Topic 10 Thermal Physics


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Topic 10 Thermal Physics

  1. 1. Thermal Physics AHL Topic 10
  2. 2. Thermodynamics <ul><li>Thermodynamics is the study of heat and </li></ul><ul><ul><li>its transformation into mechanical energy , </li></ul></ul><ul><ul><li>as heat and work. </li></ul></ul><ul><li>The word is derived from the Greek meaning </li></ul><ul><ul><li>‘ movement of heat’. </li></ul></ul><ul><li>It was developed in the mid 1800’s </li></ul><ul><ul><li>before atomic and molecular theory was developed. </li></ul></ul>
  3. 3. Thermodynamics <ul><li>Work is defined as : </li></ul><ul><li>T he quantity of energy transferred from one system to another by ordinary mechanical processes. </li></ul><ul><li>Heat is defined as: </li></ul><ul><li>A transfer of energy from one body to another body at a lower temperature. </li></ul>
  4. 4. Thermodynamics <ul><li>From this we can see that thermodynamics describes the relation ship between heat and work. </li></ul><ul><li>To distinguish the two: </li></ul><ul><ul><li>Heat is the transfer of energy due to a temperature difference. </li></ul></ul><ul><ul><li>Work is the transfer of energy that is not due to a temperature difference. </li></ul></ul>
  5. 5. Thermodynamics <ul><li>The foundation of this area of study is </li></ul><ul><li>T he law of conservation of energy </li></ul><ul><ul><li>and the fact that heat flows from hot to cold. </li></ul></ul><ul><li>In discussing thermodynamics, we will refer to different systems. </li></ul><ul><li>A system is just a group of objects we wish to consider. </li></ul><ul><li>Everything else in the universe will be called the environment. </li></ul>
  6. 6. Thermodynamics <ul><li>Consider a hot gas separated from a cold gas by a glass wall. </li></ul><ul><li>In macroscopic terms, </li></ul><ul><ul><li>we know that the hot gas gets cooler and the cool gas gets hotter. </li></ul></ul><ul><li>The molecules in the hot gas hit the glass </li></ul><ul><ul><li>and set those molecules in faster motion. </li></ul></ul>
  7. 7. Thermodynamics <ul><li>This then sets in train a set of collisions </li></ul><ul><ul><li>which sees the energy being transferred to the cold gas. </li></ul></ul><ul><li>If we were to observe a single collision, </li></ul><ul><ul><li>we could analyse the energy transfer </li></ul></ul><ul><ul><li>using the laws of mechanics. </li></ul></ul>
  8. 8. Thermodynamics <ul><li>We could say that one molecule has transferred energy </li></ul><ul><ul><li>by doing work on another. </li></ul></ul><ul><li>Heat is therefore the work done on a molecular level. </li></ul>
  9. 9. Thermodynamics <ul><li>This is not the complete story. </li></ul><ul><li>Although the cool gas contains, on average, </li></ul><ul><ul><li>slower molecules than in the hot gas, </li></ul></ul><ul><ul><li>it does contain some fast moving molecules. </li></ul></ul><ul><li>L ikewise, the hot gas contains slow moving molecules. </li></ul>
  10. 10. Thermodynamics <ul><li>From above, it should be possible to for the cold gas to transfer </li></ul><ul><ul><li>energy to the hot gas </li></ul></ul><ul><li>S o the cool gas would get cooler </li></ul><ul><ul><li>and the hot gas hotter. </li></ul></ul><ul><li>This does not disobey any classical theory of mechanics. </li></ul><ul><li>We do know however that this cannot occur. </li></ul>
  11. 11. Thermodynamics <ul><li>To explain this, we cannot look at this the effects of single molecules </li></ul><ul><ul><li>or even a few molecules. </li></ul></ul><ul><li>We must, when discussing heat, </li></ul><ul><ul><li>look at the overall effects of a large number of molecules </li></ul></ul><ul><ul><li>and the average energies </li></ul></ul><ul><ul><li>and distribution of energies and velocities. </li></ul></ul>
  12. 12. Thermodynamics <ul><li>This is what is meant by a system of particles in thermodynamics. </li></ul><ul><li>A system could be any group of atoms, </li></ul><ul><ul><li>molecule or particles we wish to deal with. </li></ul></ul><ul><li>It may be the steam in a steam engine, </li></ul><ul><ul><li>the earth’s atmosphere </li></ul></ul><ul><ul><li>or the body of a living creature. </li></ul></ul>
  13. 13. Thermodynamics <ul><li>The operation of changing the system from its initial state to a final state is called the, </li></ul><ul><li>T hermodynamic process . </li></ul>
  14. 14. Thermodynamics <ul><li>During this process, </li></ul><ul><ul><li>heat may be transferred into or out of the system , </li></ul></ul><ul><ul><li>and work may be done on or by the system. </li></ul></ul><ul><li>We assume all processes are carried out very slowly , </li></ul><ul><ul><li>so that the system remains in thermal equilibrium at all stages. </li></ul></ul>
