Chapter 17 Lecture

Chapter 17 Work, Heat, and the First Law of Thermodynamics Chapter Goal: To develop and apply the first law of thermodynamics. Slide 17-2

Chapter 17 Preview Slide 17-3

Chapter 17 Preview Slide 17-4

Chapter 17 Preview Slide 17-5

Chapter 17 Preview Slide 17-6

Chapter 17 Preview Slide 17-7

Chapter 17 Reading Quiz Slide 17-8

Reading Question 17.1 What quantities appear in the first law of thermodynamics? Force, mass, acceleration. Inertia, torque, angular momentum. Work, heat, thermal energy. Work, heat, entropy. Enthalpy, entropy, heat. Answer: C Slide 17-9 9

Reading Question 17.1 What quantities appear in the first law of thermodynamics? Force, mass, acceleration. Inertia, torque, angular momentum. Work, heat, thermal energy. Work, heat, entropy. Enthalpy, entropy, heat. Answer: C Slide 17-10 10

Reading Question 17.2 What was the original unit for measuring heat? BTU. Watt. Joule. Pascal. Calorie. Answer: E Slide 17-11 11

Reading Question 17.2 What was the original unit for measuring heat? BTU. Watt. Joule. Pascal. Calorie. Answer: E Slide 17-12 12

Reading Question 17.3 What is the name of an ideal-gas process in which no heat is transferred? Isochoric. Isentropic. Isothermal. Isobaric. Adiabatic. Answer: E Slide 17-13 13

Reading Question 17.3 What is the name of an ideal-gas process in which no heat is transferred? Isochoric. Isentropic. Isothermal. Isobaric. Adiabatic. Answer: E Slide 17-14 14

Reading Question 17.4 Heat is The amount of thermal energy in an object. The energy that moves from a hotter object  to a colder object. A fluid-like substance that flows from a  hotter object to a colder object. Both A and B. Both B and C. Answer: B Slide 17-15 15

Reading Question 17.4 Heat is The amount of thermal energy in an object. The energy that moves from a hotter object  to a colder object. A fluid-like substance that flows from a  hotter object to a colder object. Both A and B. Both B and C. Answer: B Slide 17-16 16

Reading Question 17.5 The thermal behavior of water is characterized by the value of its Heat density. Heat constant. Specific heat. Thermal index. Answer: C Slide 17-17 17

Reading Question 17.5 The thermal behavior of water is characterized by the value of its Heat density. Heat constant. Specific heat. Thermal index. Answer: C Slide 17-18 18

Chapter 17 Content, Examples, and QuickCheck Questions Slide 17-19

Energy Review The total energy of a system consists of the macroscopic energy plus the microscopic thermal energy. The final energy statement of Chapter 11 was: The total energy of an isolated system, for which Wext = 0, is constant. Slide 17-20

Energy Transfer by Work Doing work on a system increases its energy. Consider lifting a block with a rope at a steady speed. The rope’s tension is an external force doing work Wext. Energy transferred into the system goes entirely into the macroscopic potential energy Ugrav. Slide 17-21

Energy Transfer by Work Doing work on a system increases its energy. Consider dragging a block with a rope at a steady speed. The rope’s tension is an external force doing work Wext. Energy transferred into the system goes entirely into the thermal energy of the object + surface system Eth. Slide 17-22

Energy Transfer by Heat Work is energy transferred in a mechanical interaction. Energy can also be transferred between the system and the environment if they have a thermal interaction. The energy transferred in a thermal interaction is called heat. The symbol for heat is Q. The complete energy equation is now: Slide 17-23

QuickCheck 17.1 A steady force pushes in the piston of a well-insulated cylinder. In this process, the temperature of the gas Increases. Stays the same. Decreases. There’s not enough information to tell. Slide 17-24 24

QuickCheck 17.1 A steady force pushes in the piston of a well-insulated cylinder. In this process, the temperature of the gas Increases. Stays the same. Decreases. There’s not enough information to tell. First law: Q + W = ΔEth No heat flows (well insulated) ... ... but work is done on the gas. Work increases the gas’s thermal energy and with it the temperature. Slide 17-25 25

