Chapter 14 Temperature and Heat

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1 Nicholas J. Giordano Chapter 14 Temperature and Heat

2 Thermodynamics Starting a different area of physics called thermodynamics Thermodynamics focuses on energy rather than forces Conservation of energy is a key pillar of thermodynamics Thermodynamics is about the transfer of energy between systems of particles It is also about the way changes in the energy of a system affects its properties Several new quantities, such as temperature and heat, are needed to describe the properties of systems and their interactions Introduction

3 System A thermodynamic system contains multiple particles, usually a very large number The particles in a system are able to exchange energy with one another Via collisions Systems are able to exchange energy with other systems The balloon filled with oxygen molecules is an example of a system Section 14.1

4 Properties of a System Because of the extremely large numbers of molecules, it is not feasible (although it is possible) to describe the system in terms of Newton s Laws In comparing two systems, they may not be identical on the molecular level The positions and velocities of all the molecules won t be the same Various properties of the systems as a whole will be the same Systemwide properties include temperature and pressure Section 14.1

5 Properties of a System, cont. We are generally interested in the macroscopic properties of the system They describe the behavior of the system on a scale much larger than the individual particles Macroscopic properties contrast with microscopic properties such as position and velocity The macroscopic and microscopic properties are connected Section 14.1

6 Temperature Temperature is not contained in nor derivable from Newton s laws Temperature is connected with hotness or coldness A macroscopic definition can be determined from looking at two systems Section 14.2

7 Temperature, cont. Assume each system has its own temperature and T 1 > T 2 System 1 is hotter than system 2 If the systems are brought into contact, energy is transferred spontaneously from system 1 to system 2 Eventually, the two systems will have the same temperature They will reach thermal equilibrium Their final temperature will be somewhere between the two initial temperatures Section 14.2

8 Heat The energy that flows between the systems is called heat or heat energy Heat is energy that passes from one system to another by virtue of a temperature difference The terms heat and heat energy are often used interchangeably In physics, they always refer to the transfer of energy between systems Section 14.2

9 Heat, cont. According to the principle of conservation of energy, the amount of heat energy that leaves system 1 must equal the amount of heat energy that enters system 2 The transfer can take place in different ways The direction of the transfer depends only on the temperature difference Section 14.2

10 Units of Heat The SI unit of heat is the same as for energy, the Joule (J) A unit called the calorie is widely used for heat 1 cal = J The Calorie, with an uppercase C, is used to measure the energy content of food 1 Calorie = 1000 calories Section 14.2

11 Heat and Mechanical Energy James Joule measured the mechanical equivalent of heat energy The apparatus he used is similar to the one shown As the mass fell, its potential energy rotated the paddle, raising the temperature of the liquid Joule could then relate the mechanical energy to the heat energy Section 14.2

12 Temperature: Microscopic Picture The systems in contact approach gave no way to measure the actual value of the temperature of a system You could place the system of interest in contact with a gas-filled container If the temperature of the gas increases, the average speed of the gas atoms increases, and the pressure will also increase Section 14.2

13 Temperature Microscopic Picture, cont. A measurement of the pressure gives a direct way to find the temperature Such a device is called a gas thermometer The temperature of a system of particles is related to the average particle speed Section 14.2

14 Temperature Microscopic Picture, final The temperature is linearly proportional to the gas pressure This holds for a dilute gas A dilute gas is one with low density Section 14.2

15 Temperature Scales The three scales shown are in common use today: Fahrenheit Celsius Kelvin Section 14.2

16 Temperature Scales, cont. Celsius Water freezes at 0 C Water boils at 100 C Fahrenheit Water freezes at 32 F Water boils at 212 F Kelvin Water freezes at K Water boils at K No degree symbol is used with kelvins Section 14.2

17 Temperature Conversions All three scales are linear The freezing and boiling points of water can be used to develop conversions among the scales T K = T C From Celsius to Kelvin The size of the temperature units are the same so a change of 1 degree on the Celsius scale is the same as the change of one kelvin on the Kelvin scale Section 14.2

18 Temperature Conversions, cont. From Celsius to Fahrenheit The different sizes of the degree as well as different freezing points of water both have to be taken into account Table 14.1 gives some temperatures in each scale Section 14.2

19 Temperature Limits Temperatures extend well above the boiling point of water They also extend below the freezing point of water The lower limit to temperature is absolute zero 0 K Section 14.2

20 Zeroth Law of Thermodynamics Assume the three systems are initially isolated and then brought into contact A and B are brought into contact, then B and C are brought into contact Section 14.3

21 Zeroth Law, cont. If two systems A and B are in thermal equilibrium (so that T A = T B ) and systems B and C are in thermal equilibrium (T B = T C ), systems A and C are in thermal equilibrium (T A = T C ) This tells us The basic concept of temperature is meaningful Temperature is a unique property of a system that is allowed to come into thermal equilibrium Temperature is the only property of a system that will determine heat flow between it and another system Section 14.3

