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1
Polymer Thermodynamics
Prof. Dr. rer. nat. habil. S. Enders
Faculty III for Process ScienceInstitute of Chemical EngineeringDepartment of Thermodynamics
Lecture
0331 L 337
1. Introduction and Basic Thermodynamics
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2Polymer Thermodynamics
Lectures Friday 12.00 – 16.00 o‘clockRoom: TK 17
schedule
from 17. of April until 22. of May 2009
1. of May is official holiday
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3Polymer Thermodynamics
Contact Information:Tel.: 030 314 22755 Fax: 030 314 22406 E-Mail: [email protected] or [email protected]: TU Berlin, Sekr. TK 7, Straße des 17. Juni 135, 10623 Berlin
Consulting hours: Monday 14-15 o’clock, room TK 112
Office: Ms. Peters [email protected] hours: Wednesday 9.30-11.30 o’clock
Room TK 111
Prof. Dr. rer. nat. habil. S. Enders
Faculty III for Process ScienceInstitute of Chemical EngineeringDepartment of Thermodynamics
http://www.thermodynamik.tu-berlin.deactual information's:
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4Polymer Thermodynamics
Prof. Dr. rer. nat. habil. S. Enders
Faculty III for Process ScienceInstitute of Chemical EngineeringDepartment of Thermodynamics
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5Polymer Thermodynamics
Material: available as downloads
Newslecture presentations and exercisesinternet Links
Lehre → Polymer Thermodynamics
Downloads http://www.thermodynamik.tu-berlin.de/
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6
Polymer ThermodynamicsRecommended literature
• J. Bicerano, Prediction of Polymer Properties, Marcel Dekker, 1993.• H.G. Elias, Makromoleküle; Band 2, Physikalische Strukturen und Eigenschaften,
Wiley-VCH Verlag, 2000.• K. Kamide, Thermodynamics of Polymer Solutions Phase Equilibria and Critical
Phenomena, Elsevier, 1990.• P.J. Flory, Principles of Polymer Chemistry, Cornell University Press 1953.• G. Astarita, S.I. Sandler, Kinetic and Thermodynamic Lumping of Multicomponent
Mixtures, Elsevier, 1991.• D.W. van Krevelen, Properties of Polymers, Elsevier, 1990.• R.P. Danner, M.S. High, Handbook of Polymer Solution Thermodynamics,
American Institute of Chemical Engineers, USA, 1993. • R. Koningsveld, W.H. Stockmayer, E. Nies
Polymer Phase Diagrams: A TextbookOxford University Press (2001) ISBN-13: 9780198556343.
• L.H. Sperling, Introduction to Physical Polymer Science, 3 rd. Ed., Wiley –Interscience (2001).
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7Polymer Thermodynamics
Attention: We have prepared all materials with great care. Nevertheless some errors can be involved.
3. Error Challenge
If you have found an error, please send my an E-Mail. [email protected]
The student, having found the most errors, will win a price.
Please use in the title: Error_Polymer
Invitation
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8Polymer Thermodynamics
Examination
oral, individual examinationduration 30 minutescontent: topics of the lecturePlease, bring along student ID and personal IDPlease, make a appointment in my office or via email
characteristic feature
Time: 25. of May until 29. of May 2009
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9Polymer Thermodynamics
„If you do not know thermodynamics youwould not get a bad design, you would get a wrong design!“
M. Parker, CEO Dow Chemical Company (2002)
Why do we need polymer thermodynamics ?
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10Polymer Thermodynamics
Why do we need polymer thermodynamics ?
polystyrene
Which liquid can be put in cups made from polystyrene ?
Interaction of liquids (solvent) with polymers
solubility of polymersthermic stability of polymers
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11Polymer Thermodynamics
Why do we need polymer thermodynamics ?
Polymer Production: based on Petrol (Petrol distillation)
Which polymers can be produced ? At which temperature ? Is the polymerization reaction an voluntary process ?Which solvent should be used ?
rubber productionplant
monomer
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12Polymer Thermodynamics
Why do we need polymer thermodynamics ?
The most industrial polymer production processes take place in solutions.How it is possible to remove the solvent ?Which solvent should be used ?How we can avoid undesired phase separation in the production plant ?What are the thermodynamic properties (i.e. heat capacity, vapor pressure)
of polymer solutions?
