U dU W Q - Solid State Chemistry - Solid State ChemistryFor all ellements in their reference states at T For all ellements in their reference states at T ' 4 ' 4 ' 4 f G m ,i f H

1

Summary Lecture 1 (glossery: see App. B, SG)

- First law: conservation of energy

function state a is

0

U

dU

QWdUU

dQdWdU

- Perfect gas nRTPV Equation of state

- Perfect atomic gas PVnRTU2

3

2

3

- Mechanical work dVPdVPW ext

Reversible process

2

Summary Lecture 2 (second law and entropy)

Second law: for any spontaneous process

0surtot dSdSdST

dQdS

rev

S is a state function, so independent of path

Alternative form: Clausius inequality:

TdSdQ

TdSdQ rev

TdSdQ irr

Reversible process

Irreversible process

3

Summary Lecture 2 (alternative energy functions)

PVUH

TSHG

TSUA

V

VT

UC

P

PT

HC

UInternal energy

Enthalpy

Helmholtz free energy

Gibbs free energy

State functions

Heat capacities

PdVTdSdU TdSdUV

VdPTdSdH TdSdHP

PdVSdTdA 0,

VTdA

VdPSdTdG 0,

PTdG

4

Summary Lecture 3 (chemical equilibria)

Second law→ 0,

TPGd

QRTGG lnrr

RT

GK rexp

i

i

i GG ,mfr

Equ

ilib

riu

m s

tate

Energy minimum

T,P 0r G

0r G

Reaction progression ξ 0 1 ξeq

0r G

0r G

0r G

0r G

reaction ΔrG

Equilibrium constant bar1P

i

iiaQ

5

Summary Lecture 3 (formation energies)

0,mf

iGFor all ellements in their reference states at T

For all ellements in their reference states at T

iii STHG ,mf,mf,mf

At constant, chosen T

Partial pressure

PxP ii

Mole fraction

j

j

iii

n

n

n

nx

For gaseous mixtures For perfect gas mixtures

i

i

i

P

PQ

6

Summary Lecture 4 (activity)

For perfect gas mixtures

P

Pa i

i

For pure liquids

For pure solids

1la

1sa

iii aRT ln

c

ca ic

ii

)(

b

ba ib

ii

)( i

x

ii xa )(

mol/L1c mol/kg1b

H -logpH a

For general systems:

7

Summary Lecture 4 (electrochemistry)

QRTGG rr ln QF

RTEE ln

Nernst equation

)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt

Equ

ilib

riu

m s

tate

Energy minimum

T,P 0r G

0r G

Reaction progression ξ 0 1 ξeq

0r G

E + -

0r G

0r G

0r G

reaction

0E

0E

0E

FEGr

8

Summary Lecture 5: solutions or mixtures

Equilibrium between phases of component i in mixtures

,, ii in equilibrium:

phase α

phase β

i

iiTPG n

,

lglglglg

lg axaxnRTG ,B,,B,,A,,A,

,

mix lnln

BBAAmix lnln xxxxnRS

0mix H

Real phase mixing

lglglglg

lg xxxxnRTG ,B,,B,,A,,A,

,

mix lnln Perfect gas mixing

Ideal solution (Raoult)

9

Summary Lecture 5: colligative properties

Osmosis

P,T

h

Al

Al+

B

B*

Am,fus

*2

fusA,x

H

RTT

B*

Am,vap

*2

vapA,x

H

RTT

Freezing point depression Boiling point elevation

A*ln

mA,

aV

RTΠgh

BRTΠgh

A*

Am,fus

*2

fusA,ln a

H

RTT

A*

Am,vap

*2

vapA,ln a

H

RTT

Ideal solution: Ideal solution:

10

Lecture 6: Efficiency of processes

1690/1698

1784

1803/1824

1854/1862

Heat Work

Steam engine

Theory of efficiency

Definition Entropy

11

Lecture 6: Efficiency of processes: History

Thomas Savery 1650-1715

1698

vacuum Steam-Water

pump

12

Lecture 6: History: Convert heat to work

Denis Papin 1647-1712 1690

Steam-Water pump Using a Piston

13


Thomas Newcomen 1664-1729

+ (Thomas Savery)

The Proprietors of the Invention for Raising Water by Fire

Efficiency: 2-5 %

14


James Watt 1736-1819

1784 Steam engine

efficiency: 25 %

15


Sadi Carnot 1796-1832

Thermodynamical model system: heat engine

Is the amount of (useful) work limited? Is there an alternative medium for steam?

