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### 3 1

1. 1. Thermal Physics Topic 3.1 Thermal Concepts
2. 2. Temperature <ul><li>At a macroscopic level, temperature is the degree of hotness or coldness of a body as measured by a thermometer </li></ul><ul><li>Temperature is a property that determines the direction of thermal energy transfer between two bodies in contact </li></ul><ul><li>Temperature is measured in degrees Celsius ( o C) or Kelvin (K) </li></ul><ul><ul><li>Where Temp in K = Temp in o C + 273(.15) </li></ul></ul><ul><ul><li>Temp in K is known as the absolute temperature </li></ul></ul>
3. 3. Thermal Equilibrium <ul><li>When 2 bodies are placed in contact </li></ul><ul><li>Heat will flow from the warmer body to the colder body </li></ul><ul><li>Until the two objects reach the same temperature </li></ul><ul><li>They will then be in Thermal Equilibrium </li></ul><ul><li>This is how a thermometer works </li></ul>
4. 4. Use the idea of thermal equilibrium to explain <ul><li>Why kitchen floors are generally cold to bare feet during winter </li></ul><ul><li>Why hot water bottles are used in winter </li></ul><ul><li>Why carpet feels warmer than wood </li></ul><ul><li>Why do car windows fog in winter </li></ul>
5. 5. Thermometers <ul><li>A temperature scale is constructed by taking two fixed, reproducible temperatures </li></ul><ul><li>The upper fixed point is the boiling point of pure water at atmospheric pressure </li></ul><ul><li>The lower fixed point is the melting point of pure ice at atmospheric pressure </li></ul>
6. 6. <ul><li>These were then given the values of 100 o C and 0 o C respectively, and the scale between them was divided by 100 to give individual degrees </li></ul><ul><li>A thermometer uses the expansion and contraction of a liquid ; </li></ul><ul><ul><li>usually mercury or alcohol , </li></ul></ul><ul><ul><li>in a glass capillary tube with a scale to , </li></ul></ul><ul><ul><li>measure the expansion or contraction. </li></ul></ul>
7. 7. Temperature - Microscopic <ul><li>At a microscopic level, temperature is regarded as a measure of the average kinetic energy per molecule associated with its movement in the substance </li></ul>
8. 8. Internal Energy <ul><li>The Internal (thermal) energy of a body is the total energy associated with the thermal motions of the particles </li></ul><ul><li>It can comprise of both kinetic and potential energies associated with particle motion </li></ul><ul><li>Kinetic energy arises from the translational and rotational motions </li></ul><ul><li>Potential energy arises from the forces between the molecules </li></ul>
9. 9. Heat <ul><li>The term heat represents energy transfer due to a temperature difference </li></ul><ul><li>Occurs from higher to lower temperature regions </li></ul>
10. 10. Heat <ul><li>Most people tend to believe that all matter ; </li></ul><ul><ul><li>contains heat. </li></ul></ul><ul><li>All matter contains a number of forms of energy ; </li></ul><ul><ul><li>but not heat. </li></ul></ul><ul><li>Heat is the transfer of energy from a body with higher temperature to ; </li></ul><ul><ul><li>one of lower temperature. </li></ul></ul>
11. 11. Methods of Heat Transfer <ul><li>Heat can be transferred from one body to another by </li></ul><ul><ul><li>Conduction </li></ul></ul><ul><ul><li>Convection </li></ul></ul><ul><ul><li>Radiation </li></ul></ul>
12. 12. Conduction <ul><li>Conduction can take place ; </li></ul><ul><ul><li>within materials and , </li></ul></ul><ul><ul><li>between different materials , </li></ul></ul><ul><ul><li>that are in direct contact. </li></ul></ul><ul><li>It can be explained in terms of collisions ; </li></ul><ul><ul><li>between atoms or molecules and , </li></ul></ul><ul><ul><li>the actions of loosely bound electrons. </li></ul></ul><ul><li>How does a metal rod get hot when only part is held in a flame? </li></ul>
