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# Ch 12 Temperature and Heat

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### Ch 12 Temperature and Heat

1. 1. Chapter 12 Temperature and Heat
2. 2. Learning Objectives Temperature and heat  Mechanical equivalent of heat Students should understand the “mechanical equivalent of heat” so they can determine how much heat can be produced by the performance of a specified quantity of mechanical work.  Heat transfer and thermal expansion Students should understand heat transfer and thermal expansion, so they can:  Calculate how the flow of heat through a slab of material is affected by changes in the thickness or area of the slab, or the temperature difference between the two faces of the slab.  Analyze what happens to the size and shape of an object when it is heated.  Analyze qualitatively the effects of conduction, radiation, and convection in thermal processes.
3. 3. Table of Contents 1. Common Temperature Scales 2. The Kelvin Temperature Scale 3. Thermometers 4. Linear Thermal Expansion 5. Volume Thermal Expansion 6. Heat & Internal Energy 7. Heat & Temperature Change: Specific Heat Capacity 8. Heat and Phase Change: Latent Heat 9. Equilibrium between Phases of Matter (AP?) 10. Humidity (AP?)
4. 4. Chapter 12: Temperature and Heat Section 1: Common Temperature Scales
5. 5. Temperature  A measure of the physical quantity of the thermal energy held by an object  A measure of the average internal kinetic energy of the particles  As the particles move faster, they have stronger collisions.  That energy exchanges rapidly  Think of a bunch of kids in a “bounce house”
6. 6. Temperature Scales  First “Modern” Thermometer is thought to have been created in 1654  Simply an unmarked tube of liquid that rose and fell with different temperatures  Late 1600’s Newton first put a scale on it  0 was the freezing point of water  12 was the human body temperature  The English were fascinated with 12 when it comes to measurement  12 inches=1 ft, 12 oz = 1 lb*, 12 pence = shilling, 12 units = 1 dozen, 12 dozen = 1 gross
7. 7. Fahrenheit Scale  Why 32o and 212o ?  1701 Ole Rømer used a brine solution for freezing point (0)  Wanted 0o to be the coldest temperature at which water could be a liquid  set boiling point of water as 60 on his scale  Daniel Fahrenheit modified Rømer’s scale in 1724  Used Mercury as liquid in device which increased range of measurements  Used the temperature of the human body as 100 on scale  Adjusted the scale so the melting point and boiling point of water were whole numbers, and difference was 180.
8. 8. Celsius Scale  First proposed by the Swedish Astronomer Anders Celsius in 1742  He set it up as 100o as the freezing point and 0o as boiling point of distilled water at normal atmospheric pressure  Swedish Botanist Carolus Linnaeus is among many scientist who switched the direction of the scale around 1744  From 1744 until 1948, called the Centigrade scale  Name changed to Celsius due to conflicts in translations with measures of angles. (1 centigrade = 1/10,000 of a right angle)  1954 reformatted to directly match Kelvin Scale  Scale based on absolute zero and triple point of pure water  Correctly written as degrees Celsius (capitalization is correct!)  Zero is freezing, 10 is not. 20 is pleasant, 30 is hot.
9. 9. Temperatures are reported in degrees Celsius or degrees Fahrenheit. Temperatures changed, on the other hand, are reported in Celsius degrees or Fahrenheit degrees:  F 5 9 C1 = Note: I haven’t seen this convention anywhere other than this textbook. I don’t think AP recognizes it!
10. 10. “English” vs. SI  Most scientist agree the SI system (yes that’s redundant) is a superior system of measure  Especially when is comes to conversions due to size  How many inches are in 2.67 miles?  Some still argue about the Temperature scales.  Blame the French on this one  Fahrenheit had ties to England, Celsius to France  Lord Kelvin sealed the debate by “using” Celsius scale as basis for his absolute scale  But is it better?  Habitable Earth fluctuates from 0 to 100 o F wouldn’t that fit the SI’s power of 10 thing?