  15. 15. Isothermal & Adiabatic Processes <ul><li>Previously, we discussed the relationship between </li></ul><ul><ul><li>pressure and volume and found that: </li></ul></ul><ul><li>  P  1/V </li></ul>
  16. 16. Isothermal & Adiabatic Processes <ul><li>We also stated that this was true, </li></ul><ul><ul><li>the temperature was constant. </li></ul></ul><ul><li>A graph of P vs V is shown below. </li></ul>
  17. 17. Isothermal & Adiabatic Processes <ul><li>The volume has increased from V i to V f while the pressure has decreased. </li></ul><ul><li>The solid line is an isotherm, </li></ul><ul><ul><li>a curve giving the relationship </li></ul></ul><ul><ul><li>between V and P </li></ul></ul><ul><ul><li>at a constant temperature. </li></ul></ul><ul><li>This is known as isothermic expansion. </li></ul>
  18. 18. Isothermal & Adiabatic Processes <ul><li>The process of compression or expansion of a gas ; </li></ul><ul><ul><li>so that no heat enters or leaves the system , </li></ul></ul><ul><ul><li>is said to be adiabatic . </li></ul></ul><ul><li>This comes from the Greek which means ‘impassable’. </li></ul>
  19. 19. Isothermal & Adiabatic Processes <ul><li>Adiabatic changes of volume can be achieved by ; </li></ul><ul><ul><li>performing the process so rapidly that , </li></ul></ul><ul><ul><li>heat has little time to enter or leave the system , </li></ul></ul><ul><ul><li>like a bicycle pump . </li></ul></ul><ul><li>O r by thermally insulating a system ; </li></ul><ul><ul><li>from its surroundings , </li></ul></ul><ul><ul><li>with Styrofoam. </li></ul></ul>
  20. 20. Isothermal & Adiabatic Processes <ul><li>A common example of a near adiabatic system ; </li></ul><ul><ul><li>is the compression and expansion of gases , </li></ul></ul><ul><ul><li>in the cylinders of a car engine. </li></ul></ul><ul><li>Compression and expansion occur too rapidly ; </li></ul><ul><ul><li>for heat to leave the system. </li></ul></ul>
  21. 21. Isothermal & Adiabatic Processes <ul><li>When work is done on a gas by ; </li></ul><ul><ul><li>adiabatically compressing it, </li></ul></ul><ul><ul><li>the gas gains internal energy , </li></ul></ul><ul><ul><li>and becomes warmer. </li></ul></ul><ul><li>When the gas adiabatically expands ; </li></ul><ul><ul><li>it does work on the surroundings , </li></ul></ul><ul><ul><li>and gives up its internal energy , </li></ul></ul><ul><ul><li>and becomes cooler. </li></ul></ul>
  22. 22. Isothermal & Adiabatic Processes <ul><li>Adiabatic processes occur in the atmosphere in large masses of air. </li></ul><ul><li>Due to their large size, </li></ul><ul><ul><li>mixing of different pressures </li></ul></ul><ul><ul><li>and temperatures </li></ul></ul><ul><li>only occur at the edges of these large masses </li></ul><ul><ul><li>and do little to change </li></ul></ul><ul><ul><li>the composition of these air masses. </li></ul></ul>
  23. 23. Isothermal & Adiabatic Processes <ul><li>As it flows up the side of a mountain ; </li></ul><ul><ul><li>its pressure reduces , </li></ul></ul><ul><li>allowing it to expand and cool. </li></ul><ul><li>The reduced pressure results </li></ul><ul><ul><li>in a reduced temperature. </li></ul></ul>
  24. 24. Isothermal & Adiabatic Processes <ul><li>It has been shown that dry air will drop </li></ul><ul><ul><li>by 10 o C </li></ul></ul><ul><ul><li>for every kilometre it rises. </li></ul></ul><ul><li>Air can flow over high mountains </li></ul><ul><ul><li>or rise in thunderstorms </li></ul></ul><ul><ul><li>or cyclones </li></ul></ul><ul><ul><li>many kilometres. </li></ul></ul>
  25. 25. Isothermal & Adiabatic Processes <ul><li>If a mass was 25 o C at sea level and was lifted 6 kilometres, </li></ul><ul><ul><li>its temperature would become -35 o C . </li></ul></ul><ul><li>A n air mass that was -20 O C at 6 km , </li></ul><ul><ul><li>would be 40 o C at sea level. </li></ul></ul>
  26. 26. Isothermal & Adiabatic Processes <ul><li>An example of this is when cold air is blown over the Mt Lofty Ranges. </li></ul><ul><li>Warm moist air is cooled as it rises over the ranges </li></ul><ul><ul><li>starts to rain. </li></ul></ul><ul><li>On the other side, the air begins to warm as it flows down the other side </li></ul><ul><ul><li>causing a warm wind. </li></ul></ul>
  27. 27. Isothermal & Adiabatic Processes <ul><li>As the Mt Lofty ranges are not very high ; </li></ul><ul><ul><li>the change in temperature is not as great , </li></ul></ul><ul><ul><li>c ompare d to the Rocky Mountains in the USA. . </li></ul></ul>
  28. 28. P – V Diagrams <ul><li>Thermodynamic processes can be represented by pressure - volume graphs. </li></ul>