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13Polymer ThermodynamicsWhy do we need polymer thermodynamics ?
1. example: foam polystyrene = expanded polystyrene = EPS
Application of EPS
construction (heat, sound and tension insulation)
street buildinginsulating slab
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14Polymer Thermodynamics
Why do we need polymer thermodynamics ?
1. example: foam polystyrene = expanded polystyrene = EPS
construction (heat, sound and tension insulation)
Building by F. Hundertwasser (1928-2000) (Austrian artist) in Darmstadt (Germany)
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15Polymer ThermodynamicsWhy do we need polymer thermodynamics ?
1. example: foam polystyrene = expanded polystyrene = EPS
Application of EPSpackaging
safety helmet for bikers
blister packaging material of any shape
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16Polymer ThermodynamicsWhy do we need polymer thermodynamics ?
1. example: foam polystyrene = expanded polystyrene = EPS
1 2 3 4 5 6 7
Application of EPSlegendred: construction
(heat and sound insulation)
blue: packagingyellow: cupsgrey: others1 Europe2 North-America3 Africa/West-Asia4 Latin-America5 Japan6 Asia7 World
Caused by the great climatic differences the application depends strongly on the region.
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17Polymer Thermodynamics
Why do we need polymer thermodynamics ?
1. example: foam polystyrene = expanded polystyrene = EPS
polystyrene plant (Dow Chemical Company)
Thermodynamic task: Description of the involved phase equilibria during the whole production process.
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18Polymer Thermodynamics
Why do we need polymer thermodynamics ?
1. example: foam polystyrene = expanded polystyrene = EPS
Expansion: Polystyrene particle having a diameter of 1mm will be expanded using pentane.
first step: Heating of PS to 100-120°C(T>Tg) using hot water vapor
second step: Pentane will be evaporated and pressed into polymer particles. This leads to new particle (pearls) having a diameter of 3 mm.
Thermodynamic task: Can we predict the glass temperature
of polymers?What is the vapor pressure of pentane?Does the interfacial properties play an
important role?
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19Polymer ThermodynamicsWhy do we need polymer thermodynamics ?
1. example: foam polystyrene = expanded polystyrene = EPSExpansion: Polystyrene particle having a diameter of 1mm will be expanded using
pentane.Third step: Expanded polymer particle will be given in the desired forming.Fourth step: Little holes will be made on the polymer wall.Fifth step: Hot air will be pressed in the system in order to remove the pentane.Sixth step: Heating the polymer well above the glass transition temperature in
order to increase the volume by the factor 2 – 2.5.Seventh: Cooling down the whole system. The foam takes his final shape.Eight: The product will be stored several days in order to allow the completely remove
of pentane.
Thermodynamic task: At which conditions will the air be able to replace pentane ?How will the volume of the polymer be changed during heating and cooling procedures?Does a special interaction between the polymer and the fluid plays a role ?At which temperature the critical state of the gas can be found ?Is there a potential for simplification or improvement of the process ?What is the role of permeation in the procedure ?
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20Polymer Thermodynamics
Why do we need polymer thermodynamics ?
Foaming of Polymers
Thermodynamic task:It is possible to use an alternative gas (hydrogen, nitrogen, carbon dioxide)?At which pressure can the foaming process be carried out ?
1. example: foam polystyrene = expanded polystyrene = EPS
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21Polymer Thermodynamics
Why do we need polymer thermodynamics ?
1. example: foam polystyrene = expanded polystyrene = EPS
Application for heat insulation:Important property: heat conductivity
30
30
Polymer density [g/m3]
0.025air
0.019 to 0.024polyurethane-foam
0.032EPS
Heat conductivity[W/mK]
Material
Thermodynamic task: Why ? Which difference in layer thickness follows fromthe different heat conductivities, if the insulation power should be identical ?
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22Polymer Thermodynamics
Why do we need polymer thermodynamics ?
2. example: polymers for medical applications
glasses, contact lenses, denture
valve, blood vessels, disc, artificial nervesdialysis membranes, dialysis tubes, artificial hip joint endoprosthesisimplant for skin
artificial knee joint
others 11%
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23Polymer Thermodynamics
Why do we need polymer thermodynamics ?