11. 11. Example 1 Converting from a Fahrenheit to a Celsius Temperature A healthy person has an oral temperature of 98.6o F. What would this reading be on the Celsius scale?  F6.66F32F98.6 =− degrees above ice point ( )     C0.37 F C1 F6.66 5 9 =        C0.37C0.37C0  =+ ice point
12. 12. Example 2 Converting from a Celsius to a Fahrenheit Temperature A time and temperature sign on a bank indicates that the outdoor temperature is -20.0o C. Find the corresponding temperature on the Fahrenheit scale. ( )     F0.36 C1 F C0.20 5 9 =      degrees below ice point F0.4F0.36F0.32  −=− ice point
13. 13. 12.1.1. Three thermometers are used to measure the temperature inside a closed, insulated box. Thermometer A is calibrated in degrees Fahrenheit, thermometer B in degrees Celsius, and thermometer C in kelvin. When the thermometers reach thermal equilibrium with the interior of the box, B reads −40 °C and C reads 233 K. Which one of the following statements is necessarily true? a) Thermometer C should read −233 K. b) Thermometer A must read –40 °F. c) If the temperature of the interior of the box is increased until A reads −20 °F, thermometer B will read −10 °C. d) Thermometer B should read −77 °C. e) If the temperature of the interior of the box is increased until C reads 293 K, thermometer A will read 36 °F.
14. 14. 12.1.2. Unsatisfied with the Celsius and Fahrenheit temperature scales, you decide to create your own. On your temperature scale, the ice point is 77 °M and the steam point is at 437 °M, where “M” stands for “my scale.” What temperature on your scale corresponds to 68 °F? a) 154 °M b) 168 °M c) 140 °M d) 136 °M e) 149 °M
15. 15. Chapter 12: Temperature and Heat Section 2: The Kelvin Scale
16. 16. An Absolute Scale  Proposed by William Thomson, 1st Baron Kelvin in 1848  Does not use a “o ” as it is an absolute scale  Double the number, double the energy  The zero point is absolute zero  Temperature of zero internal energy  Second point is now defined as triple point of water  Celsius scale was slightly modified so that a change of 1 o C is a change of 1 K.  Similar scale developed by William Rankine in 1859 that was based on the Fahrenheit scale.
17. 17. The Kelvin Temperature Scale 15.273+= cTT Kelvin temperature
18. 18. A constant-volume gas thermometer.
19. 19. absolute zero point = -273.15o C
20. 20. 12.2.1. Unsatisfied with the Celsius and Kelvin temperature scales, you decide to create your own. On your temperature scale, the ice point is 0.0 °M and the steam point is at 366.1 °M, where “M” stands for “my scale.” What temperature on your scale corresponds to 0 K? a) −273.1 °M b) −500.0 °M c) −1000.0 °M d) −732.4 °M e) −633.9 °M
21. 21. Chapter 12: Temperature and Heat Section 3: Thermometers
22. 22. Thermometers make use of the change in some physical property with temperature. A property that changes with temperature is called a thermometric property. Thermometers
23. 23. Thermometers  Early thermometers used water, mercury and alcohol due to their thermal expansion  “Modern” devices often use other substances/properties  Bimetallic Coil thermometers (old A/C thermostats)  Coiled metal expands and rotates a dial  Infrared Thermometers  Measure the colors of light being produced  Thermocouples  Joined metals produce an electric potential  Thermisters  Electric Resistance depends on temperature
24. 24. 12.3.1. Which one of the following properties is not likely to be used as a temperature-sensitive property to construct a thermometer? a) The volume of a liquid increases with increasing temperature. b) A gas held within a constant volume container exhibits pressure changes with corresponding temperature changes. c) The length of a metal rod changes linearly with temperature. d) The mass of a solid decreases with increasing temperature. e) The electrical resistance of a wire increases with increasing temperature.
