01-02 Introduction to Thermodynamics

8/13/2019 01-02 Introduction to Thermodynamics

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Foundations of Nanotechnology IPhase Equilibria for Nanoscale Systems

CNSE 506Fall 2013

Professor Kathleen A. DunnNanoFab East 4316

[email protected]

Overview of Todays Lecture Course Structure & Expectations

Technical Content Classification of Systems Classification of Variables

State Functions Process Variables

Classification of Relationships

Equilibrium & the Laws of Thermodynamics


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Philosophical Statement: Text, Context, Pretext

Text: the material you are here to learn (content)

Context: the relationship of that information to other thingsyou know & understand -- that which allows you to makesense of the text

Pretext: the reason you are here to learn it & more generallythe meta-text: what you are here to learn BESIDES the text

There isnt a scientific community. Its a culture. It is avery undisciplined organization.

-- Francois Rabelais


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Course Goals & Objectives

The relationship between the fundamental concepts ofthermodynamics and the development of equilibrium structures inmaterials systems

The importance of the chemical potential in describing phase

equilibria in condensed systems equality of the chemical potentialwhen phases are in equilibrium

Goals:At the end of this module, you should understand:

Objectives (indicators of goals):At the end of this module, you should be able to:

Discriminate between equilibrium and non-equilibrium systems

Sketch free energy diagrams to describe phase equilibria

Construct and use complex phase diagrams to predict system stability

Apply the concepts of thermodynamics to nanoscale systems,

including the effect of surfaces and interfaces


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Organizational DetailsStructure

14 Lectures

Pass/Fail Homework assignments (5%)5 in-class quizzes (75 % of grade)Final Exam (20% of grade)

Office Hours Monday & Wednesday 4-5 pm, or by appointmentAll handouts available at http://blackboard.albany.edu/

Lecture Date Topic: Corresponding Text

1 8/27 Course Structure & the Language of Thermodynamics Chapters 1,22 8/29 The Laws of Thermodynamics Chapter 33 9/3 Thermodynamic Relationships Chapter 4.14 9/10 Thermodynamic Problem Solving Chapter 4.25 9/12 Equilibrium & the Chemical Potential Chapter 56 9/17 Single Component Systems (Unary Heterogenous) Chapter 77 9/19 Multicomponent Systems (Mixing) Chapter 8.1-8.38 9/24 Multicomponent Systems (Activity, Solutions, Chemical Potential) Chapter 8.4-8.8

9 9/26 Mutltiphase, Multicomponent Systems (Gibbs Rule, intro to diags) Chapter 9.1-9.410 10/1 Interpreting Phase Diagrams Chapter 9.5-9.711 10/3 Thermodynamics of Phase Diagrams Chapter 1012 10/8 Multicomponent, Multiphase, Reacting (Ellingham, Pourbaix) Chapter 1113 10/10 NanoThermo: the role of Surfaces & Interfaces (Capillarity) Chapter 1214 10/15 Review Session


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A Different

View

Final ExamTBA

Note: 10/16-10/17


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Source BooksText: Thermodynamics in Materials Science 2 nd edition, Robert T.DeHoff, New York: McGraw-Hill.

Other recommended resource materials: Phase Transformations in Metals and Alloys, D.A. Porter & K.E. Easterling,

New York: Chapman and Hall.

Introduction to Metallurgical Thermodynamics, David R. Gaskell, New York:McGraw-Hill; Introduction to the Thermodynamics of Materials, ibid.

Thermodynamics of Solids, R. A. Swalin, New York: Wiley & Sons.

Principles of Phase Diagrams in Materials Systems, Paul Gordon, New York:McGraw-Hill.

The Structure and Properties of Materials, Volume II: Thermodynamics ofStructure, Jere H. Brophy, Robert M. Rose and John Wulff, New York: Wiley

& Sons.


