Download 2 nd Law of Thermodynamics

The Laws of Thermodynamics
Macroscopic Physics:
Classical Equilibrium Thermodynamics!
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!
Ω(E)  Ef
• Specifically, all macroscopic thermodynamic
functions can be derived from Ω(E)!
d
Entropy S: S  kB ln   E 
Temperature T:
Also Define:
1
 S 

 
 E  N ,V T
  ln   E  
 

E

 N ,V
Ω(E) 
S  kB ln   E 
f
E
1
 S 

 
 E  N ,V T
  ln   E  
 

E

 N ,V
• So, the connection between  & the
absolute temperature T is clearly:
h
 [1/(kBT)]
• Also, equations of state can be
derived from Ω(E).
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.”
This allows the design & the use of
Thermometers!
The First Law of Thermodynamics
• Consider a system A1 interacting
(exchanging energy) with a system A2
Heat absorbed
by system A1
Q = ∆Ē + W
Work done by
system A1
Change in internal
energy ofL system A1
Physics: Conservation of Total Energy!!
So The Physical Meaning of the 1st Law of
Thermodynamics is that
Total Energy is Conserved
The First Law of Thermodynamics
For Infinitesimal, Quasi-Static Processes
Heat absorbed
by system A1
đQ = dĒ + đW
Change in internal
energy of system A1
Work done by
system A1
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
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!
The 2nd Law of Thermodynamics:
“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  0
Change in the
system entropy
It gives the Preferred (natural)
Direction of Energy Transfer
• It thus determines whether a process can occur or not.
The 2nd Law of Thermodynamics:
“The entropy of an isolated system never decreases”.
•Mathematically, this means that in
Change in Entropy
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 2 cases are examples of the
Association of Entropy
with Disorder.
General Features of the Entropy S
General Features of the Entropy S
• It is a state function, so that ΔS between given
macrostates is independent of the path.
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.
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.
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.
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, the mixing of gases at the same
temperature, or in the melting of a solid at the melting point.
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, 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.
Some Historical Comments
• Much of the early thermodynamics
development was driven by practical
(Engineering) 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.
Various Statements of the
nd
2 Law of Thermodynamics:
1. “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!
Two of Rudolf Clausius’
statements of the
2nd Law of Thermodynamics
2.“It will arouse changes while the heat
transfers from a low temperature object
to a high temperature object.”
Two of Rudolf Clausius’
statements of the
2nd Law of Thermodynamics
2.“It will arouse changes while the heat
transfers from a low temperature object
to a high temperature object.”
3.“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.”
Two more Rudolf Clausius’
statements of the
2nd Law of Thermodynamics
4. “During real physical processes, the entropy of an
isolated system always increases. In the state of
equilibrium the entropy attains its maximum value.”
Two more Rudolf Clausius’
statements of the
2nd Law of Thermodynamics
4. “During real physical processes, the entropy of an
isolated system always increases. In the state of
equilibrium the entropy attains its maximum value.”
5. “It is impossible to design a cyclic device that
raises heat from a lower temperature to a higher
temperature without affecting its surroundings.”
Two more Rudolf Clausius’
statements of the
2nd Law of Thermodynamics
4. “During real physical processes, the entropy of an
isolated system always increases. In the state of
equilibrium the entropy attains its maximum value.”
5. “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.
Two of Lord Kelvin’s
(William Thompson’s)
statements of the
2nd Law of Thermodynamics
6. “It will arouse other changes while the
heat from the single thermal source is
taken out & is totally changed into work.”
Two of Lord Kelvin’s
(William Thompson’s)
statements of the
2nd Law of Thermodynamics
6. “It will arouse other changes while the
heat from the single thermal source is
taken out & is totally changed into work.”
7. “A process whose effect is the
complete conversion of heat into
work cannot occur.”
Two of Kelvin’s & Planck’s
joint statements of the
2nd Law of Thermodynamics
8. “It is impossible to extract an
Lord Kelvin
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.”
Max Planck
Two of Kelvin’s & Planck’s
joint statements of the
2nd Law of Thermodynamics
8. “It is impossible to extract an
Lord Kelvin
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.”
9. “It is impossible to design a cyclic
device that takes heat from a
reservoir and converts it to work
Max Planck
only (there must be waste heat) .”
The
nd
2
Law of Thermodynamics
The Heat Flow Statement
10. “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.”
“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!
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
The Second Law Applied to Heat Engines
Efficiency  
(W/QH) = [(QH - QC)/QH]
A “Heat Engine” That Violates
nd
the 2 Law (So it is Impossible!)
Heat Reservoir
Heat q
Cyclic Machine
Work Output=q
Carnot’s Statements on the 2nd Law
• These are essentially Corollaries of the
Clausius & Kelvin-Planck versions of the
2nd Law:
11. 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
Carnot’s Statements on the 2nd Law
• These are essentially Corollaries of the
Clausius & Kelvin-Planck versions of the
2nd Law:
11. 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
12. Reversible Engines (ideal or Carnot
engines) operating between the same
temperatures have the same th,rev
The Carnot (Ideal, Reversible) Cycle
(Carnot Engine)
• This is assumed to be internally reversible.
• Its interaction with the environment is reversible.
Carnot Cycle
Reversible Work:
T
Schematic:
Qh
Win
 Entropy S = constant
Reversible Heat Transfer:
 Temperature T = constant
Wout
QL
S
Carnot Efficiency of a Heat Engine
Definition: Heat Engine Efficiency 
Carnot Cycle
Schematic
W net,out
QH  QL
QL
 th 