25. 25. Chapter 12: Temperature and Heat Section 4: Linear Thermal Expansion
26. 26. Linear Thermal Expansion  Most objects expand as they rise in temperature  The particles are moving faster  The collisions have more energy  Net force of collisions is outward  Objects therefore tend to expand
27. 27. oLL ∝∆ Linear Thermal Expansion T L L o ∆∝ ∆ Tk L L o ∆= ∆
28. 28. The length of an object changes when its temperature changes: TLL o∆=∆ α coefficient of linear expansion Common Unit for the Coefficient of Linear Expansion: ( ) 1 C C 1 − =   LINEAR THERMAL EXPANSION OF A SOLID
29. 29. Example 3 The Buckling of a Sidewalk A concrete sidewalk is constructed between two buildings on a day when the temperature is 25 o C. As the temperature rises to 38 o C, the slabs expand, but no space is provided for thermal expansion. Determine the distance y in part (b) of the drawing. TLL o∆=∆ α ( ) ( )22 m00000.3m00047.3 −=y ( )[ ]( )( ) C13m0.3C1012 16 −− ×=∆L m00047.0= LLLL o ∆+= mmL 47000.000000.3 +=∆ m47000.3= m053.0=
30. 30. The Bimetallic Strip
31. 31. The Bimetallic Strip
32. 32. Conceptual Example 5 The Expansion of Holes The figure shows eight square tiles that are arranged to form a square pattern with a hold in the center. If the tiled are heated, what happens to the size of the hole? The Expansion of Holes
33. 33. A hole in a piece of solid material expands when heated and contracts when cooled, just as if it were filled with the material that surrounds it. The Expansion of Holes
34. 34. Conceptual Example 7 Expanding Cylinders Each cylinder is made from a different material. All three have the same temperature and they barely fit inside each other. As the cylinders are heated to the same, but higher, temperature, cylinder C falls off, while cylinder A becomes tightly wedged to cylinder B. Which cylinder is made from which material? ( ) ( ) ( ) 16 16 16 1029 1012 1019 −− −− −− ×= ×= ×= C C C o Lead o Steel o Brass α α α
35. 35. 12.4.1. An artist wishes to insert a gold pin into a hole in an iron sculpture and have it held permanently. The pin is slightly larger than the hole. The coefficient of linear thermal expansion of gold is slightly larger than that of iron. Consider the following options: (1) increase the temperature of the pin and the sculpture by the same amount, (2) decrease the temperature of the pin and the sculpture by the same amount, (3) increase the temperature of the pin and decrease the temperature of the sculpture, and (4) decrease the temperature of the pin and increase the temperature of the sculpture. Which of the choices would most likely accomplish the artist’s task? a) 1 b) 2 c) 3 d) 4 e) 2 and 4
36. 36. 12.4.2. The length of an aluminum pendulum in a certain clock is 0.2480 m on a day when the temperature is 23.30 °C. This length was chosen so that the period of the pendulum is exactly 1.000 s. The clock is then hung on a wall where the temperature is −5.00 °C and set to the correct local time. Assuming the acceleration due to gravity is the same at both locations, by how much time is the clock incorrect after one day at this temperature? a) 69.3 s b) 115 s c) 87.2 s d) 31.0 s e) 11.5 s
37. 37. 12.4.3. A rod of length L is heated so that its temperature increases by ∆T. As a result, the length of the rod increases by ∆L. The rod is then cut into two pieces, one of length L/3 and one of length 2L/3. What is the ratio of the change in length of the rod of length 2L/3 to ∆L of the original rod when its temperature is increased by ∆T? a) 1/3 b) 2/3 c) 1 d) 3/2 e) 3
38. 38. 12.4.4. A square piece of metal has a hole drilled through its center. If the metal piece is uniformly heated, what is the effect on the hole? a) The diameter of the hole will decrease, but remain open, as the temperature increases. b) The diameter of the hole will increase as the temperature increases. c) The diameter of the hole will not change, but the area of the square will increase as the temperature increases. d) The diameter of the hole may either increase or decrease depending on the type of metal.
