1. The Laws of Thermodynamics Classical Equilibrium Thermodynamics!
Macroscopic Physics:
Classical Equilibrium Thermodynamics!

2. First: 3 Slides of Some Results from Microscopic Statistical Physics
Fundamental Statistical Physics Concept 
# of accessible microstates for a macroscopic system with huge particle number N + huge number f degrees of freedom.
Suppose we know that the energy of the system is in the range E to E + δE. Define:
Ω(E) ≡ Number of accessible micro states for this system.
It can be shown that Ω(E) varies with E approximately as
Ω(E)  Ef
This is the starting point for the connection between microscopic physics & classical thermodynamics!
It’s the starting point for the Pathria book Ch. 1, p. 3.

3. Ω(E)  Ef Temperature T:
Specifically, all macroscopic thermodynamic functions can be derived from Ω(E)! d
Entropy S:
Temperature T:
Also Define:

4.  [1/(kBT)] Ω(E)  Ef So, the connection between  & the
absolute temperature T is clearly:
 [1/(kBT)] h
Also, equations of state can be derived from Ω(E).

5. The Zeroth Law of Thermodynamics
Definition: If 2 systems are in thermal equilibrium, their
absolute temperatures are equal! (Isn’t this obvious)??
“If two systems are separately in
thermal equilibrium with a third system, they are in thermal equilibrium with each other.”

6. This allows the design & the use of Thermometers!

7. Total Energy is Conserved
The First Law of Thermodynamics
Consider a system A1 interacting (exchanging energy) with a system A2
Q = ∆Ē + W L
Physics: Conservation of Total Energy!!
So The Physical Meaning of the 1st Law of Thermodynamics is that
Total Energy is Conserved
Work done by system A1
Heat absorbed
by system A1
Change in internal energy of system A1

8. Total Energy is Conserved
The First Law of Thermodynamics
For Infinitesimal, Quasi-Static Processes
đQ = dĒ + đW T
This is another form of
Conservation of Total Energy!!
So The Physical Meaning of the 1st Law of Thermodynamics is still that
Total Energy is Conserved
Work done by system A1
Heat absorbed
by system A1
Change in internal energy of system A1

9.  Conservation of Total Energy!!!! The Direction of Energy Transfer!
Rudolf Clausius’ statement of the
1st Law of Thermodynamics
“Energy can neither be created nor destroyed. It can only be changed from one form to another.”
Rudolf Clausius (1850)
The Physical Meaning of the 1st Law of Thermodynamics
 Conservation of Total Energy!!!!
However, it says nothing about
The Direction of Energy Transfer!

10. DS ³ 0 The 2nd Law of Thermodynamics: Direction of Energy Transfer
“The entropy of an isolated system
increases in any irreversible process & unaltered in any reversible process.”
This is sometimes called
The Principle of Increasing Entropy
DS ³ 0
It gives the Preferred (natural)
Direction of Energy Transfer
It thus determines whether a process can occur or not.
Change in the
system entropy

11. The 2nd Law of Thermodynamics: Association of Entropy with Disorder.
“The entropy of an isolated system never decreases”.
Mathematically, this means that in any process
ΔS ≥ 0
or, at equilibrium, S → Smax.
For (idealized) reversible processes only,
ΔS = 0, dS = đQ/T.
Examples of irreversible (real) processes:
Temperature Equalization, Mixing of Gases, & Conversion of Macroscopic (ordered) KE to Thermal (random) KE
The last two cases are obvious examples of the
Association of Entropy with Disorder.
Change in Entropy 11

12. General Features of the Entropy S12

13. General Features of the Entropy S
It is a state function, so that ΔS between given macrostates is independent of the path. 13

14. General Features of the Entropy S
It is a state function, so that ΔS between given macrostates is independent of the path.
It is a quantitative measure of the disorder in a system. 14

15. General Features of the Entropy S:
It is a state function, so that ΔS between given macrostates is independent of the path.
It is a quantitative measure of the disorder in a system.
It gives a criterion for the direction of a process, since an isolated system will reach a state of maximum entropy. 15