Work in Ideal-Gas Processes Consider a gas cylinder sealed at one end by a movable piston. The external force does work on the gas as the piston moves. Slide 17-26

The Sign of Work Slide 17-27

Work in Ideal-Gas Processes On a pV diagram, the work done on a gas W has a nice geometric interpretation. W = the negative of the area under the pV curve between Vi and Vf. Slide 17-28

QuickCheck 17.2 The work done on the gas in this process is 8000 J. Slide 17-29 29

QuickCheck 17.2 The work done on the gas in this process is 8000 J. W = –(area under pV curve) Slide 17-30 30

QuickCheck 17.3 Three possible processes A, B, and C take a gas from state i to state f. For which process is the magnitude of the work the largest? Process A. Process B. Process C. The work is the same for all three. Slide 17-31 31

QuickCheck 17.3 Three possible processes A, B, and C take a gas from state i to state f. For which process is the magnitude of the work the largest? Largest area under the curve. Process A. Process B. Process C. The work is the same for all three. Slide 17-32 32

Problem-Solving Strategy: Work in a Ideal-Gas Process Slide 17-33

Example 17.1 The Work Done on an Expanding Gas Slide 17-34

Example 17.1 The Work Done on an Expanding Gas Slide 17-35

Example 17.1 The Work Done on an Expanding Gas Slide 17-36

Work Done on an Ideal Gas In an isochoric process, when the volume does not change, no work is done. Slide 17-37

Work Done on an Ideal Gas In an isobaric process, when pressure is a constant and the volume changes by V = Vf − Vi, the work done during the process is: Slide 17-38

Work Done on an Ideal Gas In an isothermal process, when temperature is a constant, the work done during the process is: Slide 17-39

Example 17.2 The Work of an Isothermal Compression Slide 17-40

QuickCheck 17.4 Dragging an object across a rough surface makes it warm, or even hot. The temperature increase occurs because of Work. Heat. Thermal energy. Both work and heat. None of these. Slide 17-41 41

QuickCheck 17.4 Dragging an object across a rough surface makes it warm, or even hot. The temperature increase occurs because of Work. Heat. Thermal energy. Both work and heat. None of these. Slide 17-42 42

Work in Ideal-Gas Processes Figure (a) shows two different processes that take a gas from an initial state i to a final state f. The work done during an ideal-gas process depends on the path followed through the pV diagram. During the multistep process of figure (b), the work done is not the same as a process that goes directly from 1 to 3. Slide 17-43

Heat In the 1840s James Joule showed that heat and work, previously regarded as completely different phenomena, are simply two different ways of transferring energy to or from a system. Slide 17-44

Heat, Temperature, and Thermal Energy Thermal energy Eth is an energy of the system due to the motion of its atoms and molecules. Heat Q is energy transferred between the system and the  environment as they interact. Temperature T is a state variable that quantifies the “hotness” or “coldness” of a system. A temperature difference is required in order for heat to be transferred between the system and the environment. Slide 17-45

The Sign of Heat Slide 17-46

Understanding Work and Heat Slide 17-47

1 food calorie = 1 Cal = 1000 cal = 1 kcal = 4186 J Units of Heat The SI unit of heat is the Joule. Historically, a unit for measuring heat, the calorie, had been defined as: 1 calorie = 1 cal = the quantity of heat needed to change the temperature of 1 g of water by 1°C In today’s SI units, the conversion is: 1 cal = 4.186 J The calorie you know in relation to food is not the same as the heat calorie. 1 food calorie = 1 Cal = 1000 cal = 1 kcal = 4186 J Slide 17-49

The First Law of Thermodynamics Work and heat are two ways of transferring energy between a system and the environment, causing the system’s energy to change. If the system as a whole is at rest, so that the bulk mechanical energy due to translational or rotational motion is zero, then the conservation of energy equation is: Slide 17-49

QuickCheck 17.5 A cylinder of gas has a frictionless but tightly sealed piston of mass M. Small masses are placed onto the top of the piston, causing it to slowly move downward. A water bath keeps the temperature constant. In this process: Q > 0. Q = 0. Q < 0. There’s not enough information to say anything about the heat. Slide 17-50 50