39. 39. Chapter 12: Temperature and Heat Section 5: Volume Thermal Expansion
40. 40. If the length expands, and Volume is L3, Then the volume must also expand TVV o∆=∆ β coefficient of volume expansion Common Unit for the Coefficient of Volume Expansion: ( ) 1 C C 1 − =   Volume Thermal Expansion
41. 41. Example 8 An Automobile Radiator A small plastic container, called the coolant reservoir, catches the radiator fluid that overflows when an automobile engine becomes hot. The radiator is made of copper and the coolant has an expansion coefficient of 4.0x10-4 (Co )-1 . If the radiator is filled to its 15-quart capacity when the engine is cold (6o C), how much overflow will spill into the reservoir when the coolant reaches its operating temperature (92o C)? ( )( )( )( ) quarts53.0C86quarts15C1010.4 14 coolant =×=∆ −−  V ( )( )( )( ) quarts066.0C86quarts15C1051 16 radiator =×=∆ −−  V quarts0.46quarts066.0quarts53.0spill =−=∆V TVV o∆=∆ β
42. 42. Thermal Volume Expansion of Water
43. 43. 12.5.1. Which one of the following statements is the best explanation for the fact that metal pipes that carry water often burst during cold winter months? a) Both the metal and the water expand, but the water expands to a greater extent. b) Water contracts upon freezing while the metal expands at lower temperatures. c) The metal contracts to a greater extent than the water. d) The interior of the pipe contracts less than the outside of the pipe. e) Water expands upon freezing while the metal contracts at lower temperatures.
44. 44. 12.5.2. Consider the four blocks made from the same material that are shown in the drawing. The sides have lengths of L, 2L, or 3L. Rank these blocks according to their expected increase, largest to smallest, in their volumes when their temperatures are increased by the same amount. a) B > C > A > D b) C > B > A > D c) D > C > A > B d) C > D > B > A e) All would have the same increase in volume.
45. 45. Chapter 12: Temperature and Heat Section 6: Heat & Internal Energy
46. 46. Heat is energy that flows from a higher- temperature object to a lower-temperature object because of a difference in temperatures. SI Unit of Heat: joule (J) Definition of Heat Think diffusion – If a bunch of particles are randomly moving, their concentration will tend to spread out until it is even. The heat that flows from hot to cold originates in the internal energy of the hot substance. It is not correct to say that a substance contains heat. It contains internal energy.
47. 47. Chapter 12: Temperature and Heat Section 7: Heat & Temperature Change: Specific Heat Capacity
48. 48. Since Solids and Liquids tend to incompressible with a fixed volume, the ambient pressure is usually insignificant. The heat that must be supplied or removed to change the temperature of a substance is TmCQ ∆= specific heat capacity Common Unit for Specific Heat Capacity: J/(kg·o C) Heat Changes in Solids and Liquids Common Units for Heat 1 Cal = 1 kcal = 4186 joules
49. 49. Example 9 A Hot Jogger In a half-hour, a 65-kg jogger can generate 8.0x105 J of heat. This heat is removed from the body by a variety of means, including the body’s own temperature-regulating mechanisms. If the heat were not removed, how much would the body temperature increase? TmCQ ∆= mC Q T =∆ ( ) ( )[ ] CkgJ3500kg65 J100.8 5 ⋅ × =  C5.3=
50. 50. Heat Changes in Gases  The value of the specific heat of a gas depends on whether the pressure or volume is held constant.  This distinction is not important for solids.  This will be discussed in greater detail later in the unit
51. 51. If there is no heat loss to the surroundings, the heat lost by the hotter object equals the heat gained by the cooler ones. Calorimetry
52. 52. Example 12 Measuring the Specific Heat Capacity The calorimeter is made of 0.15 kg of aluminum and contains 0.20 kg of water. Initially, the water and cup have the same temperature of 18.0o C. A 0.040 kg mass of unknown material is heated to a temperature of 97.0o C and then added to the water. After thermal equilibrium is reached, the temperature of the water, the cup, and the material is 22.0o C. Ignoring the small amount of heat gained by the thermometer, find the specific heat capacity of the unknown material.