  29. 29. P – V Diagrams <ul><li>In the, an ideal gas is expanding isothermally, </li></ul><ul><li>absorbing heat  Q , </li></ul><ul><li>and doing work  W . </li></ul><ul><li>T he system has not been restored ; </li></ul><ul><ul><li>to its original state , </li></ul></ul><ul><ul><li>at the end of the process. </li></ul></ul>
  30. 30. P – V Diagrams
  31. 31. P – V Diagrams <ul><li>Th e previous diagram is from a reversible heat engine. </li></ul><ul><li>Process 1-2 takes place at a constant volume ; </li></ul><ul><ul><li>Isochoric </li></ul></ul><ul><li>process 2-3 is adiabatic , </li></ul><ul><li>process 3-1 is at a constant pressure ; </li></ul><ul><ul><li>Isobaric. </li></ul></ul>
  32. 32. P – V Diagrams <ul><li>In the next case ; </li></ul><ul><li>the volume of an ideal gas is decreased , </li></ul><ul><ul><li>by adding weight to the piston. </li></ul></ul><ul><li>The process is adiabatic (  Q = 0). </li></ul>
  33. 33. P – V Diagrams
  34. 34. P – V Diagrams <ul><li>The process is as shown below on a graph . </li></ul>
  35. 35. P – V Diagrams <ul><li>In the next case, </li></ul><ul><li>the temperature of an ideal gas is raised from T ; </li></ul><ul><ul><li>to T +  T , </li></ul></ul><ul><ul><li>by a constant pressure process. </li></ul></ul><ul><li>Heat is added ; </li></ul><ul><ul><li>and work is done , </li></ul></ul><ul><ul><li>in lifting the loaded piston. </li></ul></ul>
  36. 36. P – V Diagrams
  37. 37. P – V Diagrams <ul><li>The process is shown below on a P-V diagram </li></ul>
  38. 38. P – V Diagrams <ul><li>The work ; </li></ul><ul><ul><li>P  V , </li></ul></ul><ul><ul><li>is the shaded area under the line , </li></ul></ul><ul><ul><li>connecting the initial and final states. </li></ul></ul>
  39. 39. Work Done By a Gas <ul><li>To calculate the work done in a process, </li></ul><ul><ul><li>some Year 10 knowledge is important. </li></ul></ul><ul><li>Imagine the pressure is kept constant during a process. </li></ul>
  40. 40. Work Done By a Gas
  41. 41. Work Done By a Gas <ul><li>If the gas expands slowly against the piston ; </li></ul><ul><ul><li>the work done to raise the piston is the force F multiplied by the distance d . </li></ul></ul><ul><li>But the force is just the pressure P of the gas ; </li></ul><ul><ul><li>multiplied the area A of the piston, </li></ul></ul><ul><ul><li>F = PA . </li></ul></ul>
  42. 42. Work Done By a Gas <ul><li>W = Fd = PAd </li></ul><ul><li>W = P  V = p(V 2 – V 1 ) </li></ul><ul><li>The sign of the work done depends on whether the gas expands or is compressed. </li></ul>
  43. 43. Work Done By a Gas <ul><li>If the gas expands, </li></ul><ul><ul><li>V is +ive and </li></ul></ul><ul><ul><li> work is +ive. </li></ul></ul><ul><li>The equation also is valid if the gas is compressed. </li></ul>
  44. 44. 1 st Law of Thermodynamics <ul><li>A long, long time ago; </li></ul><ul><ul><li>heat was thought to be an invisible fluid , </li></ul></ul><ul><ul><li>called a caloric , </li></ul></ul><ul><ul><li>which flowed like water , </li></ul></ul><ul><ul><li>from hot objects , </li></ul></ul><ul><ul><li>to cold objects. </li></ul></ul>
  45. 45. 1 st Law of Thermodynamics <ul><li>Caloric was conserved in its interactions which led to the discovery of the conservation of energy. </li></ul><ul><li>Within any system, </li></ul><ul><ul><li>the less heat energy it has, </li></ul></ul><ul><ul><li>the more ordered is the motion of its molecules. </li></ul></ul>
  46. 46. 1 st Law of Thermodynamics <ul><li>This can be seen in solids ; </li></ul><ul><ul><li>where the molecules all vibrate , </li></ul></ul><ul><ul><li>about a mean position. </li></ul></ul><ul><li>As heat is added ; </li></ul><ul><ul><li>the more disorderly the motion until in a gas , </li></ul></ul><ul><ul><li>we say that all molecules , </li></ul></ul><ul><ul><li>move in random motion. </li></ul></ul>
  47. 47. 1 st Law of Thermodynamics <ul><li>In a sense then, heat is the disordered energy of molecules. </li></ul><ul><li>There can be no heat in a single molecule. </li></ul><ul><li>Heat is a statistical concept ; </li></ul><ul><ul><li>applies only to a large number of molecules . </li></ul></ul>
  48. 48. 1 st Law of Thermodynamics <ul><li>I t is only when there is a great number of molecules </li></ul><ul><ul><li>does the concept of random </li></ul></ul><ul><ul><li>or disorderly movement have meaning. </li></ul></ul>
  49. 49. 1 st Law of Thermodynamics <ul><li>The discussion of heat, </li></ul><ul><ul><li>internal energy and temperature . </li></ul></ul><ul><li>H as given rise to the law of conservation of energy, </li></ul><ul><ul><li>and when applied to thermal systems , </li></ul></ul><ul><ul><li>is often referred to as the , </li></ul></ul><ul><li>F irst law of thermodynamics . </li></ul>
