1 / 80

Chapter 18 Lecture

Chapter 18 Lecture. Chapter 18 The Micro/Macro Connection. Chapter Goal: To understand a macroscopic system in terms of the microscopic behavior of its molecules. Slide 18-2. Chapter 18 Preview. Slide 18-3. Chapter 18 Preview. Slide 18-4. Chapter 18 Preview. Slide 18-5.

jcone
Télécharger la présentation

Chapter 18 Lecture

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 18 Lecture

  2. Chapter 18 The Micro/Macro Connection Chapter Goal: To understand a macroscopic system in terms of the microscopic behavior of its molecules. Slide 18-2

  3. Chapter 18 Preview Slide 18-3

  4. Chapter 18 Preview Slide 18-4

  5. Chapter 18 Preview Slide 18-5

  6. Chapter 18 Preview Slide 18-6

  7. Chapter 18 Preview Slide 18-7

  8. Chapter 18 Preview Slide 18-8

  9. Chapter 18 Reading Quiz Slide 18-9

  10. Reading Question 18.1 What is the name of the quantity represented as vrms? • Random-measured-step viscosity. • Root-mean-squared speed. • Relative-mean-system velocity. • Radial-maser-system volume. Slide 18-10

  11. Reading Question 18.1 What is the name of the quantity represented as vrms? • Random-measured-step viscosity. • Root-mean-squared speed. • Relative-mean-system velocity. • Radial-maser-system volume. Slide 18-11

  12. Reading Question 18.2 What additional kind of energy makes CV larger for a diatomic than for a monatomic gas? • Charismatic energy. • Translational energy. • Heat energy. • Rotational energy. • Solar energy. Slide 18-12

  13. Reading Question 18.2 What additional kind of energy makes CV larger for a diatomic than for a monatomic gas? • Charismatic energy. • Translational energy. • Heat energy. • Rotational energy. • Solar energy. Slide 18-13

  14. Reading Question 18.3 The second law of thermodynamics says that • The entropy of an isolated system never decreases. • Heat never flows spontaneously from cold to hot. • The total thermal energy of an isolated system is constant. • Both A and B. • Both A and C. Slide 18-14

  15. Reading Question 18.3 The second law of thermodynamics says that • The entropy of an isolated system never decreases. • Heat never flows spontaneously from cold to hot. • The total thermal energy of an isolated system is constant. • Both A and B. • Both A and C. Slide 18-15

  16. Reading Question 18.4 In general, • Both microscopic and macroscopic processes are reversible. • Both microscopic and macroscopic processes are irreversible. • Microscopic processes are reversible and macroscopic processes are irreversible. • Microscopic processes are irreversible and macroscopic processes are reversible. Slide 18-16

  17. Reading Question 18.4 In general, • Both microscopic and macroscopic processes are reversible. • Both microscopic and macroscopic processes are irreversible. • Microscopic processes are reversible and macroscopic processes are irreversible. • Microscopic processes are irreversible and macroscopic processes are reversible. Slide 18-17

  18. Chapter 18 Content, Examples, and QuickCheck Questions Slide 18-18

  19. Molecular Speeds and Collisions • A gas consists of a vast number of molecules, each moving randomly and undergoing millions of collisions every second. • Shown is the distribution of molecular speeds in a sample of nitrogen gas at 20C. • The micro/macro connection is built on the idea that the macroscopic properties of a system, such as temperature or pressure, are related to the averagebehavior of the atoms and molecules. Slide 18-19

  20. Mean Free Path • A single molecule follows a zig-zag path through a gas as it collides with other molecules. • The average distance between the collisions is called the mean free path: • (N/V) is the number density of the gas in m−3. • r is the the radius of the molecules when modeled as hard spheres; for many common gases r ≈ 10−10 m. Slide 18-20

  21. QuickCheck 18.1 The temperature of a rigid container of oxygen gas (O2) is lowered from 300C to 0C. As a result, the mean free path of oxygen molecules Increases. Is unchanged. Decreases. Slide 18-21

  22. QuickCheck 18.1 The temperature of a rigid container of oxygen gas (O2) is lowered from 300C to 0C. As a result, the mean free path of oxygen molecules Increases. Is unchanged. Decreases. λ depends only on N/V, not T. Slide 18-22

  23. Example 18.1 The Mean Free Path at Room Temperature Slide 18-23

  24. Pressure in a Gas • Why does a gas have pressure? • In Chapter 15 we suggested that the pressure in a gas is due to collisions of the molecules with the walls of its container. • The steady rain of a vast number of molecules striking a wall each second exerts a measurable macroscopic force. • The gas pressure is the force per unit area (p = F/A) resulting from these molecular collisions. Slide 18-24

  25. Pressure in a Gas • The figure shows a molecule which collides with a wall, exerting an impulse on it. • The x-component of the impulse from a single collision is: • If there are Ncoll such collisions during a small time interval t, the net impulse is: Slide 18-25

  26. Pressure in a Gas • The figure reminds you that impulse is the area under the force-versus-time curve and thus Jwall = Favgt. • The average force on the wall is: • where the rate of collisions is: Slide 18-26

