1. Entropy
Time’s Arrow

2. Objectives
Explain the tendency of matter and energy to spread out over time.
Identify entropy changes in familiar processes.

3. Poll Question
I heard of “entropy” before this course.
True.
False.

4. Poll Question
I think I know what “entropy” means.
True.
False.

5. The Flow of Matter
particles disperse

6. Gas Molecule in a Box
No energy transfer to walls: elastic collisions

7. Gas Molecule in a Box
Double the size of the box!

8. Gas Molecule in a Box
Double the size of the box!

9. Poll Question
What portion of the time will the molecule spend in the original volume (left half of the box)?
a. All b. Half
c. none d. 75%

10. Poll Question
What portion of the time will the molecule spend in the original space if we quadruple the volume of the box?

11. Poll Question
What portion of the time will the molecule spend in the original space if we quadruple the volume of the box?
a. All b. Half
c. 1/3 d. 1/4

12. Poll Question
What is the probability that the molecule will be in the original space at any given time?
a. 1 b. 1/2
c. 1/3 d. 1/4 V
V/4

13. Two Molecules (Poll)
What is the probability that both will be in the left half of the container at the same time?
a. 1 b. 1/2
c. 1/4 d. 0

14. Three Molecules (Poll)
What is the probability that all three will be in the left half of the container at the same time?
a. 1/2 b. 1/3
c. 1/4 d. 1/8

15. Whiteboard Work
What is the probability that all N will be in the given sector of the container at the same time? xV V

16. Expansion Summary
Random motions cause particles to spread out. The chance that they will randomly come back together decreases tremendously as the number of molecules increases.
Spreading out is irreversible.

17. Group It!
Discuss all succeeding poll questions with your group before answering.

18. The Flow of Energy
energy disperses

19. Collision! A moving object rams a stationary object.
Before impact: Kinetic Energy of projectile > 0 Kinetic Energy of target = 0

20. Group Poll Question
What happens to the kinetic energy after the collision?
All of it goes to the target.
The projectile and target have equal kinetic energies.
The projectile keeps it all.
It depends; there isn’t enough information to know for sure.

21. I did the math!
I calculated the kinetic energies of object 1 (projectile) and object 2 (target) as a function of
Offset
Relative masses

22. Energy Transfer: Mass Effect

23. Energy Transfer: Mass Effect

24. Energy Transfer: Offset Effect

25. Energy Transfer: Offset Effect

26. Energy Transfer: Offset Effect

27. Collision Summary
Before impact, all the kinetic energy is in the motion of the projectile.
At impact, the kinetic energy almost always distributes to motion of both the projectile and target.
When two objects collide, their kinetic energies are usually closer after the collision than before.
Spreading out is irreversible.

28. Kinetic Energy Randomizes
Spreads out over more objects
Spreads out in more directions
Work becomes internal energy

29. PE  KE  random molecular KE
Example
How does entropy increase when a ball is dropped, bounces, and eventually stops?
How is energy conserved?
PE  KE  random molecular KE

30. multiple interactions
Heat Transfer
multiple interactions

31. Heat Flow
Two solids with different temperatures (average molecular kinetic energies) are brought into contact.

32. Heat Flow
Two solids with different temperatures (average molecular kinetic energies) are brought into contact. What happens to the atoms’ kinetic energies (temperatures)?

33. Heat Flow Summary
Molecular kinetic energy flows from high temperature objects to low temperature objects, but not the other way around.
This is because kinetic energy tends to even out between colliding objects.
There are more ways to distribute energy among many molecules than among few molecules.

34. Heat Generation Any energy  molecular motion
Raises entropy
Energy less constrained
Effect more important at low temperatures
DS = q/T
Greater proportional increase in thermal energy at low T

35. Temperature Difference
Hot
Cold
heat
Until
Warm
Equilibrium

36. Temperature Difference
Hot
Cold
heat
low DS DU
high DS DU
Heat flows until total entropy stops increasing
Thermal equilibrium
Same temperature

37. Thermodynamic Temperature
Hot
Cold
heat
low DS DU
high DS DU
1/T = DS/DU DS = q/T

38. Overall Summary
Particles and energy tend to become spread out uniformly.
Entropy is a measure of how many different ways a state can be arranged.
library analogy
Total entropy increases in all processes that actually occur.

39. What It Means
examples

40. Interesting but vital point
We cannot see most of the motion that occurs in our world.

41. The Funnel and the Ice Pack
How can matter ever become localized?
Stars form
Rain falls
How can thermal motion ever decrease?
Refrigerators and heat pumps
First aid cold packs
Any time one thing becomes localized, something else spreads out more

42. Entropy, Technically W = number of “configurations” of a state
S = kB ln(W) = entropy of the state
DS = entropy change
DS = S2 − S1
= kB ln(W2) − kB ln(W1)
= kB ln(W2/W1)

43. Free Expansion ExamplexV V N
W2/W1 =
= xN
DS = kN ln(x) xV V

44. Ice Melting Example Solid  liquid disperses matter DSc > 0
constrains energy DST < 0
temp DS
DSc DS
melting temperature
DST

45. Add Salt Salt dissolves in liquid only Raises S of liquid (+ salt)
Raises DSc
lower melting temperature
temp DS
DSc
DSc DS DS
original melting temperature
DST

46. General Physics L03_entropy.ppt
Group Work
Explain how your process increases entropy. Think about:
Could the reverse process occur?
What spreads out: matter, energy or both? How?
Why does total entropy increase?
Processes: 1. Humpty Dumpty 2. NH4NO3 in water 3. coffee freezes outside 4. Log burns 5. Student tidies his room 6. vinegar + baking soda 7. quartz crystallizes underground 8. egg develops into a chick

47. Overall Pessimistic View
Energy degrades from more to less useful forms
Order becomes disorder
Rather: Increasing entropy is how we know something will happen!

48. Chemical Thermodynamics
Enthalpy (DH) is heat transfer to surroundings
Spontaneous if DG = DH – TDS < 0
Equivalent to DS – DH/T > 0
DS is entropy change of system
DH/T is entropy change of surroundings
If a state changes spontaneously, entropy increases.

49. Entropy and Evolution
Darwinian evolution is perfectly consistent with thermodynamics.
Energy from the sun powers life processes.
Energy from earth radiates into space.
Material order on earth can increase because energy is dispersed.
Entropy always increases!

50. General Physics L03_entropy.ppt
Sun, Earth, and Life
Tsun = 6000 K, Tearth = 300 K, Tspace = 3 K
DSsun = –Q/Tsun; DSearth = ±Q/Tearth
In a year, Q  8 GJ/m2 of earth surface
DSsun = –1.3 MJ/K m2
DSearth = 0
DSsurr = +2.7 GJ/K m2
1000 kg/m2 “orderly” life diverts > 1.3 MJ/K
Plenty of entropy is created

51. Congratulations!
“[Asking someone to] describe the Second law of thermodynamics is about the scientific equivalent of: Have you read a work of Shakespeare’s?”
– C.P. Snow, Rede Lecture, Cambridge, May 7, 1959.