PHY101: Major Concepts in Physics I

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1 Welcome back to PHY101: Major Concepts in Physics I Photo: S. T. Cummins

2 Photo: S. T. Cummins

3 Announcements Today is our final class! We will first discuss more on Chapters and then conduct a short course review via several example problems. Our final lab is this week on the Stirling engine. HW 11 is due by next Monday at noon in your TA s mailbox. Our final exam is on Friday, December 14, from 5:15-7:15PM in Stolkin.

4 See the updated equation sheet now containing all the formulas you need to know for the final exam!

5 Tenth (and final) set of Three Big Questions What is the molecular basis of temperature? How does temperature allow one tune between gases, liquids, and solids? What are the laws of thermodynamics? And how can we use them to do work? 5

6 Kinetic Theory of Ideal Gases Slide 6

7 Zeroth Law of Thermodynamics: If two objects are each in thermal equilibrium with a third object, then the two are in thermal equilibrium with one another. Different thermometers give the same results! Slide 7

8 First Law of Thermodynamics: The change in internal energy of a system is equal to the heat flow into the system plus the work done on the system. Slide 8

9 Slide 9

10 14.3 Example problem: In an experiment similar to that done by Joule (next slide), an object of mass 12.0 kg descends a distance of 1.25 m at constant speed while causing the rotation of a paddle wheel in an insulated container of water. If the descent is repeated 20.0 times, what is the internal energy increase of the water in joules? Slide 10

11 14.3 Slide 11

12 14.3 Strategy Each time the object descends, it converts gravitational potential energy into kinetic energy of the paddle wheel, which in turn agitates the water and converts kinetic energy into internal energy. Slide 12

13 Solution 14.3 Slide 13

14 Heat Capacity For a large number of substances, under normal conditions, the temperature change ΔT is approximately proportional to the heat Q. The constant of proportionality is called the heat capacity (symbol C ): The heat capacity depends both on the substance and on how much of it is present. Slide 14

15 Specific Heat The heat capacity of the water in a drinking glass is much smaller than the heat capacity of the water in Lake Ontario. Since the heat capacity of a system is proportional to the mass of the system, the specific heat capacity (symbol c ) of a substance is defined as the heat capacity per unit mass: Specific heat capacity is often abbreviated to specific heat. Slide 15

16 The equation applies when no phase change occurs. Slide 16

17 Slide 17

18 Slide 18

19 From Joule s 1849 paper

20 PHASE TRANSITIONS A phase transition occurs whenever a material is changed from one phase, such as the solid phase, to another, such as the liquid phase. During the two phase transitions, heat flow continues, and the internal energy changes, but the temperature of the mixture of two phases does not change. Slide 20

21 Slide 21

22 Definition of latent heat: The heat required per unit mass of substance to produce a phase change is called the latent heat ( L ). The word latent is related to the lack of temperature change during a phase transition. The sign of Q depends on the direction of the phase transition. For melting or boiling, Q > 0 (heat flows into the system). For freezing or condensation, Q < 0 (heat flows out of the system). Slide 22

23 Microscopic View of a Phase Change When a substance is in solid form, bonds between the atoms or molecules hold them near fixed equilibrium positions. Energy must be supplied to break the bonds and change the solid into a liquid. When the substance is changed from liquid to gas, energy is used to separate the molecules from the loose bonds holding them together and to move the molecules apart. Slide 23

24 Microscopic View of a Phase Change Temperature does not change during these phase transitions because the kinetic energy of the molecules is not changing. Instead, the potential energy of the molecules changes as work is done against the forces holding them together. Slide 24

25 Phase Diagrams A useful tool in the study of phase transitions is the phase diagram a diagram on which pressure is plotted on the vertical axis and temperature on the horizontal axis. Slide 25

26 Phase Diagrams The curves on the phase diagram are the demarcations between the solid, liquid, and gas phases. At the triple point, all three phases (solid, liquid, and gas) can coexist in equilibrium. Notice that the vapor pressure curve ends at the critical point. Slide 26

27 Phase Diagrams The curves on the phase diagram are the demarcations between the solid, liquid, and gas phases. At the triple point, all three phases (solid, liquid, and gas) can coexist in equilibrium. Notice that the vapor pressure curve ends at the critical point. Slide 27

28 Slide 28

29 A thermodynamic process is the method by which a system is changed from one equilibrium state to another. The equilibrium state of a system is described by a set of state variables such as pressure, temperature, volume, number of moles, and internal energy. State variables describe the equilbrium state of a system at some instant of time but not how the system got to that state. Heat and work are not state variables they describe how a system gets from one equilibrium state to another. Slide 29

30 The PV Diagram Each point on the curve represents an equilibrium state of the system. The PV diagram is a useful tool for analyzing thermodynamic processes. One of the chief uses of a PV diagram is to find the work done on the system. Slide 30

31 Work and Area Under a PV Curve Slide 31

32 Slide 32

33 On a PV diagram, what kind of process is represented by a horizontal line with an arrow pointing to the right? A. Isochoric process B. Isobaric compression C. Isothermal compression D. Isobaric expansion

34 On a PV diagram, what kind of process is represented by a horizontal line with an arrow pointing to the right? A. Isochoric process B. Isobaric compression C. Isothermal compression D. Isobaric expansion

35 A heat engine is a device designed to convert disordered energy (heat) into ordered energy (work). We will see that there is a fundamental limitation on how much ordered energy (mechanical work) can be produced by a heat engine from a given amount of disordered energy (heat) using the various thermodynamic processes. Slide 35