QuickCheck 17.5 Eth = W + Q + – No temperature change A cylinder of gas has a frictionless but tightly sealed piston of mass M. Small masses are placed onto the top of the piston, causing it to slowly move downward. A water bath keeps the temperature constant. In this process: Q > 0. Q = 0. Q < 0. There’s not enough information to say anything about the heat. Eth = W + Q + – No temperature change Energy flows out to the water to keep the temperature from changing Slide 17-51 51 51

Three Special Ideal-Gas Processes For an isochoric process, insert the locking pin so the volume cannot change. For an isothermal process, keep the thin bottom in thermal contact with the flame or the ice. For an adiabatic process, add insulation beneath the cylinder, so no heat is transferred in or out. Slide 17-52

Three Special Ideal-Gas Processes Shown is the first-law bar chart for an isochoric cooling process. The gas is cooled by allowing heat energy to transfer out of the system to a cooler environment. The volume of the gas does not change, so no work is done (W = 0). Slide 17-53

QuickCheck 17.6 Which first-law bar chart describes the process shown in the pV diagram? Slide 17-54 54

QuickCheck 17.6 Which first-law bar chart describes the process shown in the pV diagram? Slide 17-55 55

Three Special Ideal-Gas Processes Shown is the first-law bar chart for an isothermal expansion. The gas is heated by allowing heat energy to transfer into the system from a warmer environment. The volume of the gas expands as the pressure drops. Negative work is done on the gas, and the thermal energy is constant (Eth = 0). Slide 17-56

Three Special Ideal-Gas Processes Shown is the first-law bar chart for an adiabatic compression. The gas is compressed by shrinking the volume. Insulation prevents heat energy from entering or leaving the gas (Q = 0). Positive work is done on the gas, which increases the temperature. Slide 17-57

QuickCheck 17.7 Three possible processes A, B, and C take a gas from state i to state f. For which process is the heat transfer the largest? Process A. Process B. Process C. The heat is the same for all three. Slide 17-58 58

QuickCheck 17.7 Three possible processes A, B, and C take a gas from state i to state f. For which process is the heat transfer the largest? Process A. Process B. Process C. The heat is the same for all three. Eth = W + Q Same for all three Most negative for A ... ... so Q must be most positive. Slide 17-59 59

Temperature Change and Specific Heat The amount of energy that raises the temperature of 1 kg of a substance by 1 K is called the specific heat c of that substance. If W = 0, so no work is done by or on the system, then the heat needed to bring about a temperature change T is: The molar specific heat C is the amount of energy that raises the temperature of 1 mol of a substance by 1 K. Slide 17-60

QuickCheck 17.8 Two liquids, A and B, have equal masses and equal initial temperatures. Each is heated for the same length of time over identical burners. Afterward, liquid A is hotter than liquid B. Which has the larger specific heat? Liquid A. Liquid B. There’s not enough information to tell. Slide 17-61 61

QuickCheck 17.8 Two liquids, A and B, have equal masses and equal initial temperatures. Each is heated for the same length of time over identical burners. Afterward, liquid A is hotter than liquid B. Which has the larger specific heat? Liquid A. Liquid B. There’s not enough information to tell. T = Q mc so larger c gives smaller T. Slide 17-62 62

Specific Heats of Various Materials Slide 17-63

Example 17.3 Running a Fever Slide 17-64

QuickCheck 17.9 1 kg of silver (c = 234 J/kg K) is heated to 100C. It is then dropped into 1 kg of water (c = 4190 J/kg K) at 0C in an insulated beaker. After a short while, the common temperature of the water and silver is 0C. between 0C and 50C. 50C. between 50C and 100C. 100C. Slide 17-65 65

QuickCheck 17.9 1 kg of silver (c = 234 J/kg K) is heated to 100C. It is then dropped into 1 kg of water (c = 4190 J/kg K) at 0C in an insulated beaker. After a short while, the common temperature of the water and silver is 0C. between 0C and 50C. 50C. between 50C and 100C. 100C. Slide 17-66 66