22 Heat Flow and Zeroth Law Heat flows from system 1 into system 2 It then flows from system 2 into system 3 The zeroth law indicates heat cannot flow from system 3 into system 1 Heat must always flow from high temperature to low temperature Section 14.3

23 Phases of Matter There are three states of matter shown: Solid Liquid Gas Section 14.4

24 Solids The atoms in many solids are arranged in an orderly and repeating pattern called a crystalline lattice Each atom is held in place by the forces exerted by neighboring atoms These forces are a result of chemical bonds within the solid The atoms actually vibrate about their positions as simple harmonic oscillators An amorphous solid has atoms arranged without the repeating structure found in a crystal Section 14.4

25 Solids, Examples Section 14.4

26 Liquids The atoms in a liquid are not held in fixed locations by the forces of neighboring atoms The atoms are able to move about The atoms adjacent to a particular atom are not likely to be adjacent a short time later This motion helps liquids to flow Although the bonds between neighboring atoms do not persist, there is still potential energy associated with the forces between the molecules Section 14.4

27 Gases In some ways, a gas is similar to a liquid The molecules are able to move over long distances The density of a gas is generally much lower than that of a liquid The spacing between the molecules of a gas is larger The magnitude of the intermolecular force, and therefore potential energy, is much smaller Most of the mechanical energy in a gas is found in the kinetic energies of its molecules Section 14.4

28 Internal Energy The mechanical energy of the molecules in a system is called the internal energy of the system Denoted by U The internal energy of a system is the sum of all potential energies associated with all the intermolecular bonds plus the kinetic energies of all the molecules The value of U increases as we go from solid to liquid to gas In general, the internal energy of all systems increases as the temperature is increased Section 14.4

29 Phase Changes The transformation of a solid to a liquid, a liquid to a gas, etc. is called a phase change Phase changes can be produced by changing the temperature or by changing the pressure of the system A phase diagram shows the phases found at different temperatures and pressures Section 14.4

30 Phase Changes, cont. Phase diagrams show the phase changes a system can experience Phase changes include Melting from solid to liquid Freezing from liquid to solid Evaporation from liquid to gas Sublimation from solid to gas The line that separates liquid and gas ends at the critical point The triple point is where solid, liquid, and gas phase regions all meet For water, this is K Table 14.2 lists the melting and evaporation temperatures of some common substances Section 14.4

31 Melting and Evaporation Temperatures Section 14.4

32 Heat Capacity and Specific Heat Heat capacity is the ratio between the heat energy added to a system and the resulting change in temperature Specific heat takes into account the size (mass) of the system The specific heat is the same for any sample of a certain substance At a particular temperature and pressure Section 14.4

33 Specific Heat, cont. The equation for specific heat is often rearranged: Q = m c ΔT Knowing the value of c allows you to calculate how much heat energy is needed to increase the temperature of a mass m by ΔT Values of c are given in table 14.3 Note units Section 14.4

34 Specific Heat, final By convention, +Q indicates heat was added to the system A negative value of Q would indicate heat is flowing out of the system Adding or subtracting heat from the system will change its internal energy The value of c can vary a small amount with temperature Specific heats tend to be larger for liquids than for solids or gases Section 14.4

35 Specific Heat of Water The specific heat of water was used in the original definition of a calorie The value of c for water is much higher than for most other substances A large body of water has a very large heat capacity relative to the surrounding air and soil As a result, the temperature of an ocean or lake changes relatively little even when there are large changes in energy around it Large bodies of water moderate temperature fluctuations Section 14.4

36 Importance of Specific Heat Specific heat allows the calculation of how the temperature of an object will change when a certain amount of heat is added or removed The value of specific heat gives information about the internal energy of a system If an amount of heat is added to a system, its internal energy must increase by that amount From conservation of energy Specific heat tells how changes in internal energy are related to changes in temperature Section 14.4

37 Calorimetry Calorimetry can be used to find the specific heat of a system The system of interest is placed in contact with a reference system If it is very large, the reference system is called a thermal reservoir The system of interest is thermally isolated from everything but the thermal reservoir Section 14.4

38 Calorimetry, cont. The general principles of calorimetry can used to analyze processes that do not include thermal reservoirs Conservation of energy tells us that all the energy leaving one system will enter the other system The change in temperature that occurs will depend on the initial temperatures of both systems and their specific heats Section 14.4

39 Problem Solving: Calorimetry Recognize the principle All calorimetry problems are based on the principle of conservation of energy Sketch the problem Show the system or systems of interest Indicate how the heat flows between them Identify the relationships Determine the initial and final temperatures of the system(s) When possible Section 14.4