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Rubric for Homeworks & Quizzes

(1) Responds fully to theassignment (answers eachproblem)

(2) Invokes and uses disciplinaryfacts correctly

Excellent Very good Adequate Weak Poor



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Recall of Facts and Details

(a)

(f)

(k)

(b)

(g)

(l)

(c)

(h)

(m)

(d)

(i)

(n)

(e)

(j)

(o)

(From Nickerson & Adams, 1979)


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Rubric for Homeworks & Quizzes

(1) Responds fully to theassignment (answers eachproblem)

(2) Invokes and uses disciplinaryfacts correctly

(3) Avoids brain-dumpresponses (dont make meguess which of youranswers you meant)

(4) Identifies correct &necessary calculations

(5) Performs necessarycalculations correctly

(6) Is written legibly







Anything I cant read,

or have to guess which answer you meantwill always be misinterpreted!

This big and copper isnt good enough!


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Course Goal: Phase Equilibria

What do we mean by equilibrium?


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Stability: Identifying the Proper Potential

Analogously, we want to determine the thermodynamicpotential that will be minimized at thermodynamic equilibrium

First: what is thermodynamics & why study it?

In solid body mechanics: aminimum in potential energyrepresents the equilibriumposition of a system

E

x

A

B

C


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What is Thermodynamics?

The study of energy transformations and the relationships

among physical properties of substances which are affectedby these transformations.-- K. Wark, Thermodynamics, 5th Edition, 1988

Classical thermodynamics Deals with macroscopic systems, without recourse to the nature of the individual particles

and their interactions Requires no hypothesis about detailed structure of matter on the atomic scale, thus laws

are not subject to change as knowledge concerning nature of matter is discovered

Statistical thermodynamics Based on statistical behavior of large groups (ensembles) of individual particles, and

postulates that values of macroscopic properties merely reflect some sort of statisticalbehavior of enormous ensembles

Thermodynamics for Phase Equilibrium Based on the interactions between phases

Dont have to count every particle, consider just subsets of the full ensemble

We will allow particles to interact (react, change phase, etc.)


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Why Study Thermodynamics?

Predictions of behavior based on known properties(dont necessarily have to do EVERY experiment!)

What happens at 500 C ?Will the layers stay intact? Or mix?

substrate

Why do Peeps expand whenmicrowaved?


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Thermodynamics applies even to complexsystems

How strong can we make these MRI magnetsbefore they lose their superconductivity?

What happens to this system when we applyan electric field (and the transistor heats up)?

Before we can address thesequestions, we have to agree

on terminology & rules!Magic Trick


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Language Describing the Behavior of Matter

system

boundary

Universe(everything else)

We need to be explicit aboutthe condition of the system

Properties Temperature (T) Pressure (P) Volume (V) Chemical composition (X

i)

Phase assembly ( , ,)


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What happens to these properties when thesystem is subjected to a process?

System in

State A

T A, P A, V A

Process

System in

State B

TB, P B, VBTPV

Classifications will help us organize our understanding ofthermodynamic systems, properties, and relationships


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Classification of Systems

Questions to ask:1. How many reacting components

(unary, binary, ternary) 2. Is it homogeneous or heterogeneous?

Solution vs. Mixture Sidebar: definition of phases

3. Is this system open or closed (with respect tointeractions with the universe)

4. Is anything reacting? (Big One for us!)5. Are there other complexities affecting the state of

the system? Electric field, magnetic field,gravitational fields


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Sidebar: What is a phase?

How many phases exist?

a) 3b) 4c) 6d) millions

Phase State of Aggregation

Phase Different Composition


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Definition of Phase

Phase

a portion of the system whose properties andcomposition are homogeneous and which is

physically distinct from other parts of the system

vs.steel salt & pepper S o

l u t i o n

= 1 p

h a s e

Mi x

t ur e=

2 or m

or

e ph

a s e s

salt wateroil

watervs.


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Definition of Phase

Phase

a portion of the system whose and. are and which is

. from other parts of the system

vs.steel salt & pepper S o

l u t i o n

= 1 p

h a s e

Mi x

t ur e=

2 or m

or

e ph

a s e s

salt wateroil

watervs.


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Back to: Classification of Systems

Questions to ask:1. How many reacting components

(unary, binary, ternary) 2. Is it homogeneous or heterogeneous?

