1. The Second Law of Thermodynamics
SCI340 L35 Entropy
The Second Law of Thermodynamics
this is cool
§ 15.7, 15.11

2. Outline Multiplicity Free expansion Heat transfer
Possibility and efficiency of heat engines
Evolution and life
Gibbs free energy

3. Multiplicity and Probability
Order, disorder, and usefulness
Library analogy
Poker hands
Literature
Configurations with more multiplicity are more common.
Multiplicity tends to increase. (Probably.)

4. Probability and Time Multiplicity increases with time
Maximum multiplicity ≡ equilibrium
Time is the direction of increasing multiplicity!

5. Time’s Arrow
Most laws of physics don’t distinguish the direction of time
Conservation laws tell us what doesn’t change
Entropy is different in the past, present, and future
Time leads to increasing entropy

6. The Flow of Matter
particles disperse

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

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

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

10. Question
What portion of the time will the molecule spend in the original volume (left half of the box)?

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

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

13. Poll Question
What is the probability that the molecule will be in the original space at any given time? V
V/4

14. Two Molecules (Poll)
What is the probability that both will be in the left half of the container at the same time?

15. Three Molecules (Poll)
What is the probability that all three will be in the left half of the container at the same time?

16. Sub-Space
What is the probability that all N will be in the given sub-volume of the container at the same time? V2 N V1 V2 V1

17. 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.

18. Collision! A moving object rams a stationary object.
Before impact: KE of projectile > 0 KE of target = 0

19. Energy Transfer: Mass Effect

20. Energy Transfer: Offset Effect

21. Collision Summary
Before impact, projectile has all the kinetic energy.
KE more evenly distributed after unless:
Equal masses
Direct hit
Energy spreading out is irreversible.

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

23. 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

24. Entropy, Technically W = multiplicity of a state
S = k ln(W) = entropy of the state
DS = entropy change
DS = S2 − S1
= k ln(W2) − k ln(W1)
= k ln(W2/W1)
Intensive!
k = × 1023 J/K

25. To thermal equilibrium
Heat Transfer
To thermal equilibrium

26. Temperature Difference
Hot
Cold
heat
Until
Warm
Equilibrium

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

28. Thermodynamic Temperature
Hot
Cold
heat
low DS DU
high DS DU
1/T = DS/DU DS = Q/T

29. Heat Engines
Divert heat flow

30. Heat Engine Qh = W + Qc Qh/Th ≤ Qc/Tc
Heat flow can be diverted to useful work
As long as entropy still increases

31. Sun, Earth, and Life Tsun = 6000 K, Tearth = 300 K, Tsurr = 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 = MJ/K m2
1000 kg/m2 life diverts < 1.3 MJ/K
Plenty of entropy is created

32. Chemical Thermodynamics
Enthalpy (DH) is heat transfer to surroundings (const P)
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
In a spontaneous change, entropy increases.

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