16. General Features of the Entropy S
It is a state function, so that ΔS between given macrostates is independent of the path.
It is a quantitative measure of the disorder in a system.
It gives a criterion for the direction of a process, since an isolated system will reach a state of maximum entropy.
ΔS may be negative for a portion of a composite system. 16

17. General Features of the Entropy S
It is a state function, so that ΔS between given macrostates is independent of the path.
It is a quantitative measure of the disorder in a system.
It gives a criterion for the direction of a process, since an isolated system will reach a state of maximum entropy.
ΔS may be negative for a portion of a composite system.
An increase in S does not require an increase in temperature. For example, in the mixing of gases at the same temperature, or in the melting of a solid at the melting point. 17

18. General Features of the Entropy S
It is a state function, so that ΔS between given macrostates is independent of the path.
It is a quantitative measure of the disorder in a system.
It gives a criterion for the direction of a process, since an isolated system will reach a state of maximum entropy.
ΔS may be negative for a portion of a composite system.
An increase in S does not require an increase in temperature. For example, in the mixing of gases at the same temperature, or in the melting of a solid at the melting point.
An increase in temperature does not necessarily imply an increase in S. For example, in the adiabatic compression of a gas. 18

19. Second Law of Thermodynamics
Some Historical Comments
Much of the early thermodynamics development was driven by practical considerations. For example, building heat engines & refrigerators.
So, the original statements of the
Second Law of Thermodynamics
may sound very different than those just mentioned.

20. Various Statements of the 2nd Law of Thermodynamics:
“No series of processes is possible whose sole result is the absorption of heat from a thermal reservoir and the complete conversion of this energy to work.” That is
There are NO perfect engines!

21. Two of Rudolf Clausius’ 2nd Law of Thermodynamics
statements of the
2nd Law of Thermodynamics
“It will arouse changes while the heat transfers from a low temperature object to a high temperature object.”
“It is impossible to devise an engine which, working in a cycle, shall produce no effect other than the transfer of heat from a colder to a hotter body.”

22. Two more Rudolf Clausius’ 2nd Law of Thermodynamics
statements of the
2nd Law of Thermodynamics
“During real physical processes, the entropy of an isolated system always increases. In the state of equilibrium the entropy attains its maximum value.”
“It is impossible to design a cyclic device that raises heat from a lower temperature to a higher temperature without affecting its surroundings.”
Stated a different way: Raising heat from a lower temperature to higher temperature always requires either doing work on or exhausting heat to the environment.

23. 2nd Law of Thermodynamics
Two of Lord Kelvin’s
(William Thompson’s)
statements of the
2nd Law of Thermodynamics
“It will arouse other changes while the heat from the single thermal source is taken out & is totally changed into work.”
“A process whose effect is the complete conversion of heat into work cannot occur.”

24. Two of Kelvin’s & Planck’s 2nd Law of Thermodynamics
joint statements of the
2nd Law of Thermodynamics
“It is impossible to extract an amount of heat QH from a hot reservoir and use it all to do work W. Some amount of heat QC must be exhausted to a cold reservoir.”
“It is impossible to design a cyclic device that takes heat from a reservoir and converts it to work only (there must be waste heat) .”
Lord Kelvin
Max Planck

25. The 2nd Law of Thermodynamics The Heat Flow Statement
“Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature. It never flows spontaneously in the reverse direction.”

26. 2nd Law of Thermodynamics!
“A universe containing mathematical physicists will at any assigned date be in the state of maximum disorganization which is not inconsistent with the existence of such creatures.”
Sir Arthur Eddington’s (joke!) version of the
2nd Law of Thermodynamics!

27. Definition: Heat Engine 
A system that can convert some of the random molecular energy of heat flow into macroscopic mechanical energy.
QH  HEAT absorbed by a Heat Engine from a hot body
-W  WORK performed by a Heat Engine on its surroundings
-QC  HEAT emitted by a Heat
Engine to a cold body

28. The Second Law Applied to Heat Engines
Efficiency  
(W/QH) = [(QH - QC)/QH]

29. A “Heat Engine” That Violates the 2nd Law (So it is Impossible!)

30. Carnot’s Statements on the 2nd Law
These are essentially Corollaries of the Clausius & Kelvin-Planck versions of the 2nd Law:
It is impossible to construct a heat engine that operates between 2 temperatures that has higher thermal efficiency  than an ideal (reversible) heat engine. th,rev > th,irrev
Reversible Engines (ideal or Carnot engines) operating between the same temperatures have the same th,rev