Phase Change and Heat of Transformation A phase change is characterized by a change in thermal energy without a change in temperature. The amount of heat energy that causes 1 kg of substance to undergo a phase change is the heat of transformation L of that substance. The heat required for a system of mass M to undergo a phase change is: Lava—molten rock—undergoes a phase change when it contacts the much colder water. This is one way in which new islands are formed. Slide 17-67

QuickCheck 17.10 If you heat a substance in an insulated container, is it possible that the temperature of the substance remains unchanged? Yes. No. Slide 17-68 68

QuickCheck 17.10 If you heat a substance in an insulated container, is it possible that the temperature of the substance remains unchanged? Yes. No. If there’s a phase change. Slide 17-69 69

Phase Change and Heat of Transformation Suppose you start with a system in its solid phase and heat it at a steady rate. The specific heat c can be measured from the slope of the linear increases. The heat needed for the phase changes is: where Lf is the heat of fusion and Lv is the heat of vaporization. Slide 17-70

Melting/Boiling Temperatures and Heats of Transformation Slide 17-71

Calorimetry Consider two systems with different temperatures T1 and T2 that can interact thermally with each other but are isolated from everything else. Heat will naturally flow from the hotter to the colder system until they reach a common final temperature Tf. If Qi is the heat transferred to system i, then: Slide 17-72

QuickCheck 17.11 50 g of ice at 0C is added to 50 g of liquid water at 0C in a well-insulated container, also at 0C. After a while, the container will hold All ice. > 50 g of ice, < 50 g of liquid water. 50 g of ice, 50 g of liquid water. < 50 g of ice, > 50 g of liquid water. All liquid water. Slide 17-73 73

QuickCheck 17.11 50 g of ice at 0C is added to 50 g of liquid water at 0C in a well-insulated container, also at 0C. After a while, the container will hold All ice. > 50 g of ice, < 50 g of liquid water. 50 g of ice, 50 g of liquid water. < 50 g of ice, > 50 g of liquid water. All liquid water. Slide 17-74 74

Problem-Solving Strategy: Calorimetry Problems Slide 17-75

Example 17.6 Three Interacting Systems Slide 17-76

Example 17.6 Three Interacting Systems Slide 17-77

The Specific Heats of Gases Processes A and B have the same T and the same Eth, but they require different amounts of heat. The reason is that work is done in process B but not in process A. The total change in thermal energy for any process, due to work and heat, is: Slide 17-78

The Specific Heats of Gases It is useful to define two different versions of the specific heat of gases, one for constant-volume processes and one for constant-pressure processes. We will define these as molar specific heats because we usually do gas calculations using moles instead of mass. The quantity of heat needed to change the temperature of n moles of gas by T is: where CV is the molar specific heat at constant volume and CP is the molar specific heat at constant pressure. Slide 17-79

CP and CV Note that for all ideal gases: where R = 8.31 J/mol K is the universal gas constant. Slide 17-80

QuickCheck 17.12 1 mol of air has an initial temperature of 20C. 200 J of heat energy are transferred to the air in an isochoric process, then 200 J are removed in an isobaric process. Afterward, the air temperature is < 20C. = 20C. > 20C. Not enough information is given to answer the question. Slide 17-81 81

QuickCheck 17.12 1 mol of air has an initial temperature of 20C. 200 J of heat energy are transferred to the air in an isochoric process, then 200 J are removed in an isobaric process. Afterward, the air temperature is < 20C. = 20C. > 20C. Not enough information is given to answer the question. T = so a smaller T in isobaric with larger C. Q nC Slide 17-82 82

Example 17.7 Heating and Cooling a Gas Slide 17-83

Example 17.7 Heating and Cooling a Gas Slide 17-84

Example 17.7 Heating and Cooling a Gas The figure shows the process on a pV diagram. The gas expands (moves horizontally on the diagram) as heat is added, then cools at constant volume (moves vertically on the diagram) as heat is removed. Slide 17-85

Heat Depends on the Path Consider the two ideal-gas processes shown. There’s more area under the process B curve, so the work |WB| > |WA|. Both values of W are negative as the gas expands. Thermal energy is a state variable, therefore Eth is the same for both processes, so WA + QA = WB + QB. This can only be true if QB > QA. Slide 17-86