Solution vs. Mixture Sidebar: definition of phases

3. Is this system open or closed (with respect tointeractions with the universe)

4. Is anything reacting? (Big One for us!)5. Are there other complexities affecting the state of

the system? Electric field, magnetic field,gravitational fields

System

Universe

Fe

O 2

rust Slightlyless O 2


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State Functions vs. Process Variables

Classification of Thermodynamic Variables

System inState A

T A, P A, V A

ProcessSystem in

State B

TB, P B, VB


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State Function/ State Variable

State variable = property of the system which has a fixed value in agiven equilibrium state regardless of how the system arrives at that state

Example: PV = nRTX = P

Y = VZ = T


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State Function/ State Variable


Example: PV = nRTX = P

Y = VZ = T

State variable = of the system which has a in agiven state regardless of at that state

In other words, the change in the value ofthe state variable will be _________ nomatter what path you take between thetwo states.


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Another view of State Variables

The change in the value of the state variable will be the same no matter whatpath you take between the two states.

If a system is carried through a cycle to itsoriginal state, the variable Z is a statevariable iff it returns to its original value.

cycle

dZ 0

State variable = of the system which has a in a

given state regardless of at that state


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Subdivide State Variables intoExtensive vs. Intensive Properties

Extensive vs. IntensiveExtensive properties if the

value for the whole

system is the sum of itsvalues for the parts

Intensive properties donot depend on the total

mass or amount ofmaterial, and have thesame value in all parts ofthe system at equilibrium

Think, Pair, ShareExtensive or intensive?

Mass, temperature,density, surface area,

pressure, volume


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Extensive vs. Intensive Properties

Mass is an ________ property, because its value _________ depend

on the sum of parts

Temperature is an ________ property, because its value _________depend on the sum of parts

Density is an ________ property, because its value _________depend on the sum of parts

Surface area is an ________ property, because its value _________depend on the sum of parts

Pressure is an ________ property, because its value _________depend on the sum of parts

Volume is an ________ property, because its value _________depend on the sum of parts


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State Variables & Degrees of Freedom

Any state variable (property) has a fixedvalue in a given equilibrium stateregardless of how the system arrives atthat state

All systems are describable by specifyingan ensemble of state variables.

For most systems, it is not necessary tospecify them ALL.

The smallest number that must be

specified to completely describe theentire thermodynamic state of thesystem is called the variance or thedegrees of freedom of the system.


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The State Postulate

The state of a simple compressible system can be uniquely

specified by two independent intensive properties

A quantity of gas contained in a cylinder by a piston

Microscopic state:position & momentum vector of each gas molecule (10 23 ??)

Macroscopic state:Fix 2 independent intensive properties

& the rest follows

Choices for intensive properties?

What shall we choose?

weight

State Function: PV = nRT


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Changing one of the State Variables

weight

What happens if the force on the piston is increased?

Intuitively you know the answer: the piston will sink.But how far?

Explicitly: (lets assume T is constant) the pressure exerted by the weight increases to P 2 resulting imbalance between the pressure exerted on

the gas and the pressure exerted by the gas, forces

the piston into the cylinder the volume of the gas must therefore decrease to V 2 which increases the pressure inside the cylinder untilit equalizes with the external pressure exerted by thepiston

State Function: PV = nRTweight


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In Thermodynamic Terms

The change in pressure takes the system from the

Initial state described by (P 1,T1), to theFinal state described by (P 2, T 1)

and the volume, as a dependent variable, changes from V 1 to V2.

(P 1, T 1)

P

T

V

V = V(P,T)

V2

V1

(P 2, T 1)


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System inState A

T A, P A, V A

ProcessSystem in

State B

TB, P B, VB


Process variable = _____ of the system which depends on __________


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How Does that Process Occur?

Process variable = property that only has meaning for a changing system(explicitly path-dependent!)

