The Laws of Thermodynamics

The The LawsLaws of Thermodynamics 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:

Temperature T:

Also Define:

lnBS k E

,

1

N V

S

E T

,

ln

N V

E

E

Ω(E) Ef

•So, the connection between & theabsolute temperature T is clearly:

[1/(kBT)]h

•Also, equations of state can be derived from Ω(E).

,

1

N V

S

E T

,

ln

N V

E

E

lnBS k E

TheThe Zeroth LawZeroth Law ofof ThermodynamicsThermodynamics

““If two systems are If two systems are separatelyseparately in inthermal equilibrium with a third thermal equilibrium with a third

system, they are system, they are in thermal in thermal equilibrium with each otherequilibrium with each other.”.”

•Definition: If 2 systems are in thermal equilibrium, their

absolute temperatures are equal! (Isn’t this obvious)??

This allows the design & the use of ThermometersThermometers!!

The The First LawFirst Law of Thermodynamics 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 ConservedTotal Energy is Conserved

Heat absorbed by system A1

Work done by system A1

Change in internal energy of system A1

The The First LawFirst Law of Thermodynamics of ThermodynamicsFor 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 ConservedTotal Energy is Conserved

Heat absorbed by system A1

Work done by system A1Change in internal

energy of system A1

Rudolf Clausius (1850)

The Physical Meaning of the 1st Law of Thermodynamics

Conservation of Total EnergyConservation of Total Energy!!!! !!!! However, it says nothing about

The Direction of Energy Transfer!

Rudolf Clausius’ statement of the

11stst Law of Thermodynamics Law of Thermodynamics“Energy can neither be created

nor destroyed. It can only be changed from one form to

another.”

The The 22ndnd Law Law of Thermodynamics 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

S 0It gives the Preferred (natural)

Direction of Energy Transfer• It thus determines whether a process can occur or not.

Change in the system entropy

•Mathematically, this means that in any process ΔΔS ≥ 0S ≥ 0

or, at equilibrium, S → SS → Smaxmax

For (idealized) reversibleprocesses only,

ΔS = 0, dS = đQ/T.

The The 22ndnd Law Law of Thermodynamics: of Thermodynamics:“The entropy of an isolated system never decreases”.

Change in Entropy

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 Entropywith Disorder.

General FeaturesGeneral Features of the Entropy S

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

General FeaturesGeneral 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 FeaturesGeneral 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 FeaturesGeneral 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 FeaturesGeneral 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 FeaturesGeneral 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 LawSecond Law of Thermodynamicsof Thermodynamicsmay sound very different than those just mentioned.

Various Statements of the22ndnd Law of Thermodynamics 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 There are NO perfect NO perfect enginesengines!!

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

22ndnd Law of Thermodynamics 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 of Rudolf Clausius’statements of the


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



5.“It is impossible to design a cyclic device that raises heat from a lower temperature to a higher temperature without affecting its surroundings.”




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.



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


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 Lord Kelvin’s(William Thompson’s)

statements of the


8. “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.”

Two of Kelvin’s & Planck’s joint statements of the


Lord Kelvin

Max Planck

8. “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.”

9. “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) .”

Two of Kelvin’s & Planck’s joint statements of the


Lord Kelvin

Max Planck

The The 22ndnd Law Law of Thermodynamics of Thermodynamics

The Heat Flow Statement10.“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

22ndnd Law of Thermodynamics 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 HeatEngine to a cold body

The Second Law Applied to Heat Engines

Efficiency (W/QH) = [(QH - QC)/QH]

A “Heat Engine” That Violatesthe 2nd 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.

Qh

QL

Win Wout

T

S

Carnot CycleSchematic:

Reversible Work: Entropy S = constant

Reversible Heat Transfer: Temperature T = constant

Carnot Efficiency of a Heat EngineDefinition: Heat Engine Efficiency

th Wnet,out

QH

QH QL

QH

1 QL

QH

PS QH

TH

Ql

TL

over a reversible cycle PS 0QH

TH

Ql

TL

QH

QL

TH

TL

Carnot efficiency :

QH

W

TH

th,Carnot 1TL

TH

CarnotEfficiency:

Carnot CycleSchematic

QL

TL

This is the Maximum Efficiency possible for real engines!

Definition: Refrigerator •A system that can do macroscopic work toextract heat from a cold body & exhaust it to ahot 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 bodyW WORK performed by a Refrigerator

on the surroundings-QH HEAT emitted by a Refrigerator

to a hot body

The 2nd Law of ThermodynamicsClausius’ 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 2nd Law of ThermodynamicsClausius’ 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 2the 2ndnd Law of Thermodynamics Law of Thermodynamics•Question: Is it possible to cool your kitchen byleaving the refrigerator door open or cool yourbedroom by putting a window air conditioner on thefloor by the bed?


the 2the 2ndnd Law of Thermodynamics Law of Thermodynamics•Question: Is it possible to cool your kitchen byleaving the refrigerator door open or cool yourbedroom by putting a window air conditioner on thefloor by the bed? (Hint: Recall the amusing video clip inwhich the teenage girl asks why air conditionerscouldn’t be used to cool the outside!)


the 2the 2ndnd Law of Thermodynamics Law of Thermodynamics•Question: Is it possible to cool your kitchen byleaving the refrigerator door open or cool yourbedroom by putting a window air conditioner on thefloor by the bed? (Hint: Recall the amusing video clip inwhich the teenage girl asks why air conditionerscouldn’t be used to cool the outside!)

•Answer: NO!!! Rather than cooling thekitchen, the open refrigerator will warm it up!!The air conditioner also will warm the bedroom.

Entropy & The 2nd Law:For a System in Equilibrium with a Heat

Reservoir at Temperature T The 2The 2ndnd Law of Themodynamics Law of Themodynamics::

•Heat flows from high temperature objects to low temperatureobjects 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:

.T

QS

The The 22ndnd Law Law of Thermodynamicsof Thermodynamicscan be used to generally classify

Thermodynamic Processes intoThree 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 LawThird Law of Thermodynamics

“It is Impossible to Reach a Temperature of Absolute Zero.”On the Kelvin Temperature Scale,

T = 0 Kis often referred to as

“Absolute 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.”

Another Statement ofThe 3rd Law of Thermodynamics:“The entropy of a true equilibrium

state of a system at T = 0 K is zero.”

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 suggestthat 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 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.

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 ofThe LawsThe Laws of Thermodynamics

11stst Law Law:: You can’t win.

22ndnd Law Law:: You can’t break even.

33rdrd Law Law:: There’s no point in trying.

Version 1Zeroth 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.

Other Popular Versions ofThe LawsThe Laws of Thermodynamics of Thermodynamics

Version 1Zeroth 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 2Zeroth Law: You must play the game.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!

Other Popular Versions ofThe LawsThe Laws of Thermodynamics of Thermodynamics

Version 3Zeroth 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 3Zeroth Law: You must play the game.


Second Law: You can't break even except

on a very cold day.

Third Law: It never gets that cold!

Version 4Zeroth Law: There is a game.


Second Law: You must lose the game.

Third Law: You can't quit the game.

“Murphy's Law”of Thermodynamics:“Things get worse under pressure!!”

A joke!!

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 thesekinds of “Laws” applied to various situations.

Documents

The Laws of Thermodynamics