  50. 50. 1 st Law of Thermodynamics <ul><li>In a general form it is: </li></ul><ul><li>Whenever heat is added to a system, </li></ul><ul><ul><li>it transforms to an equal amount of some other form of energy. </li></ul></ul>
  51. 51. 1 st Law of Thermodynamics <ul><li>The added energy does one or both of two things to the system: </li></ul><ul><li>1. It increases the internal energy of the system if it remains in the system. </li></ul><ul><li>2. It does external work if it leaves the system. </li></ul>
  52. 52. 1 st Law of Thermodynamics <ul><li>Heat added = increase in internal energy + external work done by the system. </li></ul><ul><li>It can also be described mathematically: </li></ul><ul><li>   Q =  U +  W </li></ul><ul><ul><li>Q = heat energy </li></ul></ul><ul><ul><li>U = internal energy </li></ul></ul><ul><ul><li>W = work </li></ul></ul><ul><li>For an isolated system ; </li></ul><ul><ul><li>W = Q = 0 and  U = 0 </li></ul></ul>
  53. 53. 1 st Law of Thermodynamics <ul><li>This can apply to a number of cases: </li></ul><ul><li>1. Adiabatic Processes. </li></ul><ul><li>In this case, no heat enters or leaves the system, </li></ul><ul><ul><li>ie  Q = 0. </li></ul></ul><ul><li>Substituting this into the 1 st Law; </li></ul>
  54. 54. 1 st Law of Thermodynamics <ul><li>0 =  U +  W or, </li></ul><ul><ul><li> U = -  W . </li></ul></ul><ul><li>This means that if work is done ; </li></ul><ul><ul><li>there must be a decrease , </li></ul></ul><ul><ul><li>in the internal energy of the system. </li></ul></ul>
  55. 55. 1 st Law of Thermodynamics <ul><li>Constant Volume Processes . </li></ul><ul><li>( Isovolumetric or Isochoric Process ) </li></ul><ul><li>If the volume of a system is held constant ; </li></ul><ul><ul><li>the system can do no work, </li></ul></ul><ul><ul><li>ie  W =0. </li></ul></ul><ul><li>Substituting this into the 1 st Law; </li></ul>
  56. 56. 1 st Law of Thermodynamics <ul><li> Q =  U . </li></ul><ul><li>If heat is added to the system ; </li></ul><ul><ul><li> Q is + ive, </li></ul></ul><ul><ul><li>the internal energy of the system increases. </li></ul></ul><ul><li>The converse is also true. </li></ul>
  57. 57. 1 st Law of Thermodynamics <ul><li>3 . Cyclical Processes . </li></ul><ul><li>There are processes in which ; </li></ul><ul><ul><li>after certain interchanges of heat and work , </li></ul></ul><ul><ul><li>the system is returned to its initial state. </li></ul></ul><ul><li>N o property of the system can change, </li></ul><ul><ul><li>including the internal energy, </li></ul></ul><ul><ul><li>ie  U =0. </li></ul></ul>
  58. 58. 1 st Law of Thermodynamics <ul><li>Substituting this into the 1 st Law; </li></ul><ul><li> Q =  W . </li></ul><ul><li>The net work done must exactly ; </li></ul><ul><ul><li>equal the net amount of heat transferred. </li></ul></ul>
  59. 59. 1 st Law of Thermodynamics <ul><li>4. Free Expansion . </li></ul><ul><li>This is an adiabatic process ; </li></ul><ul><ul><li>no work is done on or by the system, </li></ul></ul><ul><ul><li>ie Q = W = 0. </li></ul></ul>
  60. 60. 1 st Law of Thermodynamics <ul><li>Substituting this into the 1 st Law; </li></ul><ul><li> U =0. </li></ul><ul><li>An example of this is given below. </li></ul>
  61. 61. 1 st Law of Thermodynamics <ul><li>A gas confined in an insulated container ; </li></ul><ul><ul><li>is released into another container , that originally was a vacuum and then waiting until an equilibrium is established . </li></ul></ul><ul><li>as shown below. </li></ul>
  62. 62. 1 st Law of Thermodynamics <ul><li>No heat is transferred because ; </li></ul><ul><ul><li>of the insulation </li></ul></ul><ul><li>N o work is done because ; </li></ul><ul><ul><li>the expanding gas rushes into an evacuated space, </li></ul></ul><ul><ul><li>its motion unopposed by any counteracting pressure. </li></ul></ul>
  63. 63. 1 st Law of Thermodynamics <ul><li>A summary is given: </li></ul> U = 0  Q =  W = 0 Free Expansion  Q =  W  U = 0 Closed Cycle  U =  Q  W = 0 Const V  U = -  W  Q = 0 Adiabatic Consequence Restriction Process
  64. 64. Thermodynamic Cycles <ul><li>A thermodynamic cycle is ; </li></ul><ul><ul><li>where heat may be transferred into (or out of) , </li></ul></ul><ul><ul><li>a system , </li></ul></ul><ul><ul><li>or work may be done on or by the system. </li></ul></ul><ul><li>It is assumed that all transfers are done ; </li></ul><ul><ul><li>very slowly so , </li></ul></ul><ul><ul><li>the system remains essentially , </li></ul></ul><ul><ul><li>in thermodynamic equilibrium at all stages. </li></ul></ul>
