8 g CO 2 depositing 570 k 40 000 μ g 53

49. Answers Substance Change SLH (Jkg -1 ) Mass Energy (J) water melting 336 000 4 kg 1.344 M water freezing 336 000 200 g 67.2 k water boiling 2.25 M 4 kg 9 M water condensing 2.25 M 600 mg 1 350 CO 2 subliming 570 k 8 g 4 560 CO 2 depositing 570 k 40 000 μ g 22.8 54

50. Question 55 Calculate the heat energy required to change 100g of ice at – 5 o C to steam at 100 o C. (b) the time taken to do this if heat is supplied by a 500W immersion heater. (c) Sketch a temperature-time graph of the whole process. Stage 1: ice at – 5 o C to ice at 0 o C

51. A nswer (a) 56 Stage 1: Warm the ice to 0 o C Δ Q = m c Δθ = 0.100 kg x 2100J kg -1 o C -1 x (0 – (- 5)) o C = 0.100 x 2100 x 5 = 1 050 J Stage 2: ice at 0 o C to water at 0 o C Δ Q = m l = 0.100 x 336 000 = 33 600 J Stage 3: water at 0 o C to water at 100 o C Δ Q = m c Δ θ = 0.100 x 4200 x 100 = 42 000 J Stage 4: water at 100 o C to steam at 100 o C Δ Q = m l = 0.100 x 2 250 000 = 225 000 J Stage 5: Add them together : 1 050J 33 600J 42 000J 225 000J 301 650J

52. Answer (b) 57 Stage 1: Warm the water to 0 o C 1 050J / 500W = 2.1 seconds Stage 2: ice at 0 o C to water at 0 o C 33 600J / 500W = 67.2s Stage 3: water at 0 o C to water at 100 o C 42 000J / 500W = 84s Stage 4: water at 100 o C to steam at 100 o C 225 000J / 500W = 450s Stage 5: 2.1+67.2+84+450= 603.3s The heater supplies 500J per second to water. Assume no heat loss to the surroundings:

53. (c) Sketch graph 100 200 300 400 500 600 time / s temperature / o C 100 -5 stage 2 stage 1 stage 3 stage 4 58

54. Heat transfers – Tricky question 50 g of Ice at -18 C is added to a 100g glass containing 300g of water at 20 C. Assuming no heat is gained or lost from the surroundings what is the temperature of the water when thermal equilibrium is reached? c water = 4200 Jkg -1 K -1 c ice = 2100 Jkg -1 K -1 c glass = 840 Jkg -1 K -1 L fusion = 334 kJkg -1