1. Ch18 The Micro/Macro Connection
講者： 許永昌 老師

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

3. 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

4. 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.

5. 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:
~0.1 s (of course not)
~10m

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

7. 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?

8. 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. = +
+ …

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

10. 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.

11. Homework
Student workbook:
18.5, 18.6

12. 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

13. 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.

14. Homework
Student workbook:
18.10

15. 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?

16. 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

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

18. 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)

19. 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

20. 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=?

21. Homework
Student Workbook:
18.13, 18.15, 18.16

22. 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

23. 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)

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