  65. 65. Thermodynamic Cycles <ul><li>An engine is a device that changes heat into mechanical work. </li></ul><ul><li>Example s include : </li></ul><ul><li>T he steam engine </li></ul><ul><ul><li>external combustion </li></ul></ul><ul><li>P etrol & diesel </li></ul><ul><ul><li>internal combustion engines. </li></ul></ul><ul><li>I t is impossible to convert all the heat energy into mechanical work. </li></ul>
  66. 66. Thermodynamic Cycles <ul><li>Consider the internal combustion engine. </li></ul><ul><li>Once the fuel is injected into the cylinder ; </li></ul><ul><ul><li>the piston moves up , </li></ul></ul><ul><ul><li>compresses the gas , </li></ul></ul><ul><ul><li> Q = 0 . </li></ul></ul>
  67. 67. Thermodynamic Cycles <ul><li>S park plug fires , </li></ul><ul><ul><li>temperature increases. </li></ul></ul><ul><li>Adiabatic expansion pushes the piston down , </li></ul><ul><ul><li>burnt gases are pushed out. </li></ul></ul>
  68. 68. Thermodynamic Cycles <ul><li>A heat engine is a device that changes internal energy into mechanical work. </li></ul><ul><li>Examples include ; </li></ul><ul><ul><li>S team engine , </li></ul></ul><ul><ul><li>I nternal combustion engine , </li></ul></ul><ul><ul><li>J et engine. </li></ul></ul>
  69. 69. Thermodynamic Cycles <ul><li>The mechanical work can only be obtained when ; </li></ul><ul><ul><li>heat flows from a high to low temperature , </li></ul></ul><ul><ul><li>only some of the heat is transferred into work. </li></ul></ul>
  70. 70. Thermodynamic Cycles <ul><li>Every heat engine will: </li></ul><ul><li>absorb internal energy from a reservoir of higher temperature . </li></ul><ul><li>convert some of this energy into mechanical work expel the remaining energy to some lower temperature reservoir , </li></ul><ul><ul><li>often called a sink. </li></ul></ul>
  71. 71. Thermodynamic Cycles
  72. 72. Thermodynamic Cycles <ul><li>Sadi Carnot ; </li></ul><ul><ul><li>a French engineer , </li></ul></ul><ul><ul><li>In 1924 , </li></ul></ul><ul><li>A nalysed the compression and expansion of in a heat engine </li></ul><ul><li>M a de a fascinating discovery </li></ul><ul><ul><li>when he examined the ideal engine , </li></ul></ul><ul><ul><li>now called a Carnot engine. </li></ul></ul>
  73. 73. Thermodynamic Cycles <ul><li>The upper fraction of heat that can be converted to useful work ; </li></ul><ul><ul><li>even under ideal conditions, </li></ul></ul><ul><ul><li>depends on the temperature difference between , </li></ul></ul><ul><ul><ul><li>the hot reservoir and the cold sink. </li></ul></ul></ul><ul><li>The cycle starts at a in the diagram below. </li></ul>
  74. 74. Thermodynamic Cycles
  75. 75. Thermodynamic Cycles <ul><li>a  b </li></ul><ul><ul><li>The gas expands isothermally by </li></ul></ul><ul><ul><li>adding heat Q H at temp T H . </li></ul></ul><ul><li>b  c </li></ul><ul><ul><li>Gas then expands adiabatically </li></ul></ul><ul><ul><li>no heat is exchanged but temp drops to T L </li></ul></ul>
  76. 76. Thermodynamic Cycles <ul><li>c  d </li></ul><ul><ul><li>Compressed at const temp T L and heat Q L flows out. </li></ul></ul><ul><li>d  a </li></ul><ul><ul><li>Gas then compressed adiabatically to its original sta t e. </li></ul></ul>
  77. 77. Thermodynamic Cycles <ul><li>His equation gives the ideal or Carnot efficiency of a heat engine. </li></ul>
  78. 78. Thermodynamic Cycles <ul><li>The efficiency of the cycle only depends on ; </li></ul><ul><ul><li>the absolute temperature of the high and , </li></ul></ul><ul><ul><li>low temperature reservoirs. </li></ul></ul><ul><li>The greater the difference between them ; </li></ul><ul><ul><li>the greater the efficiency. </li></ul></ul>
  79. 79. Entropy <ul><li>Heat flows naturally from a hot object to a cold object; heat will not flow spontaneously from a cold object to a hot object. </li></ul><ul><li>Clausius introduced the word entropy ; </li></ul><ul><ul><li>from the Greek words meaning , </li></ul></ul><ul><ul><li>transformation content. </li></ul></ul>
  80. 80. Entropy <ul><li>Entropy is a function of ; </li></ul><ul><ul><li>the state of the system. </li></ul></ul><ul><li>Entropy can be interpreted as ; </li></ul><ul><ul><li>a measure of of the order or disorder of a system. </li></ul></ul>
  81. 81. Entropy <ul><li>No device is possible whose sole effect is to transform a given amount of heat completely into work. </li></ul><ul><li>This is the Kelvin-Planck formulation of the Second Law. </li></ul>
  82. 82. Entropy <ul><li>The second law suggests that everything ; </li></ul><ul><ul><li>is tending to disorder. </li></ul></ul><ul><li>Heat is a lower form of energy ; </li></ul><ul><ul><li>so when heat is given off, </li></ul></ul><ul><ul><li>it suggests that the system is tending to disorder. </li></ul></ul><ul><li>When your parents ask you to clean your room, you might like to suggest that you are only obeying entropy </li></ul>