13. 13. Convection <ul><li>This involves the transfer of energy ; </li></ul><ul><ul><li>from one molecule to another , </li></ul></ul><ul><ul><li>with the molecules moving. </li></ul></ul><ul><li>Another way in which convection works is ; </li></ul><ul><ul><li>for the hotter material to move up such as hot air. </li></ul></ul><ul><li>Convection occurs in all fluids ; </li></ul><ul><ul><li>w h ether they are liquids or gases. </li></ul></ul><ul><li>Hot air above a stove becomes less dense ; </li></ul><ul><ul><li>and moves up toward the ceiling… </li></ul></ul><ul><li>Explain how it is possible to fly in hot air balloon </li></ul>
14. 14. Radiation <ul><li>All energy, including heat ; </li></ul><ul><ul><li>which is transferred by radiation, </li></ul></ul><ul><ul><li>is called radiant energy . </li></ul></ul><ul><li>Higher temperature objects emit ; </li></ul><ul><ul><li>shorter wavelengths </li></ul></ul><ul><ul><li>and vice - versa. </li></ul></ul><ul><li>The coolest objects that emit light ; </li></ul><ul><ul><li>we can see (red) , </li></ul></ul><ul><ul><li>are at a temperature of 500 o C. </li></ul></ul>
15. 15. Thermal Properties of Gases <ul><li>Investigations involved the measurement of </li></ul><ul><ul><li>Pressure </li></ul></ul><ul><ul><li>Volume </li></ul></ul><ul><ul><li>Temperature </li></ul></ul><ul><li>These experiments used these macroscopic properties of a gas to formulate a number of gas laws </li></ul>
16. 16. Units <ul><li>Temperature is always measured in K </li></ul><ul><li>Volume is usually in m 3 </li></ul><ul><li>Pressure can be different units as long as you are consistent </li></ul><ul><li>But 1 atm = 1.01 x 10 5 Nm -2 = 101.3 kPa = 760 mmHg </li></ul>
17. 17. Gas Laws <ul><li>1. Boyle’s Law : </li></ul><ul><li>Variation of volume with pressure (const T). </li></ul><ul><li>eg Bike pump . </li></ul>
18. 18. Gas Laws <ul><li>Boyle’s experiment can be repeated ; </li></ul><ul><ul><li>by using a flexible J-tube containing mercury , </li></ul></ul><ul><ul><li>and a barometer to measure atmospheric pressure. </li></ul></ul><ul><li>Air was trapped in one end ; </li></ul><ul><ul><li>and varied the pressure on it , </li></ul></ul><ul><ul><li>by raising the other end of the tube as shown below: </li></ul></ul>
19. 19. Gas Laws
20. 20. Gas Laws <ul><li>The gas pressure of the enclosed air ; </li></ul><ul><ul><li>is equal to the atmospheric pressure plus , </li></ul></ul><ul><ul><li>the pressure resulting from , </li></ul></ul><ul><ul><li>the height difference of Hg in the two arms. </li></ul></ul><ul><li>Taking a number of pressure and volume readings ; </li></ul><ul><ul><li>the graph looks like: </li></ul></ul>
21. 21. Gas Laws
22. 22. Gas Laws <ul><li>A more revealing graph is obtained by plotting p vs 1/V </li></ul>
23. 23. Gas Laws <ul><li>As a straight line is obtained ; </li></ul><ul><ul><li>that passes through the origin, </li></ul></ul><ul><ul><li>we can say mathematically: </li></ul></ul><ul><li>p  1/V </li></ul>
24. 24. Gas Laws <ul><li>If the same experiment is performed ; </li></ul><ul><ul><li>at different temperatures, </li></ul></ul><ul><ul><li>a curve is still obtained but at different positions. </li></ul></ul>
25. 25. Gas Laws
26. 26. Gas Laws <ul><li>The curves are called isotherms ; </li></ul><ul><ul><li>as the temp at each point on the curve is the same. </li></ul></ul>
27. 27. Gas Laws <ul><li>We have assumed ; </li></ul><ul><ul><li>that there is a fixed amount of gas , </li></ul></ul><ul><ul><li>maintained at a constant temperature. </li></ul></ul><ul><li>We can also write, p = k /V or pV = k </li></ul>
28. 28. Gas Laws <ul><li>k is a constant of proportionality ; </li></ul><ul><ul><li>and is equal to the slope. </li></ul></ul><ul><li>For different points on the graph ; </li></ul><ul><ul><li>p 1 V 1 = k and p 2 V 2 = k </li></ul></ul><ul><li> p 1 V 1 = p 2 V 2 (for const. temp) </li></ul>