Process vs. Path A process is any transformation

of the system from oneequilibrium state to another

The path of a process refers tothe specification of the series ofstates through which the system

passes

State variable example:

PV = nRTX = PY = VZ = T

But each path has a differentWORK done & HEAT added


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Process Variable: Work

F

ds

ds F W

Forces may be due to:

Applied pressure Gravity Rotation Electric fields Magnetic fields Surface tension

Any force that causes a displacement of the point of application can do work

Displacement implies change, so work is a process variable and not a state variable

d f h h


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An Aside for the Physicists

Work is only path- independent for conservative forcesgravity in the absence of air resistanceideal springs, pendula, etc.

cycle

conserv ds F 0

RE: work as a path-dependent quantity

cycle

conservnon ds F 0

Work is path- dependent for non-conservative forcesfriction & other dissipative forces can still do work

m

m

bl


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Process Variable: Heat

What is Heat?(as opposed to Temperature)

Rigid, impermeable boxCan system ever change?

Temperature measures thestate RIGHT NOW

Heat changes the system

Heat content of thesystem is meaningless

Cl ifi i f Th d i V i bl


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Can we describe these mathematically?


System inState A

T A, P A, V A

ProcessSystem in

State B

TB, P B, VB

M h i l D i i f R l i hi


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Mathematical Descriptions of Relationships

... NdY MdX dZ

Infinitesimal steps in functions X, Y, result ininfinitesimal change in state function Z:

Where the coefficients M & N are

the partial derivatives:

,...Y X Z

M

,... X Y Z

N

Maxwells relations tell us howthose coefficients are related

,...,... Y X X N

Y M


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What is Equilibrium?

A system in balance

C di i f E ilib i


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Conditions for Equilibrium

Equilibrium A system is in thermodynamic

equilibrium if it is not capable of a finitespontaneous change to another statewithout a finite change in the state of

the environment

A system not in equilibrium with itsenvironment will change

spontaneously until it hasexhausted its capacity for change

Types of EquilibriumThermal: equality of T across the system boundaryMechanical: equality of P across the system boundaryPhase Equilibrium: no tendency for net transfer of one

or more species from one phase to another

Chemical: no tendency for chemical reaction

Ice & Water in a closedsystem at 1 atm.

Whats the conditionfor equilibrium?

C di i f E ilib i


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Conditions for Equilibrium

Equilibrium A system is in thermodynamic

equilibrium if it is not capable of a ___, _________ change to another state

without a _____ _____ in the state of _________________

A system not in equilibrium with itsenvironment will change

__________ until it has exhaustedits ______________

Types of EquilibriumThermal: equality of T across the system boundaryMechanical: equality of P across the system boundaryPhase Equilibrium: no tendency for net transfer of one

or more species from one phase to another

Chemical: no tendency for chemical reaction

Ice & Water in a closedsystem at 25 C. Whats

the condition forequilibrium?

Di i


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Discussion

Ice & Water in a closed, thermally

isolated system.True/False & why?

Ice and water can never be in phase

equilibrium because they are different statesof aggregation (1 Liquid, 1 Solid)

If we removed the thermally isolatedconstraint, the system would absorb heat

from the environment and melt the ice.

The system will never be in phaseequilibrium because molecules are

constantly transferring from ice to water andback again

A id E ilib i St d St t


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Aside: Equilibrium vs. Stead-StateWhats the difference?

Equilibrium: all state variables areconstant and net reaction rate = 0

Example: Pour 80 L of water into a empty tub and let itsettle, the state variables (volume, pressure,temperature, composition) are constant.

Steady-state: all state variables maybe constant but net reaction rate

may be nonzeroExample: Start with empty tub, pull out the drain plug &

turn on the faucet. After some time, the flow in willequal the flow out so again the volume will stabilize.Net reaction rate (in this case, mass flow), is nonzero.


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Laws of Thermodynamics

E

x

A

B

C

1 t L C ti f M & E g


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1st Law: Conservation of Mass & Energy

Mass Conservation:the ancient Greeks, really1774: Lavoisier conclusively demonstrated conservation

of mass in chemical reactions

1st L Conser tion of M ss & Energ


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What do we mean by energy?

The capacity to do work ?

vs.

The capacity to induce a changein that which inherently resists

change

Capacity = Effort & Change= Driving Force x Displacement

If DF + displacement contained in system, thisresults in a change in internal energy, which is as

important to thermodynamics as changes in

position or motion of entire system.