  83. 83. Entropy <ul><li>Entropy can only remain the same ; </li></ul><ul><ul><li>for an idealised (reversible) process. </li></ul></ul><ul><li>For any real process ; </li></ul><ul><ul><li>the change in entropy is greater than zero. </li></ul></ul><ul><li>The general statement of the second law of thermodynamics becomes : </li></ul>
  84. 84. Entropy <ul><li>According to Clausius, the change in entropy S of a system ; </li></ul><ul><ul><li>when an amount of heat Q is added to it , </li></ul></ul><ul><ul><li>by a reversible process , </li></ul></ul><ul><ul><li>at constant temperature, is given by: </li></ul></ul><ul><li> S = Q/T </li></ul><ul><li>The units of entropy are J K -1 </li></ul>
  85. 85. Entropy <ul><li>In the example, although one part of the system decreased in entropy ; </li></ul><ul><ul><li>the total entropy for the system increased. </li></ul></ul><ul><li>The second law stated in terms of entropy becomes: </li></ul><ul><li>The entropy of an isolated system never decreases. It can only stay the same or increase. </li></ul>
  86. 86. Entropy <ul><li>Although the entropy of one part of the universe may decease in any process ; </li></ul><ul><ul><li>the entropy is some other part of the universe increases by a greater amount, </li></ul></ul><ul><ul><li>the total entropy always increases. </li></ul></ul>
  87. 87. Entropy <ul><li>The total entropy of any system plus that of its environment increases as the result of any natural process. </li></ul>
  88. 88. 2 nd Law of Thermodynamics <ul><li>A coin, when put flat on a table ; </li></ul><ul><ul><li>cannot spontaneously rise into the air, </li></ul></ul><ul><ul><li>suddenly get too hot to touch , </li></ul></ul><ul><ul><li>flatten out to something twice its diameter. </li></ul></ul><ul><li>These phenomena can easily be explained. </li></ul>
  89. 89. 2 nd Law of Thermodynamics <ul><li>Each of these situations requires energy to be added to the system and so violate the conservation of energy. </li></ul>
  90. 90. 2 nd Law of Thermodynamics <ul><li>We also know that coffee in a cup cannot ; </li></ul><ul><ul><li>s pontaneously cool down and start to swirl around, </li></ul></ul><ul><ul><li>one end of a spoon gets hot while the other end cools down . </li></ul></ul><ul><li>molecules of air in the room do not move to one corner of the room and stay there. </li></ul>
  91. 91. 2 nd Law of Thermodynamics <ul><li>These events however do obey the conservation of energy </li></ul><ul><ul><li>and the first law of thermodynamics. </li></ul></ul>
  92. 92. 2 nd Law of Thermodynamics <ul><li>The coffee could get its energy from the cooling process, </li></ul><ul><ul><li>the hot end of the spoon could get its energy from the cool end </li></ul></ul><ul><ul><li>molecules of air do not need to change their kinetic energy, only their position. </li></ul></ul>
  93. 93. 2 nd Law of Thermodynamics <ul><li>These events , however, do not happen although the reverse does happen. </li></ul><ul><li>There are many other cases where an event will happen in one direction but not the other. </li></ul>
  94. 94. 2 nd Law of Thermodynamics <ul><li>The direction in which natural events happen is </li></ul><ul><li>D etermined by the Second Law of Thermodynamics . </li></ul><ul><li>It can be described on a macroscopic and microscopic base: </li></ul>
  95. 95. 2 nd Law of Thermodynamics <ul><li>In the process of heat conduction from a hot body to a cold one ; </li></ul><ul><ul><li>entropy increases and order goes to disorder. </li></ul></ul><ul><li>Useful work can be obtained while there is a temperature difference but ; </li></ul><ul><ul><li>when the two heat reservoirs reach the Vale temperature, </li></ul></ul><ul><ul><li>no work can be obtained from them. </li></ul></ul>
  96. 96. 2 nd Law of Thermodynamics <ul><li>No energy is lost, it instead becomes less useful ; </li></ul><ul><ul><li>the energy becomes degraded. </li></ul></ul><ul><li>The natural outcome of this is that as time goes on ; </li></ul><ul><ul><li>the universe will reach a state of maximum disorder. </li></ul></ul>
  97. 97. 2 nd Law of Thermodynamics <ul><li>The whole universe will be at one temperature ; </li></ul><ul><ul><li>no work can be done. </li></ul></ul><ul><li>All the energy will have become degraded ; </li></ul><ul><ul><li>to thermal energy. </li></ul></ul><ul><li>All change will cease. </li></ul><ul><li>This is known as heat death . </li></ul>