53. 53. ( ) ( ) ( )unknownwaterAl TmCTmCTmC ∆=∆+∆ ( ) CkgJ1300unknown ⋅=C ( ) ( ) ( )unknown waterAl unknown Tm TmcTmc C ∆ ∆+∆ = ( )[ ]( )( ) ( )[ ]( )( ) ( )( )  C0.75kg040.0 C0.4kg20.0CkgJ4186C0.4kg15.0CkgJ1000.9 2 unknown ⋅+⋅× =C
54. 54. 12.7.1. A certain amount of heat Q is added to materials A, B, and C. The masses of these three materials are 0.04 kg, 0.01 kg, and 0.02 kg, respectively. The temperature of material A increases by 4.0 C° while the temperature of the other two materials increases by only 3.0 C°. Rank these three materials from the largest specific heat capacity to the smallest value. a) A > B > C b) C > B > A c) B > A > C d) B = C > A e) A > B = C
55. 55. 12.7.2. A swimming pool has a width of 9.0 m and a length of 12.0 m. The depth of the water is 1.83 m. One morning, the temperature of the pool water was 15.0 °C. The water then absorbed 2.00 × 109 J of heat from the Sun. What is the final temperature of the water? Assume no heat loss to the surroundings. a) 16.9 °C b) 18.1 °C c) 17.4 °C d) 19.6 °C e) 20.2 °C
56. 56. 12.7.3. Which of the following substances would be the most effective in cooling 0.300 kg of water at 98 °C? a) 0.100 kg of lead at 22 °C b) 0.100 kg of water at 22 °C c) 0.100 kg of glass at 22 °C d) 0.100 kg of aluminum at 22 °C e) 0.100 kg of copper at 22 °C
57. 57. 12.7.4. Elena’s normal body temperature is 36.5 °C. When she recently became ill, her body temperature increased to 38.0 °C. What was the minimum amount of heat required for this increase in body temperature if her weight is 561 N? a) 2.96 × 106 J b) 3.50 × 103 J c) 4.98 × 104 J d) 3.00 × 105 J e) 7.60 × 105 J
58. 58. 12.7.5. Four 1-kg cylinders are heated to 100 °C and placed on top of a block of paraffin wax, which melts at 63 °C. There is one cylinder made from lead, one of copper, one of aluminum, and one of iron. After a few minutes, it is observed that the cylinders have sunk into the paraffin to differing depths. Rank the depths of the cylinders from deepest to shallowest. a) lead > iron > copper > aluminum b) aluminum > copper > lead > iron c) aluminum > iron > copper > lead d) copper > aluminum > iron > lead e) iron > copper > lead > aluminum
59. 59. 12.7.6. Why is water often used as a coolant in automobiles, other than the fact that it is abundant? a) Water expands very little as it is heated. b) The freezing temperature of water has a relatively large value. c) The specific heat of water is relatively small and its temperature can be rapidly decreased. d) The specific heat of water is relatively large and it can store a great deal of thermal energy. e) Water does not easily change into a gas.
60. 60. Chapter 12: Temperature and Heat Section 8: Heat & Phase Change: Latent Heat
61. 61. The 3 Basic Phases of Matter
62. 62. During a phase change, the temperature of the mixture does not change (provided the system is in thermal equilibrium). Heating Curve
63. 63. Conceptual Example 13 Saving Energy Suppose you are cooking spaghetti for dinner, and the instructions say “boil pasta in water for 10 minutes.” To cook spaghetti in an open pot with the least amount of energy, should you turn up the burner to its fullest so the water vigorously boils, or should you turn down the burner so the water barely boils?