2. example: polymers for medical applications
Application: bags for blood, drug-formulations,safety gloves, tubes, blister-package
Advantage: suitable for thermic formability,high flexibility, excellent chemical resistance, very low potential for allergy
Disadvantage: phthalates is used as softener, but they can be toxic (teratogen and cancerogen) for humans
Challenge for thermodynamics:How can we produce ultra pure PVC with a negligible amount of softener ?How are the relation between polymer properties (i.e. molecular weight distribution ) and flexibility ?Can we use phase equilibria (demixing of polymer solution) to made tailor-made polymers?Which procedure can be applied for sterilization ?
PVC = poly(vinyl chloride)
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24Polymer Thermodynamics
Why do we need polymer thermodynamics ?
2. example: polymers for medical applications
PE – poly(ethylene)
Application: foil, packaging, containerstubes, bottles, implant (knee, hip)
Advantage: excellent chemical resistancehigh stiffness
Challenge for thermodynamics:How we can produce ultra pure PE ?What are the relations between polymer properties (i.e. molecular weight distribution )and other physical properties, like permeation, solubility?
Can we use phase equilibria (demixing of polymer solution) to made tailor-made polymers?Which procedure can be applied for sterilization ?LDPE is produced via high-pressure polymerization. What do we know about the influence of pressure on the phase equilibria ?
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25Polymer Thermodynamics
Why do we need polymer thermodynamics ?
2. example: polymers for medical applications
PS = polystyrene
Application: package, infusion equipment, tubes
Advantage: chemical resistanceexcellent deformability excellent transparence
Thermodynamic challengeHow can we produce tailor-made polymers basedon polystyrene, maybe copolymerization?Which copolymer should be applied for which purpose?What is the influence of chemical composition onthe properties of the copolymer ?
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26Polymer Thermodynamics
Why do we need polymer thermodynamics ?
2. example: polymers for medical applications
Application: artificial thread, artificial tissuemembranes for dialysisheart valve, syringe
Advantage: chemical resistanceexcellent deformability
Challenge for thermodynamics:How can we produce ultra pure PP ?What are the relations between polymer properties (i.e. molecular weight
distribution ) and other physical properties, like permeation, solubility chrystallinity?
Can we use phase equilibria (demixing of polymer solution) to made tailor-made polymers?
Which procedure can be applied for sterilization ?
PP = polypropylene
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27Polymer Thermodynamics
Why do we need polymer thermodynamics ?
2. example: polymers for medical applications
PLA = poly(lactic acid) O R C
O
O R1 O C
O
R2 C
O nI II
R = CH-CH3Advantage: biological degradation is possibletwo optical isomers poly( L-lactic acid) and poly( D-lactic acid)
Properties: partial crystallinemelting temperature 180°C
Properties: amorphousmelting temperature 75°C
copolymerization in order to tune the physical properties
Thermodynamic challenge: How is the influence of copolymer composition onphysical properties (chrystallinity, degradation, pH-stability)?
Application: tissue-engineering,artificial bone and articular
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28Polymer Thermodynamics
Why do we need polymer thermodynamics ?
2. example: polymers for medical applicationsPLA = poly(lactic acid) as controlled drug delivery systems
encapsulation of drugs
Diseases: chemotherapy, hormone therapy
Advantage: long-term therapy over monthsis possible
Thermodynamic challenge: Can we predict the maximal amount of drug in the polymerparticles? Do we have any influence on this amount ?What do we know about the involved swelling equilibria ?How can we optimized the degradation behavior ?
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29Polymer Thermodynamics
Why do we need polymer thermodynamics ?
Let us start to learn something about polymer thermodynamics !
The department of Thermodynamics und Thermic Engineering wishes you a lot of fun with thermodynamics and complete success.
Let us start to repeat the basics of thermodynamics, namely some basic terms, the first and second law of thermodynamics.