40 Problem Solving: Calorimetry cont. Identify the relationships, cont. Determine the heat energy added to each system Solve If energy flows into a system, Q is positive If energy flows out of a system, Q is negative Apply Q = m c Δ T This relates Q and ΔT for each system Solve for the quantities of interest So far, we have assumed no phase changes Check Consider what your answer means Check that your answer makes sense Section 14.4

41 Latent Heat When a system undergoes a phase change, the latent heat must be accounted for Specific heat assumes the system will not change phase The latent heat associated with phase changes is connected to the energies of the atoms within the substance Section 14.4

42 Latent Heat of Fusion Substantial energy is stored in the atomic bonds holding the atoms within a solid These bonds store potential energy For a solid to melt, energy is required to overcome the potential energy and break the bonds The latent heat of fusion is the amount of heat that must be added to change a substance from a solid to a liquid The same amount must be removed to change a substance from a liquid to a solid Section 14.4

43 Latent Heat of Vaporization The latent heat of vaporization is associated with the phase change from a liquid to a gas When the liquid becomes a gas, the weak atomatom interactions in the liquid become even weaker in the gas as the atoms are moved even farther apart This, again, requires the addition of energy Section 14.4

44 Latent Heat Summary By convention, the latent heat, L, is a positive quantity For a system of mass m To melt: Q melt = m L fusion To freeze: Q freeze = - m L fusion To vaporize (boil): Q vaporization = m L vaporization To condense: Q condensation = - m L vaporization The negative signs indicate the heat must be removed from the system Section 14.4

45 Latent Heat, Table The table lists the latent heats of fusion and vaporization for some common substances Notice that for a given substance, the latent heats of vaporization and fusion are not the same Section 14.4

46 Calorimetry with Latent Heat Move along the horizontal dashed line in A Start with the solid and add heat Region I: the temperature increases, Q = m c Δ T c is the specific heat of the solid Section 14.4

47 Calorimetry with Latent Heat, cont. Region II: phase change from solid to liquid, Q = m L fusion The temperature remains constant Region III: the substance is completely melted Adding heat again increases the temperature, Q = m c Δ T c is the specific heat of the liquid Region IV: phase change from liquid to gas, Q = m L vaporization The temperature remains constant Region V Adding more heat will raise the temperature of the gas Section 14.4

48 Problem Solving: Calorimetry with Latent Heat Recognize the principle All calorimetry problems are based on the principle of conservation of energy Sketch the problem Show the system or systems of interest Indicate how the heat flows between them Identify the relationships When possible, determine the initial and final temperatures of the system(s) Section 14.4

49 Problem Solving: Calorimetry with Latent Heat, cont. Identify the relationships, cont. Determine the heat energy added to each system If energy flows into a system, Q is positive If energy flows out of a system, Q is negative Solve Apply Q = m c Δ T for temperature changes that do not include phase changes If there is a phase change, apply Q = m L Solve for the quantities of interest Check Consider what your answer means Check that your answer makes sense Section 14.4

50 Thermal Expansion Temperature changes can affect many properties of the system The size of the system will usually change with temperature, an effect called thermal expansion Two specific types of thermal expansion are Linear expansion Volume expansion Section 14.5

51 Thermal Expansion Linear If a piece of metal undergoes a temperature change of Δ T, then its length changes by ΔL α is the coefficient of linear expansion Section 14.5

52 Thermal Expansion Volume The length and height of the solid will also change If an object undergoes a temperature change of ΔT, then its volume changes by ΔV β is the coefficient of volume expansion Fluids will also undergo volume expansions Section 14.5

53 Effects of Thermal Expansion Bridges and other objects are designed with expansion joints to allow for the expansion and contraction of the material Section 14.5

54 Thermal Expansion and a Thermometer A thermometer uses the volume expansion of mercury to measure the temperature Changes in the meniscus position are proportional to changes in temperature Section 14.5

55 Thermal Expansion of Water At temperatures well above freezing, the density decreases as T increases This is the usual thermal expansion Just above freezing, however, the density of water has a maximum It cannot be described by the volume expansion equation Section 14.5

56 Water, cont. The density of ice is also less than the density of water Water contracts when it melts The reason ice floats in water Most substances do not behave this way This unusual behavior of water has many important consequences: In winter the surface of a lake freezes first Fish can live in the water underneath and have access to food Section 14.5

57 Heat Transfer Heat is the energy that flows between systems at different temperatures This transfer can take place in three ways Conduction Convection Radiation Section 14.6

58 Heat Conduction The bar is placed between two separate systems at different temperatures The bar conducts heat The bar s temperature varies smoothly from T 1 to T 2 Section 14.6