29. 29. Gas Laws <ul><li>Boyle’s law states ; </li></ul><ul><ul><li>at constant temperature, </li></ul></ul><ul><ul><li>the volume of a fixed mass of gas , </li></ul></ul><ul><ul><li>varies inversely with its pressure. </li></ul></ul>
30. 30. Gas Laws <ul><li>2. Charles’ Law : </li></ul><ul><li>Variation of volume with temperature (const p). </li></ul><ul><li>To verify this ; </li></ul><ul><ul><li>a capillary tube is sealed at one end , </li></ul></ul><ul><ul><li>and a small mercury piston is included, </li></ul></ul><ul><ul><li>trapping a sample of air. </li></ul></ul>
31. 31. Gas Laws <ul><li>A thermometer is strapped to the tube ; </li></ul><ul><ul><li>and both are placed in glycerol. </li></ul></ul><ul><li>The pressure is fixed ; </li></ul><ul><ul><li>and is equal to atmospheric pressure. </li></ul></ul>
32. 32. Gas Laws <ul><li>The glycerol is heated ; </li></ul><ul><ul><li>and the length of the air column is noted , </li></ul></ul><ul><ul><li>at various temperatures. </li></ul></ul><ul><li>The length of the column can be read ; </li></ul><ul><ul><li>as the volume in arbitrary units , </li></ul></ul><ul><ul><li>as the cross section is uniform. </li></ul></ul>
33. 33. Gas Laws
34. 34. Gas Laws <ul><li>The results obtained can be graphed as below: </li></ul>
35. 35. Gas Laws <ul><li>This graph does not go through the origin. </li></ul><ul><li>When extrapolated ; </li></ul><ul><ul><li>it cuts the temp axis at , </li></ul></ul><ul><ul><li>-273 o C </li></ul></ul>
36. 36. Gas Laws
37. 37. Gas Laws <ul><li>This creates a new scale defined as ; </li></ul><ul><ul><li>The absolute temperature scale, where </li></ul></ul><ul><ul><li>zero degrees kelvin (0K) = -273 o C. </li></ul></ul><ul><li>A 1K rise = 1 o C rise. </li></ul><ul><li>A real gas would liquefy before it reaches 0K ; </li></ul><ul><ul><li>and so no gas is ideal. </li></ul></ul>
38. 38. Gas Laws <ul><li>Any extrapolation should not continue ; </li></ul><ul><ul><li>past the liquefaction point. </li></ul></ul><ul><li>No gas can reach a temperature below 0K ; </li></ul><ul><ul><li>as no gas could have a negative volume. </li></ul></ul><ul><li>Graphing for two different pressures: </li></ul>
39. 39. Gas Laws
40. 40. Gas Laws <ul><li>Using the Kelvin scale ; </li></ul><ul><ul><li>we can say mathematically: </li></ul></ul><ul><li>V  absolute T </li></ul><ul><li>V = k T or k = V/T </li></ul><ul><ul><li>where k is the gradient of the graph. </li></ul></ul><ul><li>For two points, (V 1 ,T 1 ) and (V 2 ,T 2 ) </li></ul><ul><li>V 1 /T 1 = V 2 /T 2 </li></ul>
41. 41. Gas Laws <ul><li>Charles’ law states ; </li></ul><ul><ul><li>at constant pressure, </li></ul></ul><ul><ul><li>the volume of a fixed mass of gas , </li></ul></ul><ul><ul><li>varies directly with its absolute temperature. </li></ul></ul>
42. 42. Gas Laws <ul><li>3. Guy-Lussac’s Law : (Law of pressures)   </li></ul><ul><li>Variation of pressure with temperature (const V). </li></ul>
43. 43. Gas Laws <ul><li>A bulb enclosing a fixed volume of gas ; </li></ul><ul><ul><li>is placed in a beaker of water , </li></ul></ul><ul><ul><li>and attached to a mercury manometer , </li></ul></ul><ul><ul><li>as shown below: </li></ul></ul>
44. 44. Gas Laws
45. 45. Gas Laws <ul><li>The water is warmed ; </li></ul><ul><ul><li>the air expands in the bulb and tube , </li></ul></ul><ul><ul><li>and causes the Hg , </li></ul></ul><ul><ul><li>to be forced up the manometer. </li></ul></ul>
46. 46. Gas Laws <ul><li>One arm is then raised ; </li></ul><ul><ul><li>to increase pressure , </li></ul></ul><ul><ul><li>and compress the air , </li></ul></ul><ul><ul><li>back to the original volume. </li></ul></ul><ul><li>The height difference is recorded. </li></ul>
47. 47. Gas Laws
48. 48. Gas Laws <ul><li>As the graph does not pass through the origin ; </li></ul><ul><ul><li>it must be extrapolated. </li></ul></ul>
49. 49. Gas Laws <ul><li>We can now mathematically say: </li></ul><ul><li>  p  absolute T </li></ul><ul><li>  p = k T or k = p/T; </li></ul><ul><ul><li>where k is the gradient of the graph. </li></ul></ul><ul><li>Using two points on the graph; </li></ul><ul><li>p 1 /T 1 = p 2 /T 2 </li></ul>
