Ch18 The Micro/Macro Connection 講者： 許永昌 老師

Contents Molecular Speeds and Collisions Pressure Temperature Thermal energy and Specific heat Thermal interaction and Heat Irreversible Processes & the 2nd Law of thermodynamics.

The aim of this chapter Understand Microscopic Collision Average translational kinetic energy Microscopic energies Molecular basis Energy transfer Probability Macroscopic Pressure Temperature Thermal energy Ideal-gas law Specific Heat Heat and Thermal equilibrium Entropy

Molecule Speeds (請預讀P542) Changing the (1)temperature or changing to a (2) different gas changes the most likely speed, but it does not change the shape of the distribution.

Mean Free Path (請預讀P543) The average speed of N2 at 20oC is about 500 m/s There must be some collisions happened. Reference: http://en.wikipedia.org/wiki/Diffusion ~0.1 s (of course not) ~10m

Mean Free Path (continue) More careful calculation (all molecules move)

Stop to Think What would happen in the room if the molecules of the gas were not moving? What would happen in an isolated room if the molecular collisions were not perfectly elastic?

Pressure in a Gas (請預讀P544~P545) Objects: A wall whose normal is x direction. Molecules in the left hand side of this wall. Condition: perfectly elastic. = + + …

The Root-Mean-Square Speed (請預讀P545~P546)

Stop to Think & Exercise What are the definitions of rms speed Average speed Average velocity What are the benefits of the definition of rms speed? Exercise: 2 particles: v=3êx+êy, 3 particles: v=-2êx+2êy, 4 particles: v=-2êy. Find: (1) rms speed (2) average speed (3) average velocity.

Homework Student workbook: 18.5, 18.6

Temperature (請預讀P546~P548) Microscopic eavg Macroscopic T. We get Average translational kinetic energy: eavg(½mv2)avg. Kinetic Theory: PV=Nm(vx2)avg. (v2)avg=3(vx2)avg. Ideal-gas Law: PV=NkBT. We get

Temperature (continue) For a gas, this thing we call temperature measures the average translational kinetic energy. This concept of temperature also gives meaning to absolute zero as the temperature at which eavg=0 and all molecular motion ceases.

Homework Student workbook: 18.10

Thermal Energy for monatomic Gases (請預讀P549~P550) Eth=Kmicro+Umicro. For monatomic gases: Eth=Kmicro. Eth=Neavg=3/2NkBT=3/2nRT. Owing to the 1st Law of thermodynamics, We get CV=3/2R=12.5 J/mol K. Q: How about other systems?

The Equipartition Theorem (請預讀P550~P551) The thermal energy of a system of particles is equally divided among all the possible energy modes. For a system of N particles at temperature T, the energy stored in each mode (each degree of freedom) is ½NkBT. It is not proved here. To prove it, you need the concepts of Probability States Phase space Boltzmann distribution Example: Solid (for high enough temperature) Dulong-Petit law Detail: Solid State Physics. It has 6 degrees of freedom Eth=6*N*½kBT  C=3R=25.0 J/mol K~6.00 cal/mol K. *Solid State Physics, Ashcroft/Mermin, P463

Specific Heat of diatomic molecules (請預讀P552~P553) Why? A: In quantum mechanics, <Li>=nћ Discrete energy levels for bounded states.

Additional Remark (補充) For two particles system <erot,z>~ mH=1.66*10-27 kg, r~3.7*10-11 m, ћ=1.05*10-34 Js, kB=1.38*10-23 J/K Teff~180K (n=1)

Thermal Interactions and Heat (請預讀P554~P555) Microscopic Collisions Thermal Equilibrium: (e1)avg= (e2)avg. Energy can transfer from 2 to 1: Yes Macroscopic Thermal interaction Thermal Equilibrium: T1=T2. Energy can transfer from 2 to 1: No Th Tc System 1 System 2 Heat Probability

Exercise Conditions: Find: System 1: 4.00 mol N2 at T1=27oC. System 2: 1.00 mol H2 at T2=327oC. 3 s.f. Find: Thermal energies Tf =? Heat transfer=?

Homework Student Workbook: 18.13, 18.15, 18.16

Irreversible Processes and the 2nd Law of Thermodynamics (請預讀P556~P558) Microscopic (reversible) One particle Macroscopic (irreversible) Many particles Go to reach Equilibrium. Probability

Order, Disorder and Entropy (請預讀P558~P560) Scientists and engineers use a state variable called entropy to measure the probability that a macroscopic state will occur spontaneously. The second Law of thermodynamics: The entropy of an isolated system never decreases. The entropy either increases, until the system reaches equilibrium, or, if the system began in equilibrium, stays the same. Th  Tc spontaneously. (Heat)

Homework Student Workbook: Student Textbook: 18.18 15, 65 製作Terms and Notation的卡片，以方便自我練習。