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30Polymer Thermodynamics
Basic terms of Thermodynamics
System and SurroundingSystem: certain sector of matter containing a large number of particles (≈1023) Examples: content of beaker, content of thermos bottle, chemical reactor, steam engine
system surrounding
material transfer energy transfer
open system closed system isolated systemFor heat and work holds the definition that heat or work put into the system has a positive sign. 0
0from surrounding to system dW or dQ endothermicfrom system to surrounding dW or dQ exothermic
→ > →→ < →
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31Polymer Thermodynamics
phase: Phase is a substance (pure phase) or a mixture of substances having spatial constant properties. The area, where the properties will bechanged is called interphase.
Liquid L
Vapor V
L
Vvapor density
ρV
liquid densityρL
interphase
Basic terms of Thermodynamics
Phase
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32Polymer Thermodynamics
phase: Phase is a substance (pure phase) or a mixture of substances having spatial constant properties. The area, where the properties will bechanged is called interphase.
Solid S
Liquid L
S
Lliquid density
ρL
solid densityρS
interphase
Basic terms of Thermodynamics
Phase
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33Polymer Thermodynamics
phase: Phase is a substance (pure phase) or a mixture of substances having spatial constant properties. The area, where the properties will bechanged is called interphase.
Liquid 2 L2
Liquid 1 L1L1liquid density
ρL1
liquid densityρL2
interphase
Basic terms of Thermodynamics
Phase
Example:oil + water
L2
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34Polymer Thermodynamics
state: Thermodynamic state of system is characterized by its state variables(i.e. temperature, pressure, density, composition, energy).
Basic terms of Thermodynamics
State
state functions (i.e h,u,f,g,s) depend on state variables (i.e. T,P,V, ni).
General: z=f(x,y)Change of state functions dz → exact differential
0 0
( , ) ( , ) ( , ) ( , ) ( , ) ( , )lim lim
( , ) ( , )( , ) ( , ) ( , ) (
( , ) ( , )( , )
, )
x yy x
y
y x
x
z x y z x x y z x y z x y z x y y z x yx x y y
z x y z x ydx z x dx y z x y
z x y z x ydz x y d
dy z x y dy z x yx y
x dyx y
Δ → Δ →
⎛ ⎞∂ + Δ − ∂ + Δ −⎛ ⎞ = =⎜ ⎟⎜ ⎟∂ Δ ∂ Δ⎝ ⎠ ⎝ ⎠
⎛ ⎞∂ ∂⎛ ⎞ = + − = + −⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠
⎛ ⎞∂ ∂⎛ ⎞= + ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠exact differential
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35Polymer Thermodynamics
state: Thermodynamic state of system characterized by its state variables(i.e. temperature, pressure, density, composition, energy).
Basic terms of Thermodynamics
State
state functions (i.e h,u,f,g,s) depend on state variables (i.e. T,P,V, ni).
General: z=f(x,y)Change of state functions dz → exact differential
, ,, q s r qr s
z z zdz dq dr dsq r s
⎛ ⎞∂ ∂ ∂⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂⎝ ⎠ ⎝ ⎠⎝ ⎠
partial differential coefficient related to experimental quantities
i.e. PP
P P T P
H S c H Vc V TT T T P T
∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = −⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠
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36Polymer Thermodynamics
Basic terms of Thermodynamics
Statestate functions: example
y
x
z(x1,y1)
z(x2,y2)
Y
Z dXX∂⎛ ⎞
⎜ ⎟∂⎝ ⎠
X
Z dYY∂⎛ ⎞
⎜ ⎟∂⎝ ⎠
2 23( , ) 3 22
z x y x xy y= + +
( ) ( )
6 2
2 3
6 2 2 3
y x
y
x
z zdz dx dyx y
z x yx
z x yy
dz x y dx x y dy
⎛ ⎞∂ ∂⎛ ⎞= + ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠∂⎛ ⎞ = +⎜ ⎟∂⎝ ⎠
⎛ ⎞∂= +⎜ ⎟∂⎝ ⎠
= + + +
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37Polymer Thermodynamics
Basic terms of Thermodynamics
State
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38Polymer Thermodynamics
Basic terms of Thermodynamics
State
ΔZ = Zend - Zbeginning
state functions depend not from the route
0 5 10 15 20-100
-80
-60
-40
-20
0
20
40
60
80
state at end
state at beginning
route 1 route 2 route 3
f(X)
X
ΔZ = Δ1Z = Δ2Z=Δ3Z
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39Polymer Thermodynamics
Basic terms of Thermodynamics
State – Functions
Calculation of changes in state functions
2 23( , ) 3 22
z x y x xy y= + +
change in state = state at end – state at beginning
i.e. state at beginning: x=2, y=4state at end: x=5, y=1
(5,1) (2,4) 86.5 52 34.5z z zΔ = − = − =
Example:
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40Polymer Thermodynamics
Basic terms of ThermodynamicsState – Change
i.e. What is the change in volume, if the substance is transferred from state V(P,T,n) into state V(P+DP, T+DT,n) ?