50. 50. Gas Laws <ul><li>The law of pressures state ; </li></ul><ul><ul><li>at a constant volume, </li></ul></ul><ul><ul><li>the pressure of a given mass of gas , </li></ul></ul><ul><ul><li>varies directly with the Kelvin temperature. </li></ul></ul>
51. 51. Gas Laws <ul><li>GENERAL GAS EQUATION </li></ul><ul><li>All three laws studied above ; </li></ul><ul><ul><li>can be combined into one. </li></ul></ul><ul><li>From Boyle’s law: </li></ul>
52. 52. Gas Laws
53. 53. Gas Laws <ul><li>The curves plotted from the above situations are shown: </li></ul>
54. 54. Gas Laws <ul><li>Going from (1) to (2) </li></ul><ul><li>V  by raising T at constant pressure. </li></ul><ul><li>V 1 /T 1 = V * /T 2 (Charles’ Law)  </li></ul><ul><li>Going from (2) to (3) temp constant ; </li></ul><ul><ul><li>piston is withdrawn causing V  & P  . </li></ul></ul><ul><li>p 1 V * = p 2 V 2 (Boyle’s Law)  </li></ul><ul><li>Multiplying  and  </li></ul>
55. 55. Gas Laws <ul><li>(V 1 x p 1 V * )/T 1 = (V * x p 2 V 2 )/T 2 </li></ul><ul><li>(p 1 V 1 )/T 1 = (p 2 V 2 )/T 2 </li></ul><ul><li>pV/T = constant </li></ul><ul><li>This is called the ideal gas law ; </li></ul><ul><ul><li>and is accurate except , </li></ul></ul><ul><ul><li>at low temperatures , </li></ul></ul><ul><ul><li>and high pressures. </li></ul></ul>
56. 56. Gas Laws <ul><li>The only gas ; </li></ul><ul><ul><li>that approximates the ideal gas law , </li></ul></ul><ul><ul><li>over a wide range of conditions , </li></ul></ul><ul><ul><li>is Helium, </li></ul></ul><ul><ul><li>to 4.2K. </li></ul></ul>
57. 57. Gas Laws <ul><li>p 1 V 1 /T 1 = C </li></ul><ul><li>C depends on the number of moles, n , and ; </li></ul><ul><ul><li>Universal gas constant, R </li></ul></ul><ul><ul><li>(8.315 J mol -1 K -1 ) </li></ul></ul><ul><li>For one mole of gas, pV = RT </li></ul><ul><li>For n moles of gas, pV = nRT </li></ul>
58. 58. Gas Laws <ul><li>One mole of a substance contains ; </li></ul><ul><ul><li>6.023 x 10 23 particles. </li></ul></ul><ul><li>This value is called Avogadro’s number ; </li></ul><ul><ul><li>and is given the symbol N A . </li></ul></ul><ul><li>To find the moles present ( n ) ; </li></ul><ul><ul><li>divide the total number of molecules N , </li></ul></ul><ul><ul><li>by Avogadro’s number. </li></ul></ul>
59. 59. Gas Laws <ul><li>n = N/N A </li></ul><ul><li>m grams of a substance contains ; </li></ul><ul><ul><li>m/m A moles, </li></ul></ul><ul><ul><li>where the molar mass is expressed in grams. </li></ul></ul><ul><li>n = m/m A </li></ul>
60. 60. The Mole <ul><li>The mole is the amount of substance which contains the same number of elementary particles as there are in 12 grams of carbon-12 </li></ul><ul><li>Experiments show that this is </li></ul><ul><li>6.02 x 10 23 particle s </li></ul><ul><li>A value denoted by N A and called the Avogadro Constant (units mol -1 ) </li></ul>
61. 61. Molar Mass <ul><li>Molar mass is the mass of one mole of the substance </li></ul><ul><li>SI units are kg mol -1 </li></ul>
62. 62. Example <ul><li>Molar mass of Oxygen gas is </li></ul><ul><li>32 x10 -3 kg mol -1 </li></ul><ul><li>If I have 20g of Oxygen, how many moles do I have and how many molecules? </li></ul><ul><li>20 x 10 -3 kg / 32 x10 -3 kg mol -1 </li></ul><ul><li> 0.625 mol </li></ul><ul><li> 0.625 mol x 6.02 x 10 23 molecules </li></ul><ul><li> 3.7625 x 10 23 molecules </li></ul>
63. 63. Use your periodic table to… <ul><li>Find out how many atoms are in </li></ul><ul><li>46g of sodium </li></ul><ul><li>64mg of copper </li></ul><ul><li>180g of water </li></ul><ul><li>Find out how many moles is </li></ul><ul><li>10g of Argon </li></ul><ul><li>1kg of Iron </li></ul>
64. 64. What is the molar mass of… <ul><li>Nitrogen </li></ul><ul><li>Chlorine </li></ul><ul><li>Neon </li></ul><ul><li>Water </li></ul><ul><li>Sulfuric acid (H 2 SO 4 ) </li></ul><ul><li>Calcium carbonate (CaCO 3 ) </li></ul>