  98. 98. Refrigerators & Heat Pumps <ul><li>Heat flows from the inside of warm houses in winter to the cold outside. </li></ul><ul><li>The reverse can happen, </li></ul><ul><ul><li>but only by imposing external effort </li></ul></ul><ul><ul><li>as do heat pumps. </li></ul></ul><ul><li>Air conditioners or refrigerators use these. </li></ul>
  99. 99. Refrigerators & Heat Pumps
  100. 100. Refrigerators & Heat Pumps <ul><li>The second form of the 2 nd law of thermodynamics states: </li></ul><ul><li>  It is not possible for heat to flow from one body to another body at a higher temperature, with no other change taking place. </li></ul>
  101. 101. Refrigerators & Heat Pumps <ul><li>A device that causes heat to move from a cold place to a hot place is called a refrigerator. </li></ul>
  102. 102. Refrigerators & Heat Pumps
  103. 103. Refrigerators & Heat Pumps <ul><li>In the diagram on the left, heat Q c is extracted from a low temperature reservoir </li></ul><ul><ul><li>the food storage area </li></ul></ul><ul><li>S ome work W is done on the system </li></ul><ul><ul><li>by an external agent. </li></ul></ul>
  104. 104. Refrigerators & Heat Pumps <ul><li>The heat and work are combined and discharged as heat Q H ; </li></ul><ul><ul><li>to a high temperature reservoir , </li></ul></ul><ul><ul><ul><li>the kitchen. </li></ul></ul></ul><ul><li>The work shows up on the quarterly electricity bill ; </li></ul><ul><ul><li>done by the motor that drives the unit. </li></ul></ul>
  105. 105. Refrigerators & Heat Pumps <ul><li>The diagram on the right shows a perfect refrigerator where no work is required. </li></ul><ul><li>This fridge is yet to be built. </li></ul>
  106. 106. Refrigerators & Heat Pumps <ul><li>In an air-conditioner, </li></ul><ul><ul><li>the low temperature reservoir is the room to be cooled </li></ul></ul><ul><ul><li>the high temperature reservoir is the outside air </li></ul></ul><ul><ul><ul><li>where the condenser coils are located. </li></ul></ul></ul><ul><li>Again, the motor does the work. </li></ul>
  107. 107. Refrigerators & Heat Pumps <ul><li>For interest </li></ul><ul><ul><li>not in syllabus </li></ul></ul><ul><li>Both the fridge and the air-conditioner are rated by the amount of work they have to do. </li></ul><ul><li>The ratings are by the </li></ul><ul><li>coefficient of performance K . </li></ul>
  108. 108. Refrigerators & Heat Pumps <ul><li>This is defined from: </li></ul><ul><li>Design engineers want the performance of a fridge to be high as possible. </li></ul>
  109. 109. Refrigerators & Heat Pumps <ul><li>A value of 5 is typical for a household fridge, </li></ul><ul><ul><li>while a room air-conditioner </li></ul></ul><ul><ul><li>range 2-3. </li></ul></ul><ul><li>If there was a perfect fridge, </li></ul><ul><ul><li>the value of K =  . </li></ul></ul>
  110. 110. The 2 nd Law & Technology <ul><li>The second law indicates limits for technology. </li></ul><ul><li>Heat engines and refrigerators cannot be perfect. . </li></ul><ul><li>It is not possible for heat to flow from one body to another ; </li></ul><ul><ul><li>at a higher temperature, </li></ul></ul><ul><ul><li>with no other changes. </li></ul></ul>
  111. 111. The 2 nd Law & Technology <ul><li>As the world is full of low - grade thermal energy from concept of entropy , </li></ul><ul><li>W hy can’t we concentrate and harvest that energy? </li></ul><ul><li>Why not lower the temperature of the oceans by 1 o C </li></ul><ul><ul><li>and use that enormous amount of energy? </li></ul></ul>
  112. 112. The 2 nd Law & Technology <ul><li>It can be done but it requires ; </li></ul><ul><ul><li>work be put into the system which requires , </li></ul></ul><ul><ul><li>energy to drive a fridge like machine. </li></ul></ul><ul><li>This energy input would make it unfeasible from an energy perspective. </li></ul>
  113. 113. The 2 nd Law & Technology <ul><li>E very living creature from bacteria </li></ul><ul><ul><li>to higher life forms such as </li></ul></ul><ul><ul><li>you </li></ul></ul><ul><li>E xtract energy from their surroundings </li></ul><ul><ul><li>to increase their own organisation. </li></ul></ul>
  114. 114. The 2 nd Law & Technology <ul><li>This tends to indicate that all life ; </li></ul><ul><ul><li>Including you , </li></ul></ul><ul><ul><li>plus their waste products </li></ul></ul><ul><ul><li>have a net increase in entropy. </li></ul></ul><ul><li>The 1 st law is a universal law for which no exceptions have been observed. </li></ul>
  115. 115. The 2 nd Law & Technology <ul><li>The 2 nd law is a probability statement. </li></ul><ul><li>Given enough time, </li></ul><ul><ul><li>even the most improbable states could exist. </li></ul></ul><ul><li>The 2 nd law tells us the most probable event, </li></ul><ul><ul><li>not the only possible event. </li></ul></ul>