59 Heat Conduction, cont. In any particular region of the bar, the atoms closer to the hot end will be at a slightly higher temperature that the neighboring atoms nearer the cold end The atoms at a higher temperature have a larger vibration amplitude, corresponding to larger potential and kinetic energies As the atom vibrates, some of the extra vibrational energy is transfer to nearby colder atoms Energy flows from the hot end to the cold end of the bar Section 14.6

60 Heat Conduction, final The amount of energy that flows depends on The area of the bar, A The length of the bar, L The temperature difference between the two ends A property of the bar called thermal conductivity, κ Various values of κ are given in table 14.6 The rate of heat flow is given by Section 14.6

61 Metals Feel Cold If a metal and another material (such as Styrofoam) are at the same temperature, they generally do not feel the same The metal feels colder The thermal conductivity of metal is much higher than that of Styrofoam The rate of heat flow from your fingers to the metal is much higher than to the Styrofoam Therefore, the metal causes your skin to have a lower temperature and it feels colder Section 14.6

62 Convection Convection is based on thermal expansion The warmer material on the bottom (nearer the heat source) becomes less dense The warm, low-density material moves upward due to the buoyant force associated with Archimedes principle Section 14.7

63 Convection, cont. As the warmer material moves upward, it cools through conduction to heat the cooler parts of the container and the air above A circular pattern is developed Convection plays a role in heating and transporting energy in A house Oceans Atmosphere Section 14.7

64 Wind Chill Your skin is moist, and the water from it evaporates slowly This places a small amount of water vapor in the air near your skin The energy for the evaporation comes from your skin and causes it to cool This process is called evaporative cooling It can occur over a wide range of temperatures On a windy day, the layer of vapor filled air near your skin is carried away The rate of evaporation into the dry air is faster than into the moist layer More latent heat is removed from your skin on the windy day Section 14.7

65 Radiation Radiative heat flow involves energy carried by electromagnetic (em) radiation Electromagnetic radiation is a type of wave and can be characterized by frequency, wavelength and speed The waves carry energy Section 14.8

66 Radiation, cont. Electromagnetic radiation is generated any time an electric charge vibrates or undergoes an acceleration The vibrations of the atoms generate em radiation that carries energy away The vibration amplitude of the atoms depends on the temperature, so the radiated energy depends on temperature The energy is absorbed by another object when the radiation produces a force on the electric charges in that object Section 14.8

67 Blackbody When em radiation bombards an object, some of the radiation may be absorbed and some reflected A blackbody is an object that absorbs all em radiation at all frequencies A perfect blackbody does not exist, but the concept is very useful Radiation can be described by two laws Stefan-Boltzmann Wein s Section 14.8

68 Stefan-Boltzmann Law The amount of energy radiated by an object depends on its temperature If an object has a temperature T and a surface area A, the rate of energy radiated is given by the Stefan- Boltzmann Law σ = 5.67 x 10-8 W/ (m 2. K 4 ) is Stefan s constant e is the emissivity of the object It measures how efficiently it radiates energy e = 1 for a blackbody The rate at which the energy is radiated is the radiated power Section 14.8

69 Wein s Law The energy radiated is distributed as a function of wavelength The power is largest at λ max The temperature and wavelength are related by Section 14.8

70 Stefan-Boltzmann and Heat Flow The total power varies as the fourth power of the temperature Radiated power increases rapidly as T is increased The power is proportional to the emissivity e = 1 only for a blackbody It is smaller than 1 for any real object Its value depends on the properties of the material and will be a function of frequency Many objects are close to being blackbodies and so the Stefan-Boltzmann Law provides an approximate description of most radiating objects Section 14.8

71 Stefan-Boltzmann and Heat Flow, cont. The Stefan-Boltzmann Law applies to all objects at all temperatures Two objects will both radiate energy, but the net transfer will be from the hotter to the cooler The Stefan-Boltzmann Law also describes how heat is absorbed by an object In thermal equilibrium, (Q/t) absorbed = (Q/t) emitted Section 14.8

72 Sun and Earth s Temperature The Sun has a surface temperature of approximately 6000 K From the Stefan- Boltzmann Law, Q/t = 4.6 x W This is the rate at which the energy leaves the Sun This produces an Earth temperature of ~290 K Section 14.8

73 Medical Uses of Heat Radiation Medical thermography is an important medical use of heat radiation It measures the heat radiation emitted by the body and forms an image based on wavelength Applying Wein s Law, this will indicate where a body is warmest and where it is the coolest Section 14.8

74 Greenhouse Effect The atmosphere is not a blackbody The atmosphere allows most of the Sun s visible radiation to reach the surface It absorbs much of the infrared radiation The Earth radiates in infrared This energy is absorbed by the atmosphere and not released to space The trapped infrared radiation makes the Earth s surface warmer than it would be without the atmosphere Section 14.8

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