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

Transcription

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

2 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. Lab is this week reviews your understanding of ideal gases. Homework 10 on Chapters 20 and 13 is due Friday, November 30, by 5PM in your TA s mailbox outside of PB201. Our third in-class exam is on Monday, December 3. It will focus on Chapters and 13, keeping in mind that physics is cumulative. Our final exam is on Friday, December 14, from 5:15-7:15PM in Stolkin.

3 Tenth (and final) set of Three Big Questions What is temperature and what is its molecular basis? How does temperature allow one to tune between gases, liquids, and solids? What are the laws of thermodynamics? And how can we use them to do work? 3

4 The energy that flows between two objects or systems due to a temperature difference between them is called heat. If heat can flow between two objects or systems, the objects or systems are said to be in thermal contact. To measure the temperature of an object, we put a thermometer into thermal contact with the object. Temperature measurement relies on the zeroth law of thermodynamics. Slide 4

5 Zeroth Law of Thermodynamics 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. Slide 5

6 Ideal Gas Law (Microscopic Form) Ideal Gas Law k = J/K Boltzmann s constant Slide 6

7 Slide 7

8 It is common to express the amount of a substance in units of moles (abbreviated mol). The mole is an SI base unit and is defined as follows: one mole of anything contains the same number of units as there are atoms in 12 grams (not kilograms) of carbon-12. The number of molecules per mole is called Avogadro s number and has the value: Slide 8

9 KINETIC THEORY OF THE IDEAL GAS The ideal gas is a simplified model of a dilute gas in which we think of the molecules as point-like particles that move independently in free space with no interactions except for elastic collisions. This simplified model is a good approximation for many gases under ordinary conditions. Many properties of gases can be understood from this model; the microscopic theory based on it is called the kinetic theory of the ideal gas. Slide 9

10 Microscopic Basis of Pressure Slide 10

11 KINETIC THEORY OF THE IDEAL GAS mdv x For one particle: mdv x For N particles: Slide 11

12 KINETIC THEORY OF IDEAL GASES Slide 12

13 Temperature and Translational Kinetic Energy Slide 13

14 Maxwell-Boltzmann Distribution Collisions keep the kinetic energy distributed among the gas molecules in the most disordered way possible, which is the Maxwell-Boltzmann distribution. O 2 Slide 14

15 RMS Speed The speed of a gas molecule that has the average kinetic energy is called the rms (root mean square) speed. The rms speed is not the same as the average speed. Instead, the rms speed is the square root of the mean (average) of the speed squared. Slide 15

16 A container holds oxygen and helium gases at the same temperature. Which one of the following statements is correct? A. the oxygen molecules have the greater kinetic energy B. the helium molecules have the greater kinetic energy C. the oxygen molecules have the greater speed D. the helium molecules have the greater speed

17 13.7 Example problem: Find the average translational kinetic energy and the rms speed of the O 2 molecules in air at room temperature (20 C). Strategy The average translational kinetic energy depends only on temperature. We must remember to use absolute temperature. The rms speed is the speed of a molecule that has the average kinetic energy. Slide 17

18 Now get ready for some definitions so that we can quantitatively define heat and construct the remaining laws of thermodynamics so that we get ready for the Stirling engine lab next week.

19 A system is whatever we define it to be: one object or a group of objects. Everything that is not part of the system is considered to be external to the system, or in other words, in the surroundings of the system. So what is internal energy (energy internal to the system)? Slide 19

20 Molecules inside the system move about in random directions. This random microscopic kinetic energy is part of what we call the internal energy of the system: Slide 20

21 Internal energy includes Translational and rotational kinetic energy of molecules due to their individual random motions. Vibrational energy both kinetic and potential of molecules and of atoms within molecules due to random vibrations about their equilibrium points. Potential energy due to interactions between the atoms and molecules of the system. Chemical and nuclear energy the kinetic and potential energy associated with the binding of atoms to form molecules, the binding of electrons to nuclei to form atoms, and the binding of protons and neutrons to form nuclei. Slide 21

