1 / 73

Chapter 16

Chapter 16. Thermal Properties of Matter. Macroscopic Description of Matter. State Variables. State variable = macroscopic property of thermodynamic system Examples: pressure p volume V temperature T mass m. State Variables.

alec
Download Presentation

Chapter 16

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 16 Thermal Propertiesof Matter

  2. Macroscopic Descriptionof Matter

  3. State Variables • State variable = macroscopic property of thermodynamic system • Examples: pressure p volume V temperature T mass m

  4. State Variables • State variables: p, V, T, m • I general, we cannot change one variable without affecting a change in the others • Recall: For a gas, we defined temperature T (in kelvins) using the gas pressure p

  5. Equation of State • State variables: p, V, T, m • The relationship among these:‘equation of state’ • sometimes: an algebraic equation exists • often: just numerical data

  6. Equation of State • Warm-up example: • Approximate equation of state for a solid • Based on concepts we already developed • Here: state variables are p, V, T Derive the equation of state

  7. The ‘Ideal’ Gas • The state variables of a gas are easy to study: • p, V, T, mgas • often use: n = number of ‘moles’ instead of mgas

  8. Moles and Avogadro’s Number NA • 1 mole = 1 mol = 6.02×1023 molecules = NA molecules • n = number of moles of gas • M = mass of 1 mole of gas • mgas = n M Do Exercise 16-53

  9. The ‘Ideal’ Gas • We measure: the state variables (p, V, T, n) for many different gases • We find: at low density, all gases obey the same equation of state!

  10. Ideal Gas Equation of State • State variables: p, V, T, n pV = nRT • p = absolute pressure (not gauge pressure!) • T = absolute temperature (in kelvins!) • n = number of moles of gas

  11. Ideal Gas Equation of State • State variables: p, V, T, n pV = nRT • R = 8.3145 J/(mol·K) • same value of R for all (low density) gases • same (simple, ‘ideal’) equation Do Exercises 16-9, 16-12

  12. Ideal Gas Equation of State • State variables: p, V, T, and mgas= nM • State variables: p, V, T, and r = mgas/V Derive ‘Law of Atmospheres’

  13. Non-Ideal Gases? • Ideal gas equation: • Van der Waals equation: Notes

  14. pV–Diagram for an Ideal Gas Notes

  15. pV–Diagram for a Non-Ideal Gas Notes

  16. Microscopic Descriptionof Matter

  17. Ideal Gas Equation pV = nRT • n = number of moles of gas = N/NA • R = 8.3145 J/(mol·K) • N = number of molecules of gas • NA = 6.02×1023 molecules/mol

  18. Ideal Gas Equation • k = Boltzmann constant = R/NA = 1.381×10-23 J/(molecule·K)

  19. Ideal Gas Equation pV = nRT pV = NkT • k = R/NA • ‘ RT per mol’ vs. ‘kT per molecule’

  20. Kinetic-Molecular Theory of an Ideal Gas

  21. Assumptions • gas = large number N of identical molecules • molecule = point particle, mass m • molecules collide with container walls= origin of macroscopic pressure of gas

  22. Kinetic Model • molecules collide with container walls • assume perfectly elastic collisions • walls are infinitely massive (no recoil)

  23. Elastic Collision • wall: infinitely massive, doesn’t recoil • molecule: vy: unchanged vx : reverses direction speed v : unchanged

  24. Kinetic Model • For one molecule: v2 = vx2 + vy2 + vz2 • Each molecule has a different speed • Consider averaging over all molecules

  25. Kinetic Model • average over all molecules: (v2)av= (vx2 + vy2 + vz2)av = (vx2)av+(vy2)av+(vz2)av = 3 (vx2)av

  26. Kinetic Model • (Ktr)av= total kinetic energy of gas due to translation • Derive result:

  27. Kinetic Model • Compare to ideal gas law: pV = nRT pV = NkT

  28. Kinetic Energy • average translational KE is directly proportional to gas temperature T

  29. Kinetic Energy • average translational KE per molecule: • average translational KE per mole:

  30. Kinetic Energy • average translational KE per molecule: • independent of p, V, and kind of molecule • for same T, all molecules (any m) have the same average translational KE

  31. Kinetic Model • ‘root-mean-square’ speed vrms:

  32. Molecular Speeds • For a given T, lighter molecules move faster • Explains why Earth’s atmosphere contains alomost no hydrogen, only heavier gases

  33. Molecular Speeds • Each molecule has a different speed, v • We averaged over all molecules • Can calculate the speed distribution, f(v)(but we’ll just quote the result)

  34. Molecular Speeds f(v) = distribution function f(v) dv = probability a molecule has speed between v and v+dv dN = number of molecules with speed between v and v+dv = N f(v) dv

  35. Molecular Speeds • Maxwell-Boltzmann distribution function

  36. Molecular Speeds • At higher T:more molecules have higher speeds • Area under f(v) = fraction of molecules with speeds in range: v1 < v < v1 or v > vA

  37. Molecular Speeds • average speed • rms speed

  38. Molecular Collisions? • We assumed: • molecules = point particles, no collisions • Real gas molecules: • have finite size and collide • Find ‘mean free path’ between collisions

  39. Molecular Collisions

  40. Molecular Collisions • Mean free path between collisions:

  41. Announcements • Midterms: • Returned at end of class • Scores will be entered on classweb soon • Solutions available online at E-Res soon • Homework 7 (Ch. 16): on webpage • Homework 8 (Ch. 17): to appear soon

  42. Heat Capacity Revisited

  43. Heat Capacity Revisited DQ = energy required to change temperature of mass m by DT c = ‘specific heat capacity’ = energy required per (unit mass × unit DT)

  44. Heat Capacity Revisited • Now introduce ‘molar heat capacity’ C C = energy per (mol × unit DT) required to change temperature of n moles by DT

  45. Heat Capacity Revisited • important case:the volume V of material is held constant • CV = molar heat capacity at constant volume

  46. CV for the Ideal Gas • Monatomic gas: • molecules = pointlike(studied last lecture) • recall: translational KE of gas averaged over all molecules (Ktr)av = (3/2) nRT

  47. CV for the Ideal Gas • Monatomic gas: (Ktr)av = (3/2) nRT • note: your text just writesKtr instead of (Ktr)av • Consider changing T by dT

  48. CV for the Ideal Gas • Monatomic gas: (Ktr)av = (3/2) nRT d(Ktr)av = n (3/2)R dT • recall: dQ = n CV dT • so identify: CV= (3/2)R

  49. In General: If (Etot)av = (f/2) nRT Then d(Etot)av = n (f/2)R dT But recall: dQ = n CV dT So we identify: CV= (f/2)R

  50. A Look Ahead (Etot)av = (f/2) nRT CV= (f/2)R Monatomic gas:f = 3 Diatomic gas:f = 3, 5, 7

More Related