31. The Carnot (Ideal, Reversible) Cycle (Carnot Engine)
This is assumed to be internally reversible.
Its interaction with the environment is reversible.
Carnot Cycle
Schematic:
Reversible Work:
 Entropy S = constant
Reversible Heat Transfer:
 Temperature T = constant Qh T
Win
Wout QL S

32. Carnot Efficiency of a Heat Engine
Definition: Heat Engine Efficiency 
Carnot Cycle
Schematic QH W QL
Carnot
Efficiency:
This is the Maximum Efficiency possible for real engines!

33. Definition: Refrigerator 
A system that can do macroscopic work to
extract heat from a cold body & exhaust it to a
hot body, thus cooling the cold body further. Or,
A system that operates like a Heat Engine in reverse.
QC  HEAT extracted by a Refrigerator from a cold body
W  WORK performed by a Refrigerator on the surroundings
-QH  HEAT emitted by a Refrigerator
to a hot body

34. The 2nd Law of Thermodynamics Clausius’ Statement for Refrigerators
“It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature object.” Or:
There are no perfect Refrigerators!
This statement about refrigerators also applies to air conditioners & heat pumps which use the same principles.

35. The Second Law Applied to Refrigerators (QC/W) = [(QC)/(QH - QC)]
Efficiency  
(QC/W) = [(QC)/(QH - QC)]

36. Conceptual Example: You Can’t “Beat” the 2nd Law of Thermodynamics
Question: Is it possible to cool your kitchen by
leaving the refrigerator door open or cool your
bedroom by putting a window air conditioner on the
floor by the bed?

37. Conceptual Example: You Can’t “Beat” the 2nd Law of Thermodynamics
Question: Is it possible to cool your kitchen by
leaving the refrigerator door open or cool your
bedroom by putting a window air conditioner on the
floor by the bed? (Hint: Recall the amusing video clip in
which the teenage girl asks why air conditioners
couldn’t be used to cool the outside!)

38. Conceptual Example: You Can’t “Beat” the 2nd Law of Thermodynamics
Question: Is it possible to cool your kitchen by
leaving the refrigerator door open or cool your
bedroom by putting a window air conditioner on the
floor by the bed? (Hint: Recall the amusing video clip in
which the teenage girl asks why air conditioners
couldn’t be used to cool the outside!)
Answer: NO!!! Rather than cooling the
kitchen, the open refrigerator will warm it up!!
The air conditioner also will warm the bedroom.

39. The 2nd Law of Themodynamics:
Entropy & The 2nd Law: For a System in Equilibrium with a Heat Reservoir at Temperature T
The 2nd Law of Themodynamics:
Heat flows from high temperature objects to low temperature
objects because this process increases the system disorder.
For a system interacting with a heat reservoir at temperature T & exchanging Heat Q with it,
the entropy change is:

40. The 2nd Law of Thermodynamics
can be used to generally classify
Thermodynamic Processes into
Three Types:
1. Natural Processes
These are Always Irreversible Processes.
These are also always Spontaneous Processes.
2. Impossible Processes
These violate either the 1st Law or the 2nd Law or both.
3. Reversible Processes
These are ideal processes & are never found in nature.
We’ll briefly discuss each with examples next.

41. The Third Law of Thermodynamics
“It is Impossible to Reach a Temperature of Absolute Zero.”
On the Kelvin Temperature Scale, T = 0 K
is often referred to as
“Absolute Zero”

42. This version of the 3rd Law is Equivalent to:
Another Statement of The 3rd Law of Thermodynamics: “The entropy of a true equilibrium state of a system at T = 0 K is zero.”
Strictly speaking, this statement is true only if the quantum mechanical ground state is non-degenerate. If it is degenerate, the entropy at
T = 0 K is a small constant & not 0!
This version of the 3rd Law is Equivalent to:
“It is impossible to reduce the temperature of a system to T = 0 K using a finite number of processes.”