22 14.1 Example problem: A block of mass 10.0 kg starts at point A at a height of 2.0 m above the horizontal and slides down a frictionless incline. It then continues sliding along the horizontal surface of a table that has friction. The block comes to rest at point C, a distance of 1.0 m along the table surface. How much has the internal energy of the system (block + table) increased? Slide 22

23 HEAT Many eighteenth-century scientists thought that heat was a fluid, which they called caloric. The flow of heat into an object was thought to cause the object to expand in volume in order to accommodate the additional fluid; why no mass increase occurred was a mystery. Now we know that heat is not a substance but is a flow of energy. Heat is energy in transit between two objects or systems due to a temperature difference between them. Slide 23

24 Heat and Work Heat and work are similar in that both describe a particular kind of energy transfer. Work is an energy transfer due to a force acting through a displacement. Heat is a microscopic form of energy transfer involving large numbers of particles; the exchange of energy occurs due to the individual interactions of the particles. Some objects transfer heat better than others! Slide 24

25 THE FIRST LAW OF THERMODYNAMICS Both work and heat can change the internal energy of a system. Work can be done on a rubber ball by squeezing it, stretching it, or slamming it into a wall. Heat will flow into the ball if it is left out in the Sun or put into a hot oven. These two methods of changing the internal energy of a system lead to the first law of thermodynamics. Slide 25

26 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 26

27 Slide 27

28 When a gas is compressed, the work done on the gas is positive. When a gas expands, the work done on the gas is negative. Slide 28

29 It s demo time!

30 THERMODYNAMIC PROCESSES A thermodynamic process is the method by which a system is changed from one state to another. The 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 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 state to another. Slide 30

31 THERMODYNAMIC PROCESSES The PV Diagram If a system is changed so that it is always very near equilibrium, the changes in state can be represented by a curve on a plot of pressure versus volume (called a PV diagram ). (Shown on next slide) Slide 31

32 The PV Diagram THERMODYNAMIC PROCESSES 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 32

33 THERMODYNAMIC PROCESSES Work and Area Under a PV Curve Slide 33

34 The magnitude of the total work done on the gas is the area under the PV curve. During an increase in volume, ΔV is positive and the work done on the gas is negative. During a decrease in volume, ΔV is negative and the work done on the gas is positive. Slide 34

35 THERMODYNAMIC PROCESSES Work Done During a Closed Cycle Because the work done on a system depends on the path on the PV diagram, the net work done on a system during a closed cycle a series of processes that leave the system in the same state it started in can be nonzero. Slide 35

36 THERMODYNAMIC PROCESSES Constant-Pressure Processes A process by which the state of a system is changed while the pressure is held constant is called an isobaric process. Slide 36

37 THERMODYNAMIC PROCESSES Constant-Volume Processes A process by which the state of a system is changed while the volume remains constant is called an isochoric process. Slide 37

38 THERMODYNAMIC PROCESSES Constant-Temperature Processes A process in which the temperature of the system remains constant is called an isothermal process. Slide 38

39 THERMODYNAMIC PROCESSES Adiabatic Processes A process in which no heat is transferred into or out of the system is called an adiabatic process. An adiabatic process is not the same as a constanttemperature (isothermal) process. In an isothermal process, heat flow into or out of a system is necessary to maintain a constant temperature. In an adiabatic process, no heat flow occurs, so if work is done, the temperature of the system may change. Slide 39

40 It s demo time!

41 THERMODYNAMIC PROCESSES Slide 41

42 Stirling engine and animatedengines.com

43 In the first law of thermodynamics (U = Q + W), the variables Q and W stand for A. the heat flow out of the system and the work done on the system. B. the heat flow out of the system and the work done by the system. C. the heat flow into the system and the work done by the system. D. the heat flow into the system and the work done on the system.

44 And now onto reviewing for next week s exam!