36 Cyclical Engines The engines that we will study operate in cycles. Each cycle consists of several thermodynamic processes that are repeated the same way during each cycle. In order for these processes to repeat the same way, the engine must end the cycle in the same state in which it started. In particular, the internal energy of the engine must be the same at the end of a cycle as it was in the beginning. Slide 36

37 Cyclical Engine The net work done by an engine during one cycle is equal to the net heat flow into the engine during the cycle. We stress that it is the net heat flow since an engine not only takes in heat but exhausts some as well. The figure shows the energy transfers during one cycle of a heat engine. Slide 37

38 Stirling engine demo!

39 Application: The Internal Combustion Engine Slide 39

40 Otto engine!

41 Efficiency and the First Law According to the first law of thermodynamics, the efficiency of a heat engine cannot exceed 100%. An efficiency of 100% would mean that all of the heat input is turned into useful work and no waste heat is exhausted. It might seem theoretically possible to make a 100% efficient engine by eliminating all of the imperfections in design such as friction and lack of perfect insulation. However, it is not, as we see in a moment. Slide 41

42 Now imagine a hypothetical reversible engine exchanging heat with two reservoirs. In this engine, no irreversible processes occur: there is no friction or other dissipation of energy, and heat only flows between systems that have the same temperature. In practice, there would have to be some small temperature difference to make heat flow from one system to another, but we can imagine making the temperature difference smaller and smaller. Hence, the reversible engine is an idealization, not something we can actually build. Slide 42

43 We can now show that the efficiency of this reversible engine depends only on the absolute temperatures of the two reservoirs; and the efficiency of a real engine that exchanges heat with two reservoirs cannot be greater than the efficiency of a reversible engine using the same two reservoirs. Slide 43

44 Efficiency of a Reversible Engine For a reversible engine, the ratio of the heat magnitudes is equal to the temperature ratio. The efficiency of a reversible engine cannot reach 100 percent. This is one way of stating the second law of thermodynamics! Slide 44

45 Another way to state the second law of thermodynamics : Heat never flows spontaneously from a colder body to a hotter body. (Spontaneous heat flow from a colder body to a hotter body would decrease the total disorder in the universe. The second law of thermodynamics determines what we sense as the direction of time none of the other physical laws we have studied would be violated if the direction of time were reversed.) Slide 45

46 Entropy If an amount of heat Q flows into a system at constant absolute temperature T, the entropy change of the system is If a small amount of heat Q flows from a hotter system to a colder system ( T H > T C ), the total entropy change of the system is Slide 46

47 The entropy of the universe never decreases. Note that a reversible process causes no change in the total entropy of the universe. This is yet a third way of stating the second law of thermodynamics! And engine/device that does not obey the second law of thermodynamics does not exist! Slide 47

48 Like the second law, the third law of thermodynamics can be stated in several equivalent ways. Although it is impossible to reach absolute zero, there is no limit on how close we can get. Slide 48

49 A friend tells you that he knows of a situation in which bowl of ice sitting by itself on a table in a room whose air temperature is 20 o C gives up heat the surrounding air. What s wrong with this concept? A. It would violate the 0 th law of thermodynamics B. It would violate the 1 st law of thermodynamics C. It would violate the 2 nd law of thermodynamics D. It would violate the 3 rd law of thermodynamics

50 A friend tells you that he knows of a situation in which bowl of ice sitting by itself on a table in a room whose air temperature is 20 o C gives up heat the surrounding air. What s wrong with this concept? A. It would violate the 0 th law of thermodynamics B. It would violate the 1 st law of thermodynamics C. It would violate the 2 nd law of thermodynamics D. It would violate the 3 rd law of thermodynamics

51 What is science? What is physics? What tools do you need to learn physics? What are forces? What laws govern forces? How can we apply the laws to solve problems? How does one define position, displacement, velocity, and acceleration? How does one describe motion along a line with constant velocity? How does one describe motion along a line with constant acceleration? How does one define position, displacement, velocity, and acceleration in the plane? How does one describe motion in the plane with constant acceleration? What is work? And how is it related to energy? What is energy? How many different types of energy are there? Energy is conserved. How can we apply this principle (combined with the concept of work ) to solve problems?

52 How does a solid respond to a deformation, i.e. a change in its size or shape? In what situations does simple harmonic motion occur and how does one describe it? How do fluids behave? What is electric charge? How do electric charges interact? What is an electric field? What is electric potential energy and electric potential? How does one store/harness the electric potential energy? How do electrical circuits work? What are magnetic fields? How can we harness magnetic fields to do work? How do magnetic fields affect the motion of certain objects? What is temperature and what is its molecular basis? How does temperature all one to tune between gases, liquids, and solids? What are the laws of thermodynamics? And how can we use them to do work?

53 Example problems..

56 The equation sheet is your friend. It provides a concise summary of the course! Don t forget to fill out the on-line course evaluation!

57 The equation sheet is your friend. It provides a concise summary of the course! Don t forget to fill out the on-line course evaluation! Standing for truth, justice, and scientific method! Over and out, Professor Schwarz

PHY101: Major Concepts in Physics I. Photo: J. M. Schwarz

PHY101: Major Concepts in Physics I Photo: J. M. Schwarz Announcements We will be talking about the laws of thermodynamics today, which will help get you ready for next week s lab on the Stirling engine.