43. Now, two brief discussions of Philosophy!! (Religion?)43

44. 1. The 2nd Law & Life on Earth
Existence of low-entropy organisms like us has sometimes been used to suggest
that we live in violation of the 2nd Law!
British cosmologist Sir Roger Penrose has considered this in his book
“The Road to Reality: A Complete Guide to the Laws of the Universe” (2005). 44

45. In “The Road to Reality: a Complete Guide to the Laws of the Universe”, Penrose points out that “it is a common misconception to believe that the Sun’s energy is the main ingredient needed for our survival”.
He says,
“What is important is that the energy source be far from thermal equilibrium”.
For example, a uniformly illuminated sky supplying the same amount of energy as the Sun, but at a much lower energy, would be useless to us.
Fortunately the Sun is a hot sphere in an otherwise cold sky. So, it is a low entropy source, which keeps our entropy low. 45

46. The 2nd Law & Life on Earth
Optical photons supplied by the Sun contain much more energy than the IR photons leaving us, since εph = hν.
Since the energy reaching
us is contained in fewer photons, the Sun is a low entropy source. Plants utilize the low entropy energy, to reduce their entropy through photosynthesis.
We keep our entropy low by breathing oxygen produced by plants, and by eating plants, or animals ultimately dependent on plants. 46

47. 2. The 2nd Law & the Arrow of Time!
One of the Deepest Philosophical Paradoxes of Modern Physics:
Microscopic Physics is Time Reversal Symmetric. But, Nature is Not!!
The fundamental, Microscopic Theories of Physics (classical & quantum mechanical)
don’t care which way time goes!
Newtonian Mechanics, Electromagnetism, Relativity, & Quantum Mechanics are all
Time Reversal Symmetric. 47

48. The 2nd Law says that entropy is NOT invariant under time reversal!
Arrow of Time: Why does time have a direction? (Always forward & never back!)
It’s NOT a feature of the microscopic laws of physics!!
Those work fine forwards or backwards in time; they are
“Invariant under time reversal”! (t  -t, pi  -pi)
A common answer to why there is an arrow of time is:
Entropy & The 2nd Law of Thermodynamics
It says that entropy S increases (in closed systems) with time. So
The time derivative of the
entropy must be positive:
That is:
The 2nd Law says that entropy is NOT
invariant under time reversal! 48

49. Entropy & The 2nd Law of Thermo
Tell us that the entropy must be such that
So, The 2nd Law is NOT invariant under time reversal!
Reconciling this fundamental Law of Thermodynamics, (known to be correct) with the time reversal symmetry of the underlying microscopic physics is a
Deep, Difficult, Philosophical Problem.
Starting from well before the Boltzmann’s time until the present, many very smart people have tried to come up with a satisfactory explanation. So far, there is still no agreement among the experts on such an explanation.
To outline some solutions would require an entire lecture! No time to cover it in class. 49

50. Now, a brief (hopefully) humorous discussion L

51. Some Popular (joke!) Versions of The Laws of Thermodynamics
1st Law: You can’t win.
2nd Law: You can’t break even.
3rd Law: There’s no point in trying.

52. Other Popular Versions of
The Laws of Thermodynamics
Version 1
Zeroth Law: You must play the game.
First Law: You can't win the game.
Second Law: You can't break even in the game.
Third Law: You can't quit the game.
Version 2
First Law: You can't win the game;
You can only break even.
Second Law: You can only break even at absolute zero.
Third Law: You can't reach absolute zero!

53. Version 3 Version 4 Zeroth Law: You must play the game.
First Law: You can't win the game.
Second Law: You can't break even except
on a very cold day.
Third Law: It never gets that cold!
Version 4
Zeroth Law: There is a game.
First Law: You can't win the game.
Second Law: You must lose the game.
Third Law: You can't quit the game.

54. “Things get worse under pressure!!”
A joke!!
“Murphy's Law”
of Thermodynamics:
“Things get worse under pressure!!”

55. Murphy’s “Law”: “Anything that can go wrong,
will go wrong!”. L

56. Murphy’s “Law”: “Anything that can go wrong,
will go wrong!”. L
Mrs. Murphy’s “Corollary”: “Murphy was an optimist!”
There are many other variations of these kinds of “Laws”!
Whole books have been written compiling these kinds of
“Laws” applied to various situations.