  116. 116. The 2 nd Law & Technology <ul><li>The laws of thermodynamics are often put this way: </li></ul><ul><li>You can’t win , </li></ul><ul><ul><li>because you can’t get more energy out of a system than you put in, </li></ul></ul>
  117. 117. The 2 nd Law & Technology <ul><li>Y ou can’t break even , </li></ul><ul><ul><li>because you can’t even get as much energy as you put in, </li></ul></ul>
  118. 118. The 2 nd Law & Technology <ul><li>Y ou can’t get out of the game , </li></ul><ul><ul><li>entropy in the universe is always increasing. </li></ul></ul>
  119. 119. TRY EXAMPLE 1 <ul><li>1.00 kg of water is to be converted to steam at standard atmospheric pressure. The volume changes from an initial value of 1.00 x 10 -3 m 3 as a liquid to 1.671 m 3 as steam. </li></ul><ul><li>a) How much work is done by the system during this process? </li></ul><ul><li>b) How much heat must be added to the system during the process? ( L = 2260 kJ kg -1 ) </li></ul><ul><li>c) What is the change in the internal energy of the system during the boiling process? </li></ul>
  120. 120. Solution – Part (a) <ul><li>W = P  V </li></ul><ul><li>W = 1.01 x 10 5 (1.671 - 1 x 10 -3 ) </li></ul><ul><li>W = 1.69 x 10 5 J </li></ul>
  121. 121. Solution – Part (b) <ul><li> Q = mL </li></ul><ul><li> Q = 1 x 2260 </li></ul><ul><li> Q = 2260 kJ </li></ul><ul><li> Q = 2.26 x 10 6 J </li></ul>
  122. 122. Solution – Part (c) <ul><li> Q =  U +  W </li></ul><ul><li> U =  Q -  W </li></ul><ul><li> U = 2.26 x 10 6 - 1.69 x 10 5 </li></ul><ul><li> U = 2.090 x 10 6 J </li></ul><ul><li>As the result is positive ; </li></ul><ul><ul><li>the internal energy of the system , </li></ul></ul><ul><ul><li>has increased during the boiling process. </li></ul></ul>
  123. 123. TRY EXAMPLE 2 <ul><li>A steam turbine uses steam at 127 o C which then is cooled to 27 o C. What is the ideal efficiency of the turbine? </li></ul>
  124. 124. Solution <ul><li>Convert all temperatures to SI units </li></ul><ul><li>127 o C = 273 + 127 = 400 K </li></ul><ul><li>27 o C = 273 + 27 = 300 K </li></ul><ul><li>Efficiency = ¼ </li></ul><ul><li>This means only 25% of the energy is converted into work while 75% is expelled as waste. </li></ul>
  125. 125. TRY EXAMPLE 3 <ul><li>A household fridge, whose coefficient of performance is 4.7, extracts heat from a cooling chamber at the rate of 250 J per cycle. </li></ul><ul><li>a) How much work per cycle is required to operate the fridge? </li></ul><ul><li>b) How much heat per cycle is discharged to the room, which forms the high temperature reservoir of the fridge? </li></ul>
  126. 126. Solution – Part (a) <ul><li>From  W  =  Q c  / K </li></ul><ul><li> W  = 250/4.7 </li></ul><ul><li> W  = 53 J </li></ul><ul><li>As work is done on the system, W = -53 J </li></ul>
  127. 127. Solution – Part (b) <ul><li>The net work done per cycle must equal the heat transferred per cycle. </li></ul><ul><li> W  =  Q H  -  Q c  </li></ul><ul><li> Q H  =  W  +  Q c  </li></ul><ul><li>   Q H  = 53 + 250 = 303 J </li></ul>
  128. 128. TRY EXAMPLE 4 <ul><li>An ice cube of mass 60 g is taken from a storage compartment at 0 o C and placed in a paper cup. After a few minutes, exactly half of the mass of the ice cube has melted, becoming water at 0 o C. Find the change in entropy. </li></ul>
  129. 129. Solution <ul><li>Q = mL </li></ul><ul><li>Q = 0.06 x 3.34 x 10 5 </li></ul><ul><li>Q = 1.002 x 10 4 J </li></ul><ul><li> S = Q/T </li></ul><ul><li> S = 1.002 x 10 4 /273 </li></ul><ul><li> S = 36.7 J K -1 </li></ul>
  130. 130. TRY EXAMPLE 5 <ul><li>A sample of 50.0 kg of water at 20.0 o C is mixed with 50.0 kg of water at 24 o C. Estimate the change in entropy. </li></ul>
  131. 131. Solution <ul><li>The final temperature of the mixture will be 22 o C as we started with equal amounts of water. A quantity of heat, </li></ul><ul><li>Q = mc  T </li></ul><ul><li>Q = 50.0 x 4.18 x 10 3 x 2 </li></ul><ul><li>Q = 4.18 x 10 5 J </li></ul>
  132. 132. Solution <ul><li>flows out of the hot water and flows into the cold water. </li></ul><ul><li>The total change in entropy will be the sum of changes in entropy of the hot and cold water. </li></ul><ul><li> S =  S H +  S C </li></ul><ul><li>To calculate the entropy, we must use the average temperature of 23 o C for the hot water and 21 o C for the cold water. </li></ul>
  133. 133. Solution <ul><li> S H = 4.18 x 10 5 /296 </li></ul><ul><li> S H = -1.41 x 10 3 J K -1 (-ive as heat flows out of the hot water) </li></ul><ul><li>   S C = 4.18 x 10 5 /294 </li></ul><ul><li> S C = 1.42 x 10 3 J K -1 </li></ul><ul><li> S =  S H +  S C </li></ul><ul><li> S = -1.41 x 10 3 + 1.42 x 10 3 </li></ul><ul><li> S = 10 J K -1 </li></ul>