  27. Pressure in a Gas • The pressure is the average force on the walls of the container per unit area: • (N/V) is the number density of the gas in m−3. • Note that the average velocity of many molecules traveling in random directions is zero. • vrms is the root-mean-square speed of the molecules, which is the square root of the average value of the squares of the speeds of the molecules: Slide 18-27

  28. QuickCheck 18.2 A rigid container holds oxygen gas (O2) at 100C. The average velocity of the molecules is Greater than zero. Zero. Less than zero. Slide 18-28

  29. QuickCheck 18.2 A rigid container holds oxygen gas (O2) at 100C. The average velocity of the molecules is Greater than zero. Zero. Less than zero. Slide 18-29

  30. Example 18.2 Calculating the Root-Mean-Square Speed Units of velocity are m/s. Slide 18-30

  31. Example 18.2 Calculating the Root-Mean-Square Speed Slide 18-31

  32. Example 18.2 Calculating the Root-Mean-Square Speed Slide 18-32

  33. Example 18.3 The RMS Speed of Helium Atoms Example 18.3 The rms Speed of Helium Atoms Slide 18-33

  34. QuickCheck 18.3 A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100C. Which statement describes their rms speeds? vrmsofH2 < vrmsof N2. vrmsofH2 = vrmsof N2. vrmsofH2 > vrmsof N2. Slide 18-34

  35. QuickCheck 18.3 A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100C. Which statement describes their rms speeds? vrms of H2 < vrms of N2. vrms of H2 = vrms of N2. vrms of H2 > vrms of N2. Slide 18-35

  36. Temperature in a Gas • The thing we call temperature measures the average translational kinetic energy єavg of molecules in a gas. • A higher temperature corresponds to a larger value of єavgand thus to higher molecular speeds. • Absolute zero is the temperature at which єavg= 0 and all molecular motion ceases. • By definition, єavg = ½mvrms2, where vrms is the root mean squared molecular speed; using the ideal-gas law, we found єavg = 3/2 kBT. • By equating these expressions we find that the rms speed of molecules in a gas is: Slide 18-36

  37. QuickCheck 18.4 A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100C. Which statement describes the average translational kinetic energies of the molecules? єavg of H2 < єavg of N2. єavg of H2 = єavg of N2. єavg of H2 > єavg of N2. Slide 18-37

  38. QuickCheck 18.4 A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100C. Which statement describes the average translational kinetic energies of the molecules? єavg of H2 < єavg of N2. єavg of H2 = єavg of N2. єavg of H2 > єavg of N2. Slide 18-38

  39. The Micro/Macro Connection for Pressure and Temperature Slide 18-39

  40. Example 18.4 Total Microscopic Kinetic Energy Slide 18-40

  41. Example 18.5 Calculating an RMS Speed Slide 18-41

  42. Example 18.6 Mean Time Between Collisions Slide 18-42

  43. Thermal Energy and Specific Heat • The thermal energy of a system is Eth = Kmicro + Umicro. • The figure shows a monatomic gas such as helium or neon. • The atoms in a monatomic gas have no molecular bonds with their neighbors, hence Umicro = 0. • Since the average kinetic energy of a single atom in an ideal gas is єavg = 3/2 kBT, the total thermal energy is: Slide 18-43

  44. Thermal Energy and Specific Heat • If the temperature of a monatomic gas changes by T, its thermal energy changes by: • In Chapter 17 we found that the change in thermal energy for any ideal-gas process is related to the molar specific heat at constant volume by: • Combining these equations gives us a prediction for the molar specific heat for a monatomic gas: • This prediction is confirmed by experiments. Slide 18-44

  45. The Equipartition Theorem • Atoms in a monatomic gas carry energy exclusively as translational kinetic energy (3 degrees of freedom). • Molecules in a gas may have additional modes of energy storage, for example, the kinetic and potential energy associated with vibration, or rotational kinetic energy. • We define the number of degrees of freedom as the number of distinct and independent modes of energy storage. Slide 18-45

  46. QuickCheck 18.5 A mass on a spring oscillates back and forth on a frictionless surface. How many degrees of freedom does this system have? 1. 2. 3. 4. 6. Slide 18-46

  47. QuickCheck 18.5 A mass on a spring oscillates back and forth on a frictionless surface. How many degrees of freedom does this system have? 1. 2. 3. 4. 6. It can hold energy as kinetic energy or potential energy. Slide 18-47

  48. Thermal Energy of a Solid • The figure reminds you of the “bedspring model” of a solid with particle-like atoms connected by spring-like molecular bonds. • There are 3 degrees of freedom associated with kinetic energy + 3 more associated with the potential energy in the molecular bonds = 6 degrees of freedom total. • The energy stored in each degree of freedom is ½ NkBT, so: Slide 18-48

  49. Diatomic Molecules • In addition to the 3 degrees of freedom from translational kinetic energy, a diatomic gas at commonly used temperatures has 2 additional degrees of freedom from end-over-end rotations. • This gives 5 degrees of freedom total: Slide 18-49

  50. Thermal Energy and Specific Heat Slide 18-50

More Related