2, , ,P n T n P T
V nR V nRT V RTT P P P n P∂ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = − =⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠
, , ,
( , , )
P n T n T P
V f T P nV V VdV dT dP dnT P n
=
∂ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠
nRTPV nRT VP
= → =
2
nR nRT RTdV dT dP dnP P P
= − +
Ideal gas law:
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41Polymer Thermodynamics
Basic terms of Thermodynamics
State – Functions
ΔZ = Zend - Zbeginning
Law of Schwarz: The sequence of differentiation can be interchanged.
qr
z zdz dq drq r
⎛ ⎞∂ ∂⎛ ⎞= +⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠⎝ ⎠for
2 2z zq r r q
⎛ ⎞ ⎛ ⎞∂ ∂=⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠
( , )z f q r= is valid
qr q r
z zr q q r
⎛ ⎞⎛ ⎞⎛ ⎞∂ ∂ ∂ ∂⎛ ⎞= ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠⎝ ⎠⎝ ⎠ ⎝ ⎠
state functions depend not from the route
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42Polymer Thermodynamics
Basic terms of Thermodynamics
State – Functions
ΔZ = ZEnd - ZBeginning
( , ) ( , ) ( , ) ' ' '
( , ) ( , )( , )
( ,
( , ) ( , ) ( , ) ( , )
) ( ,, )
,
(
)
)
(
y x
y x
z x y f x y g x y y uv vu
with
f x y f x ydf x y dx dyx y
g x y g x yd
dz x y g x y df x y f x y dg
g x y dx dy
x y
x y
= = +
⎛ ⎞∂ ∂⎛ ⎞= + ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠
⎛ ⎞∂ ∂⎛ ⎞= + ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠
= +
Rule for differentiation of products
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43Polymer Thermodynamics
Basic terms of ThermodynamicsState – Quantities
state quantities can be extensive or intensive.
Extensive state quantities will double their value if two equal systems will be united toone new system.
i.e. mass m, volume V, energy U
Intensive state quantities will keep their value if two equal systems will be united toone new system.
i.e. temperature T, pressure P, molar volume v, specific volume vsp
molar quantities
Vvn
=
n = amount of substance
specific quantities
spV vvm M
= =
m = mass, M = molar mass
density [g/l]concentration [mol/l]
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44Polymer Thermodynamics
Basic terms of Thermodynamics
Processes
The equilibrium state is the final state of the process. At equilibrium no changes can be observed, experimentally.
state 1 state 2 state 3process process
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45Polymer Thermodynamics
Basic terms of Thermodynamics
ProcessesProcesses: Transfer from initial (beginning) state to the final (end) state.
Process quantities: depend on the routethey are related to a process and not to a systemi.e. work and heat
extensive quantitiesi.e. work W, heat Q
intensive quantitiesi.e. molare enthalpies of chemical reactions
no heat exchangeconstantvolume
constanttemperature
constantpressure
adiabaticisochoreisothermisobar
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46Polymer Thermodynamics
Basic terms of Thermodynamics
Processes
heat and workfrom mechanics
dW Fds=
force route
i.e. to uplift of mass m from the height h1 to the height h2
2 2
1 1
2 1( )h h
HUBh h
W Gdh mg dh mg h h= = = −∫ ∫i.e. Acceleration of mass m from speed v=0 to speed v1
1 1 121
0 0 0
12
s v v
BedvW mads m vdt mvdv mvdt
= = = =∫ ∫ ∫
WHUB=mg(h2-h1)
h2h1
mg
h
WBe=mV12/2
V1
mV
V
dv dsa vdt dt
= =
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47Polymer Thermodynamics
Basic terms of Thermodynamics
Processes
V1
V2s2
s1
weight G area A
During expansion of an ideal gas against an outside acting force F caused be the weight, G, the work is given by:
2
1
2
1
2
1
S
VolS
V
Vol
V
VolVV
W Fds F PA dV Ads
dVW PAA
W PdV
= = =
= −
−
= −
∫
∫ ∫V2
V1
pV
dW Fds=
force routethermodynamics: mechanical work Wvol caused by themovement of the system limits via volume change
Mechanical work is always connected with a vectored movement of particles.