 1
QH
QH
QH
QH
Ql
PS 

TH
TL
over a reversible cycle
P
QH
Ql
QH
T


 H
TH
TL
QL
TL
Carnot efficiency :
S
TH
0
QH

W
QL
TL
Carnot 
th,Carnot 1
Efficiency:
TH
TL
This is the Maximum Efficiency possible for real engines!

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
The
nd
2
Law of Thermodynamics
Clausius’ Statement for Refrigerators
13. “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.”
The
nd
2
Law of Thermodynamics
Clausius’ Statement for Refrigerators
13. “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.
The Second Law Applied to Refrigerators
Efficiency  
(QC/W) = [(QC)/(QH - QC)]
Conceptual Example: You Can’t “Beat”
the
nd
2
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?
Conceptual Example: You Can’t “Beat”
the
nd
2
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!)
Conceptual Example: You Can’t “Beat”
the
nd
2
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.
Entropy & The
nd
2
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:
Q
DS  .
T
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.
The Third Law of Thermodynamics
“It is Impossible to Reach a
Temperature of Absolute Zero.”
On the Kelvin Temperature Scale,
T=0K
is often referred to as
“Absolute Zero”
Another Statement of
rd
The 3 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 nondegenerate. 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.”
Now, two brief
discussions of
Philosophy!!
(Religion?)
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).
• 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.
The
nd
2
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.
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!!
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.
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!
Entropy & The 2nd Law of Thermo
• This tells us that the entropy S must
have the property that
• So,
The 2nd Law of Thermo is NOT
invariant under time reversal!
• Reconciling the 2nd 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 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 discuss this further would require at least an entire
lecture! There is no time to cover it in class.
Now, a brief (hopefully)
humorous discussion
L
Some Popular (joke!) Versions of
The Laws of Thermodynamics
1st Law: You can’t win.
nd
2
Law: You can’t break even.
3rd Law: There’s no point in trying.
Other Popular Versions of
The Laws of Thermodynamics
Version 1
Zeroth Law:
First Law:
Second Law:
Third Law:
You must play the game.
You can't win the game.
You can't break even in the game.
You can't quit the game.
Other Popular Versions of
The Laws of Thermodynamics
Version 1
Zeroth Law:
First Law:
Second Law:
Third Law:
You must play the game.
You can't win the game.
You can't break even in the game.
You can't quit the game.
Version 2
Zeroth Law:
First Law:
You must play the game.
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!
Version 3
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 3
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:
First Law:
Second Law:
Third Law:
There is a game.
You can't win the game.
You must lose the game.
You can't quit the game.
A joke!!
“Murphy's Law”
of Thermodynamics:
“Things get worse
under pressure!!”
Murphy’s “Law”:
“Anything that can go wrong,
will go wrong!”
.
L
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.