1 / 16

Lecture 25

Lecture 25. Goals:. Chapters 18, micro-macro connection. Third test on Thursday at 7:15 pm. Nitrogen molecules near room temperature. Percentage of molecules. 15. 10. 5. (m/s). 0-100. 1000-1100. 900-1000. 700-800. 800-900. 300-400. 500-600. 200-300. 400-500. 500-600. 100-200.

oma
Download Presentation

Lecture 25

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. Lecture 25 Goals: • Chapters 18, micro-macro connection • Third test on Thursday at 7:15 pm.

  2. Nitrogen molecules near room temperature Percentage of molecules 15 10 5 (m/s) 0-100 1000-1100 900-1000 700-800 800-900 300-400 500-600 200-300 400-500 500-600 100-200 600-700

  3. Atomic scale • What is the typical size of an atom or a small molecule? A) 10-6 m B) 10-10 m C) 10-15 m r r ≈1 angstrom=10-10 m

  4. Mean free path • Average distance particle moves between collisions: N/V: particles per unit volume • The mean free path at atmospheric pressure is: λ=68 nm

  5. Pressure in a gas

  6. Consider a gas with all molecules traveling at a speed vx hitting a wall. • If (N/V) increases by a factor of 2, the pressure would: A) decrease B) increase x2 C) increase x4 • If m increases by a factor of 2, the pressure would: A) decrease B) increase x2 C) increase x4 • If vx increases by a factor of 2, the pressure would: A) decrease B) increase x2 C) increase x4

  7. P=(N/V)mvx2 • Because we have a distribution of speeds: P=(N/V)m(vx2)avg • For a uniform, isotropic system: (vx2)avg= (vy2)avg= (vz2)avg • Root-mean-square speed: (v2)avg=(vx2)avg+(vy2)avg+(vz2)avg=Vrms2

  8. Microscopic calculation of pressure P=(N/V)m(vx2)avg =(1/3) (N/V)mvrms2 PV = (1/3) Nmvrms2

  9. Micro-macro connection PV = (1/3) Nmvrms2 PV = NkBT (ideal gas law) kBT =(1/3) mvrms2 • The average translational kinetic energy is: εavg=(1/2) mvrms2 εavg=(3/2) kBT

  10. The average kinetic energy of the molecules of an ideal gas at 10°C has the value K1. At what temperature T1 (in degrees Celsius) will the average kinetic energy of the same gas be twice this value, 2K1? (A) T1 = 20°C (B) T1 = 293°C (C) T1 = 100°C • Suppose that at some temperature we have oxygen molecules moving around at an average speed of 500 m/s. What would be the average speed of hydrogen molecules at the same temperature? (A) 100 m/s (B) 250 m/s (C) 500 m/s (D) 1000 m/s (E) 2000 m/s

  11. Equipartition theorem • Things are more complicated when energy can be stored in other degrees of freedom of the system. monatomic gas: translation solids: translation+potential energy diatomic molecules: translation+vibrations+rotations

  12. Equipartition theorem • The thermal energy is equally divided among all possible energy modes (degrees of freedom). The average thermal energy is (1/2)kBT for each degree of freedom. εavg=(3/2) kBT (monatomic gas) εavg=(6/2) kBT (solids) εavg=(5/2) kBT (diatomic molecules) • Note that if we have N particles: Eth=(3/2)N kBT =(3/2)nRT (monatomic gas) Eth=(6/2)N kBT =(6/2)nRT (solids) Eth=(5/2)N kBT =(5/2)nRT (diatomic molecules)

  13. Specific heat • Molar specific heats can be directly inferred from the thermal energy. Eth=(6/2)N kBT =(6/2)nRT (solid) ΔEth=(6/2)nRΔT=nCΔT C=3R (solid) • The specific heat for a diatomic gas will be larger than the specific heat of a monatomic gas: Cdiatomic=Cmonatomic+R

  14. Entropy • A perfume bottle breaks in the corner of a room. After some time, what would you expect? B) A)

  15. very unlikely • The probability for each particle to be on the left half is ½. probability=(1/2)N

  16. Second Law of thermodynamics • The entropy of an isolated system never decreases. It can only increase, or in equilibrium, remain constant. • The laws of probability dictate that a system will evolve towards the most probable and most random macroscopic state

More Related