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Energy Conservation:

1797: Count Rumford at the cannon factory showedcaloric cannot be depleted1799: Humphrey Davy melts ice in a vacuum, end of

caloric gas theory of thermal conduction

Equivalence of Work & Heat:1843-1848: Joule & Kelvin

demonstrated indisputablythe precise equivalence of

mechanical work & totalthermal energy obtainablefrom it

E, m treated separately:

What about E = mc 2 ?

Equivalence of Work & Heat


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Energy conservation: The change in internal energy (U)of a system is equal to the heat (Q) added to the systemplus the mechanical work (W) and non-mechanical work(W) done on the system.

d U = Q + W + W

Path independent Path dependent!

P

V

Initial StateFinal State

For a cycle, U=0But Q, W, W 0

Mass conservation: material neither created nor destroyed

U = Q + W + W

Heat in: Q +veHeat out : Q ve

Work done on : W +veWork done by : W -ve

W = - P dV

d U = Q - PdV + W



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True or False?Why?

Work and Heat are equivalent because they are both forms of energy.

Work and Heat are equivalent because The Prof just said so.

Work and Heat are equivalent because Joule & Kelvin said so, and theyre

names I recognize from the Nobel Prize list.

If Joule & Kelvin say so


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If Joule & Kelvin say so

Do you believe Heat & Work are equivalent?Think, Pair, Share

Do you expect that: Stones, cooling themselves, could convert their heat

contents into work: roll uphill unaided? Hot water could spontaneously convert its heat into

kinetic or potential energy?

Not in our experience. So d U = Q + W + W cannot be

the full story on thermodynamics!

Nature does not allow heat to be spontaneously convertedinto work without the accompaniment of other changes.(Kelvins formulation of 2nd law!)

2nd Law: Directionality of Processes


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2nd Law: Directionality of ProcessesTimes arrow in classical thermodynamics: Entropy (S)

Changes occur in the direction that increases entropy for theuniverse ( system + surroundings)

For any given process, entropy of the system may increase ordecrease: but the total entropy of universe must increase

heatengine

Hot r eservoir Cold re servoir

W Q h - Q c

Entropy as waste or unavailable energy

Entropy as Disorder
http://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svghttp://upload.wikimedia.org/wikipedia/commons/2/22/Carnot_heat_engine_2.svg


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Entropy as Disorder

Ordered structures (crystals) vs.

ice, H 2O water, H 2O

graphite, C amorphous C

quartz, SiO 2 silica, SiO 2

Atomic example:

Molecular examples: let = molecule

As more became known about the nature of matter, thestatistical thermodynamics concept of entropy as disorder

(mixedupness ) arose

disordered structures (gasses,most liquids, amorphous solids)

Configurational Entropy


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As more became known about the nature of matter, the

statistical thermodynamics idea of entropy as disorder(mixedupness ) arose

Configurational entropy

A

B

Case 1 Case 3Case 2

Which has the greatest (configurational) entropy? Which has the least?



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Configurational entropy

A

B

Case 1 Case 3Case 2

Which has the greatest (configurational) entropy? Which has the least?

They all have the same entropy because all microstates are equivalent.

Case 1 has the most entropy because it is the least likely to occur.

Cause 2 has the most entropy because it is the most mixed up.

True/False? Discuss your evidence.

Configurational Entropy vs Microstates


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Configurational Entropy vs. MicrostatesEach microstate is unique but there are many more essentially random ones

Consider what can be swapped for what

A

B

Case 1

Case 3

Case 2

1 2 3 4 5 6 7 8 9 10

1

2

3

4

56

7 89

10

1 2 34 5 6 7

8 9 10

Neighbor Tally38 A-B nearest neighbors9 B-B nearest neighborsx A-A nearest neighbors

74 A-B nearest neighbors0 B-B nearest neighborsy A-A nearest neighbors

22 A-B nearest neighbors37 B-B nearest neighborsz A-A nearest neighbors

Try to make an equivalent state withthe same number of interactions



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Configurational Entropy vs. Microstates

1 2 3 4 5 6 7 8 9 10Neighbor Tally38 A-B nearest neighbors9 B-B nearest neighborsx A-A nearest neighbors

