1. Entropy and the Second Law of Thermodynamics
Chapter 22
Entropy and the Second Law of Thermodynamics

2. Configuration
Configuration – certain arrangement of objects in a system
Configuration for N spheres in the box, with n spheres in the left half

3. Microstates Microstate – one of the ways to prepare a configuration
An example of 4 different microstates for 4 spheres in the box, with 3 spheres in the left half

4. Multiplicity
Multiplicity ( W ) – a number of microstates available for a given configuration
From statistical mechanics:

5. Multiplicity

6. Multiplicity

7. Multiplicity

8. Multiplicity

9. Entropy For identical spheres all microstates are equally probable
Entropy ( S ):

10. Entropy For identical spheres all microstates are equally probable
Entropy ( S ):
For a free expansion of
100 molecules
Entropy is growing for
irreversible processes in
isolated systems

11. Entropy
Entropy, loosely defined, is a measure of disorder in the system
Entropy is related to another fundamental concept – information. Alternative definition of irreversible processes – processes involving erasure of information
Entropy cannot noticeably decrease in isolated systems
Entropy has a tendency to increase in open systems

12. Entropy in cosmology
In modern cosmology, our universe is an isolated system, freely (irreversibly) expanding: total entropy of the universe increases and gives time its direction
The evolution equation of the universe (the Friedman equation) has two solutions (positive t and negative t) – entropy is increasing in two time directions from a minimum point

13. Entropy in open systems
In open systems entropy can decrease:
Chemical reactions

14. Entropy in open systems
In open systems entropy can decrease:
Chemical reactions
Molecular self-assembly

15. Entropy in open systems
In open systems entropy can decrease:
Chemical reactions
Molecular self-assembly
Creation of information

16. Entropy in thermodynamics
In thermodynamics, entropy for open systems is
The change in entropy is
For isothermal process, the change in entropy:
For adiabatic process, the change in entropy:

17. Entropy as a state function
First law of thermodynamics for an ideal gas:
For irreversible processes, to calculate the change in entropy, the process has to be replaced with a reversible process with the same initial and final states or use a statistical approach

18. The second law of thermodynamics
In closed systems, the entropy increases for irreversible processes and remains constant for reversible processes
In real (not idealized) closed systems the process are always irreversible to some extent because of friction, turbulence, etc.
Most real systems are open since it is difficult to create a perfect insulation

19. Engines
In an ideal engine, all processes are reversible and no wasteful energy transfers occur due to friction, turbulence, etc.
Carnot engine:
Nicolas Léonard
Sadi Carnot
(1796–1832)

20. Carnot engine (continued)
Carnot engine on the p-V diagram:
Carnot engine on the T-S diagram:

21. Engine efficiency
Efficiency of an engine (ε):
For Carnot engine:

22. Perfect engine Perfect engine: For a perfect Carnot engine:
No perfect engine is possible in which a heat from a thermal reservoir will be completely converted to work

23. Gasoline engine
Another example of an efficient engine is a gasoline engine:

24. Heat pumps (refrigerators)
In an ideal refrigerator, all processes are reversible and no wasteful energy transfers occur due to friction, turbulence, etc.
Performance of a refrigerator (K):
For Carnot refrigerator :

25. Perfect refrigerator Perfect refrigerator:
For a perfect Carnot refrigerator:
No perfect refrigerator is possible in which a heat from a thermal reservoir with a lower temperature will be completely transferred to a thermal reservoir with a higher temperature

26. Questions?

27. Answers to the even-numbered problems
Chapter 22
Problem 6
24.0 J

28. Answers to the even-numbered problems
Chapter 22
Problem 10
870 MJ
330 MJ

29. Answers to the even-numbered problems
Chapter 22
Problem 30
− 610 J/K

30. Answers to the even-numbered problems
Chapter 22
Problem 40
0.507 J/K