The First Law of Thermodynamics An isothermal process is one for which the temperature of a specific amount of gas is held constant (no change in total thermal energy). An isochoric process is one for which the volume of the gas is held constant. An adiabatic process is one in which no heat energy is transferred. Slide 17-87

Adiabatic Processes An adiabatic process is one for which: where: Adiabats are steeper than hyperbolic isotherms, so the temperature falls during an adiabatic expansion, and rises during an adiabatic compression. Slide 17-88

QuickCheck 17.13 A gas in a container expands rapidly, pushing the piston out. The temperature of the gas Rises. Is unchanged. Falls. Can’t say without knowing more. Slide 17-89 89

QuickCheck 17.13 A gas in a container expands rapidly, pushing the piston out. The temperature of the gas Rises. Is unchanged. Falls. Can’t say without knowing more. Slide 17-90 90

Example 17.9 An Adiabatic Compression Slide 17-91

Example 17.9 An Adiabatic Compression Slide 17-92

Example 17.9 An Adiabatic Compression Slide 17-93

Example 17.9 An Adiabatic Compression Slide 17-94

QuickCheck 17.14 A gas in a container expands rapidly, pushing the piston out. The temperature of the gas falls. This is because The gas pressure falls. The gas density falls. Heat energy is removed. Work is done. Both C and D. Slide 17-95 95

QuickCheck 17.14 A gas in a container expands rapidly, pushing the piston out. The temperature of the gas falls. This is because The gas pressure falls. The gas density falls. Heat energy is removed. Work is done. Both C and D. Slide 17-96 96

Heat-Transfer Mechanisms Conduction Convection Radiation Evaporation Slide 17-97

Conduction For a material of cross-section area A and length L, spanning a temperature difference T = TH – TC, the rate of heat transfer is: where k is the thermal conductivity, which characterizes whether the material is a good conductor of heat or a poor conductor. Slide 17-98

Conduction Slide 17-99

Example 17.10 Keeping a Freezer Cold Slide 17-100

Example 17.10 Keeping a Freezer Cold Slide 17-101

Example 17.10 Keeping a Freezer Cold Slide 17-102

Convection Thermal energy is easily transferred through air, water, and other fluids because the air and water can flow. When the fluid is heated it generally expands and becomes less dense. Buoyancy then causes the warmer fluid to flow upward, while the cooler fluid sinks to take its place. This transfer of thermal energy by the motion of a fluid is called convection. Warm water (colored) moves by convection. Slide 17-103

Radiation All objects emit energy in the form of radiation, electromagnetic waves generated by oscillating electric charges in the atoms that form the object. This satellite image shows radiation emitted by the ocean waters off the east coast of the United States. You can clearly see the warm waters of the Gulf Stream, a large-scale convection that transfers heat to northern latitudes. Slide 17-104

Radiation If heat energy Q is radiated in a time interval t by an object with surface area A and absolute temperature T, the rate of heat transfer is: The parameter e is the emissivity of the surface, a measure of how effectively it radiates. The value of e ranges from 0 to 1.  = 5.67  10–8 W/m2K4 is the Stefan-Boltzmann constant. Slide 17-105

QuickCheck 17.15 Suppose the temperature of the sun suddenly dropped to half its present value. The sun’s power output would decrease by a factor of 1. 1/2. 1/4. 1/8. 1/16. Slide 17-106 106

QuickCheck 17.15 Suppose the temperature of the sun suddenly dropped to half its present value. The sun’s power output would decrease by a factor of 1. 1/2. 1/4. 1/8. 1/16. P is proportional to T 4. Slide 17-107 107

Example 17.11 Taking the Sun’s Temperature Slide 17-108

Example 17.11 Taking the Sun’s Temperature Slide 17-109

Chapter 17 Summary Slides

General Principles Slide 17-111

General Principles Slide 17-112

Important Concepts Slide 17-113

Important Concepts Slide 17-114

Important Concepts Slide 17-115

Important Concepts Slide 17-116