42 A-B nearest neighbors7 B-B nearest neighborsx-2 A-A nearest neighbors

38 A-B nearest neighbors9 B-B nearest neighborsx A-A nearest neighbors

1 2 3 4

5

6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

Can only swap for if I swap the entire row

Case 1 (lowest entropy): limited # of equivalent states

Case 1



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Configurational Entropy vs. MicrostatesCase 2 (highest entropy): nearly infinite # of equivalent states

Case 2

1

2

3

4

56

7 89

10

Neighbor Tally74 A-B nearest neighbors0 B-B nearest neighborsy A-A nearest neighbors



1

2

3

4

56

7 89

10

1

2

3

4

56

7

8

910

In fact I can swap any for any



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Configurational Entropy vs. MicrostatesCase 3 (moderate entropy): Moderate # of equivalent arrangements

Case 3 1 2 34 5 6 7

8 9 10

Neighbor Tally22 A-B nearest neighbors37 B-B nearest neighborsz A-A nearest neighbors



1 234 5 67

8 910

1 2 3

4 5 67 8 9 10

Have to swap several for


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Entropy and Randomness


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Entropy and RandomnessConsider it atomistically: in any conglomeration of atoms, each atom has

thermal kinetic energy & an associated velocity which continually change both

in magnitude and direction by chance collisions with other atomsFrom a strictly statistical point of view, an essentially random positional

arrangement (Case 2, on previous slides) has by far the highest probability ofoccurring at any given moment.

BUT it doesnt win because it is opposed by (and at least partiallycounterbalanced by) the forces derived from the potential energy of the atoms.

HOWEVER:The tendency towards randomness is always present and is stronger when

atomic kinetic energies are higher (i.e., at higher temperatures)

Described mathematically as:

T Q

dS rev

change in heat, applied reversibly(i.e. without losses) to achieve the event

temperature at which the event occurs

incremental change in entropyfor a particular event

The 2nd Law Mathematically


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The 2nd Law, Mathematically

The entropy of an isolated system not at equilibrium will tend

to increase over time, approaching a maximum value.For a process taking place for a system at equilibrium(reversible), the entropy of a system + surroundings, theentropy of system + surroundings is constant:

In a spontaneous (irreversible) process:

0 rev surr rev sys dS dS

0 irrev surr irrev

sys dS dS

Combined Statement of 1 st & 2 nd Laws


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Combined Statement of 1 & 2 Laws

dU = Q - P dV + W 1 st Law:

2nd Law:T

QdS

rev

dU = T dS - P dV + W

A centerpiece of the mathematicalframework of thermodynamics!

3 rd Law: Absolute Zero


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3 Law: Absolute Zero

As a system approaches absolute zero of temperature allprocesses cease and the entropy of the system approachesa minimum value which is the same for all substances.

For conveniences sake, choose this minimum value to be 0

Handy for calculating the change in entropy for chemicalreactions without having to actually measure every caseexperimentally.

S (Reaction) = Products - Reactants


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S (Reaction) Products Reactants

To simplify the calculations of S for chemical reactions, the

values of S are tabulated for elements & many compounds ata standard state, taken to be 298K and 1 atm pressure: oS 298 Substance S 298

(J/mol K)C (graphite) 5.69O 2 205.03CO 197.9CO 2 213.64

First write a stoichiometricallybalanced equation for the reaction

C + O 2 = CO

)(

2

1)()()( 2298298298298 OS C S COS rxnS

oooo

)3.205(21

69.59.197)(298 rxnS o

56.89)(298 rxnS o J/mol K

Summary


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Summary

Thermodynamics describes the quest for equilibrium Classification of Systems

Classification of Variables

State Functions

Process Variables Classification of Relationships

Equilibrium & the Laws of Thermodynamics

0: You have to play the game.1: You cannot win.

2: You cannot break even, except at absolute zero.3: You cannot reach absolute zero.

The Minute Paper (Anonymous!)


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The Minute Paper (Anonymous!)

Take an index card

On the front of the cardWhat do you think was the most important point of todays

lecture?

On the back of the cardWhat was the muddiest point in this lecture? That is, whatwas least clear to you?

Turn in the index card when you leave, please!

Documents

01-02 Introduction to Thermodynamics