ds
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48Polymer Thermodynamics
Basic terms of Thermodynamics
Processes
V1
V2s2
s1
weight G area A
2 2
1 1
S V
VolS V
W Fds PdV= − = −∫ ∫
Thermodynamics: mechanical work, Wvol
The sign of mechanical work:
2 1
1 2
0 0
0 0
Vol
Vol
V V V W
V V V W
> → Δ > → <
> → Δ < → >→ work done by the system
→ work done on the system
ds
system
surrounding
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49Polymer Thermodynamics
Basic terms of Thermodynamics
Processesmechanical work at constant extern pressure (i.e. atmospheric pressure)
( )
2 2
1 1
2 1
2 1 0
S V
VolS V
Vol
Vol
W Fds PdV
W P V VV V W
= − = −
= − −
> → <
∫ ∫
V1
weight G
P
V2
weight G
P
state 1 state 2
The work is done by the system.
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50Polymer Thermodynamics
Basic terms of Thermodynamics
Processes
2
1
2 2
1 1
2
1
1 2
1
ln
0
V
VolV
V V
VolV V
Vol
Vol
W PdV mit PV nRT
nRTW dV nRT dVV V
VW nRTV
V V W
= − =
= − = −
⎛ ⎞= − ⎜ ⎟
⎝ ⎠> → >
∫
∫ ∫V2
weight G
P2
state 2
V1
weight G
P1
state 1
mechanical work at variable extern pressure
The work is done on the system.
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51Polymer Thermodynamics
Basic terms of Thermodynamics
Processes
21 2
1 1 2
lnVolV nRT nRTW nRT P PV V V
⎛ ⎞= − = =⎜ ⎟
⎝ ⎠
mechanical work at variable extern pressure
P1
P2
nRTPV
=
Isotherme
V2
V1
P
V
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52Polymer Thermodynamics
Basic terms of Thermodynamics
Processes
Two groups of hikers would like to go to mountain. The first group takes the direct way. The second group uses the serpentines.On the top of the mountains both groups have the same state (the same height), but the second group has done more work.
Change in state variables (i.e. height): depends not on the routeChange in process quantities (i.e. work): depends on the route
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53Polymer Thermodynamics
Basic terms of Thermodynamics
ProcessesHeat: is equal to the change of energy related to the energy of molecular motion.
- process quantity → depends on the way- is related to processes and not to systems
heat exchanges withchange of temperature
heat exchanges withoutchange of temperature
dQ TCd=heat capacity C
i.e. Heating of liquid in beakerlatent heat i.e. phase change,
chemical reactionsolution, adsorption
dQ qdζ=q molare heat of reactionζ reaction coordinate
dQ < 0 exothermicdQ > 0 endothermic
Ccn
=
specific heat capacity: spCcm
=
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54Polymer Thermodynamics
Basic terms of Thermodynamics
Processes
ice-20 0 20 40 60 80 100
Hea
t Q
T [°C]
water + ice
water
water + vapor
vapor
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55Polymer Thermodynamics
Basic terms of Thermodynamics
Processeswork heat
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56Polymer Thermodynamics
Basic terms of Thermodynamics
Equilibrium
a) thermic equilibrium: TI = TII = ... = T→ constant temperature
b) mechanical equilibrium: PI = PII = ... = P→ constant pressure
c) material equilibrium: μiI= μi
II= ... = μin
→ The chemical potential of the component, i, is equalin all present phases.
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57Polymer Thermodynamics
Basic terms of Thermodynamics
Equilibrium
PotE mgh=
stable
EPot→ global minimum
stable against all
perturbations
instable
EPot→ global maximum
instable against all
perturbations
metastable
EPot→ local minimum
stable against small
perturbations