64. 64. The heat that must be supplied or removed to change the phase of a mass, m, of a substance is mLQ = latent heat SI Units of Latent Heat: J/kg HEAT SUPPLIED OR REMOVED IN CHANGING THE PHASE OF A SUBSTANCE
65. 65. Example 14 Ice-cold Lemonade Ice at 0o C is placed in a Styrofoam cup containing 0.32 kg of lemonade at 27o C. The specific heat capacity of lemonade is virtually the same as that of water. After the ice and lemonade reach and equilibrium temperature, some ice still remains. Assume that mass of the cup is so small that it absorbs a negligible amount of heat. ( ) ( )    lemonade bylostHeat lemonade iceby gainedHeat ice TCmmLf ∆= ( )[ ]( )( ) kgJ103.35 C0C27kg32.0CkgJ4186 5 × −⋅ =  icem ( ) f lemonade ice L TCm m ∆ = kg11.0=
66. 66. 12.8.1. Heat is added to a substance, but its temperature does not increase. Which one of the following statements provides the best explanation for this observation? a) The substance has unusual thermal properties. b) The substance must be cooler than its environment. c) The substance must be a gas. d) The substance must be an imperfect solid. e) The substance undergoes a change of phase.
67. 67. 12.8.2. What is the final temperature when 2.50 × 105 J are added to 0.950 kg of ice at 0.0 °C? a) 0.0 °C b) 4.2 °C c) 15.7 °C d) 36.3 °C e) 62.8 °C
68. 68. 12.8.3. By adding 25 kJ to solid material A, 4.0 kg will melt. By adding 50 kJ to solid material B, 6.0 kg will melt. Solid material C requires 30 kJ to melt 3.0 kg. Which of these materials, if any, has the largest value for the heat of fusion? a) A b) B c) C d) A = B
69. 69. 12.8.4. Consider the system shown in the drawing. A test tube containing water is inserted into boiling water. Will the water in the test tube eventually boil? a) Yes, heat is continually transferred to the water inside the test tube and eventually it will boil? b) Yes, the pressure above the water in the test tube will be reduced to less than atmospheric pressure and cause the water to boil. c) No, heat will only be transferred until the water in the test tube is 100 °C. d) No, the temperature of the water in the test tube will never reach 100 °C.
70. 70. Chapter 12: Temperature and Heat Section 9: Equilibrium Between Phases of Matter
71. 71. The pressure of vapor that coexists in equilibrium with the liquid is called the equilibrium vapor pressure of the liquid. Equilibrium Between Phases
72. 72. Only when the temperature and vapor pressure correspond to a point on the curved line do the liquid and vapor phases coexist in equilibrium.
73. 73. Conceptual Example 16 How to Boil Water That is Cooling Down Shortly after the flask is removed from the burner, the boiling stops. A cork is then placed in the neck of the flask to seal it. To restart the boiling, should you pour hot or cold water over the neck of the flask?
74. 74. As is the case for liquid/vapor equilibrium, a solid can be in equilibrium with its liquid phase only at specific conditions of temperature and pressure.
75. 75. All 3 Phases can be combined Critical Point TC Most Substances Water
76. 76. Chapter 12: Temperature and Heat Section 10: Humidity
77. 77. Air is a mixture of gases. The total pressure is the sum of the partial pressures of the component gases. The partial pressure of water vapor depends on weather conditions. It can be as low as zero or as high as the vapor pressure of water at the given temperature. ( ) ( ) ( ) 100 retemperatuexistingatwaterofpressurevapormEquilibriu orwater vapofpressurePartial humidityrelativePercent ×= To provide an indication of how much water vapor is in the air, weather forecasters usually give the relative humidity:
78. 78. Example 17 Relative Humidities One day, the partial pressure of water vapor is 2.0x103 Pa. Using the vaporization curve, determine the relative humidity if the temperature is 32o C.
79. 79. ( ) ( ) ( ) 100 retemperatuexistingatwaterofpressurevapormEquilibriu orwater vapofpressurePartial humidityrelativePercent ×= %42100 Pa108.4 Pa100.2 humidityRelative 3 3 =× × × =
80. 80. The temperature at which the relative humidity is 100% is called the dew point.