16

Lecture 6: Steam engines: Convert heat to work


Thermodynamical model system: heat engine

(useful) work

Heat (flow)

Heat (flow)


17

Lecture 6: Steam engines: Convert heat to work


(useful) work

Heat (flow)

Heat (flow)

TH and TC separated: no internal losses Process steps: isotherms and adiabats Idealized cycle: reversible process Arbitrary medium: perfect gas


18

Lecture 6: Steam engines: Carnot cycle

Qin

Qout

Win

Wout


(useful) work

Heat (flow)

Heat (flow)



19



(useful) work

Heat (flow)

Heat (flow)

Maximal efficiency depends on

(TH -TC)

Transformation of heat into work always

involves losses (QC)

1824

20




Rudolf Clausius 1822-1888

WQU ddd

Äquivalenzwert der Verwandlung R. Clausius Philosophical Magazine, 12 (1856) p.81

1854

First law: conservation of energy U

Second law: transformations

(processes)

21

Lecture 6: Fundamentals of thermodynamics

Rudolf Clausius 1822-1888

WQU ddd

0d

T

QS

1824


1850

(useful) work

Heat (flow)

Heat (flow)

1865


Second law: transformations

For all reversible cyclic processes

Maximal efficiency depends on

(TH -TC)

Transformation of heat into work always

involves losses (QC)

22


The entropy (spontaneously) always increases until thermodynamic equilibrium is reached

23

Lecture 6: Modern classical thermodynamics

WQU

0surtot SSS

T

dQdS

rev

T

QS

sur

ENTROPY ║

Heat +

Temperature


Second law: processes

24


WQU

0surtot SSS

T

dQdS

rev

T

QS

sur

0tot T

dQdSdS dQTdS

for any spontaneous process:

TdSdQ Clausius inequality

25


TdSdQ

Clausius inequality

TdSdQ rev

TdSdQ irr

PdVTdSdVPdQdWdQdU ext

irr

rev. Process (mech. Work)

irr. Process (mech. Work)

any process

U is a state function, so independent of the path

Hermann von Helmholtz 1821-1894

An isothermal reversible process delivers maximal (volume) work

dWdQdU

TSUA

26


TSddUdA

dWdAT

Helmholtz free energy

SdTdWTdSSdTdWdQdA

TdSdQ

0dWfor work done by the

system on surroundings TAW max

Josiah Gibbs 1839-1903

27


dWdQdU

TSHG

TSddHdG

(Study guide: p.12)

TdSdQ

edWSdTdGP

e,dWdG

TP

TPGW

,

max

e

edWSdTTdSdQdGP

Isothermal isobaric reversible process delivers maximal (electric) work

28

Qh

Qc

Win

Wout

Sadi Carnot (1796-1832)

Carnot cycle

Reversible processes

29

Lecture 6: Energy conversion: Carnot cycle

Machine model: → cyclic process

Q→W for a steam engine

Qh

Qc

Win

Wout

Carnot cycle


30


Q→W for a steam engine or power station

Heat engine


Qh

Qc

Win

Wout

Carnot cycle


31


Q→W Heat engine

Qh

Qc

Wout

Win

Carnot cycle



W→Q for a refrigerator

or heat pump


Qh

Qc

Win

Wout

Reversible model

32

0 dS

S is state function

A

D

C

B

C

B

rev

dS0T

dQdS

c

c

h

h

T

Q

T

Q

c

c

D

C

D

C c

rev

T

Q

T

dQdS

For a (reversible) Carnot cycle

h

h

B

A

B

A h

rev

T

Q

T

dQdS

Study Guide p. 19-22


Cyclic process

33

0 dU

U is state function

ch QQdQdW

0chinout QQWWdWNet work is done by the system on surroundings

(cf. exercise 6a for gasses)

0ch QQ0,0 hc QQ and


Qh

Qc

Win

Wout

Cyclic process

34

0 dU

U is state function

(cf. exercise 6a for gasses)

ch QQdQdW

0ch QQ0,0 hc QQ and

“equilibrium” process

0T

Q

T

Q

c

c

h

hsursurtot SSSS


Qh

Qc

Win

Wout

c

c

h

h

T

Q

T

Q

Carnot cycle

Efficiency of the process:

35

hcostenergy

energyuseful

Q

W

c

c

h

h

T

Q

T

Q

h

ch

h

ch

Q

QQ

Q

QQ

)0( c Q

h

c1

Q

Q

h

c1T

T

%)100x (

Lecture 6: Conversion efficiency: Carnot cycle

Qh

Qc

Win

Wout

Power station

Thermodynamic efficiency of a Carnot cycle

36

h

c1T

T hc TT

10cT

0hc TT

1h

T

(steam) C500h

T

(dumped) C100c

T%52


Qh

Qc

Win

Wout

Qh

Qc

Win

Wout

Reversible process

Thermodynamic efficiency of a Carnot cycle

37

h

c1T

T hc TT

10cT

0hc TT

1h

T

Irreversible process: h

c1T

T


Qh

Qc

Wout

Win

Inverse Carnot cycle

38



or heat pump



Qh

Qc

Wout

Win


39

0 dS

S is state function

B

C

D

A

D

A

rev

dS0T

dQdS

h

h

A

B

A

B h

rev

T

Q

T

dQdS

c

c

C

D

C

D c

rev

T

Q

T

dQdS


c

c

h

h

T

Q

T

Q




or heat pump

Qh

Qc

Wout

Win


40


W→Q for a refridegerator

or heat pump


0ch QQ0,0 ch QQ and

0T

Q

T

Q

h

c

h

hsurtot SS


surroundings

system

Non-spontaneous process

Freezer

Qh

Qc

Wout

Win


41



or heat pump

Reversible processes 0 dU

U is state function

ch QQdQdW

0ch QQ0,0 ch QQ and

0QQ ch W


Work has to be done to run the process

Qh

Qc

Wout

Win


42



or heat pump

Reversible processes Non spontaneous (forced) process

c: performance


ch

c

ch

cc

TT

T

QQ

QQ

Wc

c

c

h

h

T

Q

T

Q

43

QF

RTEE ln

Nernst equation

)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt

Lecture 6: Conversion efficiency: Batteries

E - + 0I

E

44

QF

RTEE ln

Nernst equation

)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt


)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt

E - + 0I 0I R

E E

?E

45

QF

RTEE ln

Nernst equation

)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt


)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt

E - + 0I 0I R

E E

?E

Q

46

QF

RTEE ln

Nernst equation

)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt


)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt

E - + 0I 0I R

E E

?E

Q

?

47

QF

RTEE ln

Nernst equation

)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt


E - + 0I 0I R

E E

Q

dtR

EdtIEdtPdQ

2

e

1costenergy

energyuseful

e

dW

dQ

Joule heating: 100 % conversion

IRE

48

QF

RTEE ln

Nernst equation

)(Fe3 aq)(MnO4 aq

)(Fe2 aq)(Mn 2 aq

)(H aq

)(OH2 l)(OH2 l

Pt Pt


E - + 0I 0I R

E E

Q

dtR

EdtIEdtPdQ

2

e

1costenergy

energyuseful

e

dW

dQ

Joule heating: 100 % conversion

?E IRE

49

EMF: ElectroMotive Force


QRT

EE lnF

EMF

Nernst equation

LLterm IREE LiEMF EEE

Li

EMF

RR

EI

cellEMF EE

LiEMF IRIRE

50



LLterm IREE LiEMF EEE

Li

EMF

RR

EI

Li

LEMFL

RR

REE

LiEMF IRIRE QRT

EE lnF

EMF

Nernst equation

cellEMF EE

51


QRT

EE lnF

EMF

Nernst equation

cellEMF EE

Li

LEMFL

RR

REE

tR

Edt

R

EdQ

L

2

L

2

L

LL

constantL E

e

L

e

L

W

Q

dW

dQ

52


QRT

EE lnF

EMF

Nernst equation

cellEMF EE

Li

LEMFL

RR

REE

tR

Edt

R

EdQ

L

2

L

2

L

LL

constantL E

tGGdtdW rre

IFt /

e

L

e

L

W

Q

dW

dQ

53


QRT

EE lnF

EMF

Nernst equation

cellEMF EE

Li

LEMFL

RR

REE

tR

Edt

R

EdQ

L

2

L

2

L

LL

constantL E

tIEtWdW EMFeee

L

e

L

W

Q

dW

dQ

54


QRT

EE lnF

EMF

Nernst equation

cellEMF EE

Li

LEMFL

RR

REE

tR

Edt

R

EdQ

L

2

L

2

L

LL

constantL EEMFL

2

L

IER

E

e

L

e

L

W

Q

dW

dQ

tIEtWdW EMFee

55


QRT

EE lnF

EMF

Nernst equation

cellEMF EE

Li

L

EMF

L

EMF

L

EMFL

2

L

EMFL

2

L

/

/

RR

R

IE

IE

E

E

EE

E

IER

E

56


QRT

EE lnF

EMF

Nernst equation

cellEMF EE

Li

L

EMF

L

EMF

L

EMFL

2

L

EMFL

2

L

/

/

RR

R

IE

IE

E

E

EE

E

IER

E

Li

L

RR

R

57

Summary Lecture 6: Efficiency of processes

Qh

Qc

Wout

Win

Qh

Qc

Win

Wout

58

Summary Lecture 6: Energy conv.: Carnot cycle Carnot cycle


Q→W

Carnot cycle


W→Q c

c

h

h

T

Q

T

Q

h

c1T

T

ch

c

TT

T

c

59

Summary Lecture 6: Energy convers.: Batteries


QRT

EE lnF

EMF

Nernst equation

cellEMF EE

e

L

dW

dQ

Li

LEMFL

RR

REE

Li

L

RR

R

Documents

U dU W Q - Solid State Chemistry - Solid State ChemistryFor all ellements in their reference states at T For all ellements in their reference states at T ' 4 ' 4 ' 4 f G m ,i f H