Basic Concepts of Thermodynamics

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Basic Concepts of Thermodynamics

• Dept. Phys., Tunghai Univ.
• Biophysics, C. T. Shih

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Part.1 ????
3
Why Thermodynamics?(1/3)

• ???????,???????,?????????????????
• ????????????????,??.....

4
Why Thermodynamics?(2/3)

• ???????????????,???? mission impossible!??
• ??????????????
• ?????????????????
• ????,???????

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Why Thermodynamics(3/3)

• ????,????????,??......

• ???????????????????......????????
• ????????????,???????

???????????,???????????????,??????
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The Concept of Temperature and Thermal
Equilibrium (1/2)

• ????????????????
• ??????????????????????,????????,???????????
• ????????A?B????,B?C????,?A?C????
• ??????????????????????????????,???????,??????????,
  ??????????????

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The Concept of Temperature and Thermal
Equilibrium (2/2)

• ????????????
• ??????,?????????????(????????)
• ?????????(?????)????????????(??????????......)
• ?????????????????????????????????????????????????
  ??
• ???????????????????,???????????????,??????????

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Reaction

• ???????????????
• ??????????,???????????,??????????
• Q ???????????
• ?????????????????????????(??????......)
• ?????????,??????(?????......)

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First Law of Thermodynamics

• dUdQ-dW
• ??(????)dU??,dQ??(????),dW?(????)
• dWPdV??????????????????????????????

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Ideal Gas (1/3)

• ???????PVNkTnRT
• k Boltzmann??1.3810-23J/K
• R ??????8.31J/K-mole
• N ????,n ???
• ??????????
• ??Boyle???Charles???Gay-Lussac??

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Ideal Gas (2/3)

• ??????ltlt??????
• ??????,????????
• ????????????
• ????????????
• ???????????

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Ideal Gas (3/3)

• Kinetics
• ???????????
• ???????????????????Equipartition law

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Non-Ideal Gas (1/2)

• van der Waals Equation
• a, b ????,???????
• a ?????????????
• b ????????????????
• v???????

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Non-Ideal Gas (2/2)

• ?van der Waals ????v?????,??P,v??????????
• ???v3?
• ???P???,??????v??????,????????????,?????????
• Why? Whats the meaning of Tc?

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Phase Diagram

• ?????(equation of state)????????????????,????????
  ?????,?f(P,V,T,m)0,????????,???????????
• ???????????????????????,?????????
• ?????????,????

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Maxwell- Boltzmann Distribution (1/2)
See animation
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Maxwell- Boltzmann Distribution (2/2)

• P(v) ???P(v)dv????????v?vdv???????(v???)
• ??P(v)dvf(vx) f(vy) f(vz)dvxdvydvz
• ???????????,?P(v)P(v2)
• ??????????,??
• ??
• ??ltv2gt3kT/M ??????? N ???,????C?a,??Boltzmann-Max
  well Distribution

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Second Law of Thermodynamics

• Kelvin-Planck statement ????????(heat
  reservior)????Q??????W???(heat engine)???
• Clausius statement????????????????????????
• These two statements are equivalent!

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(No Transcript)
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Entropy

• Entropy?,????,????????????????????????? dSdQr/T
• ???????,?????????,?????????
• dQr?????????????????????(??????????)
• ?????????????????(??????)????????(??????????,??
  ???????)

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Entropy and Reaction (1/2)

• ???????????
• ??????
• ????
• ???????
• ???????????
• ???? entropy ???!

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Entropy and Reaction (2/2)

• ?????????????,????????,??????????????????????,?en
  tropy???
• ???????

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Entropy and Probability (1/2)

• ??????phase space ??,????,??x, y, z, vx, vy, vz
  ????
• ??????????????????
• ??????????????dxdydzdvxdvydvz?????
• ???N???,????????????????????WN!/(N1!
  N2!Ni!),Ni????????phase space?? i ??????

i



vx
x
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Entropy and Probability (2/2)

• ?????????????
• ?????W???????,??Maxwell-Boltzmann distribution
• ?????entropy??? SS1S2
• ???entropy??Boltzmanns entropy equation SklnW

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Free Expansion, Again

• ????????????,????????????????????,??????i?????????
  ???,??????W2NW,SklnWSNkln2SnRln2

i,1 i,2



vx
x
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Summary of Part 1

• ?????????
• ?????????
• ??????
• ????????
• ??????????????
• ?????????
• ?????

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Part.2 ?????
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Thermal Equilibrium (1/4)

• Fundamental equation?????S,V,N?external
  parameters(??????????)???,???UU(S,V,N1,N2,N3)
• ????SS(U,V,N1,N2,N3)
• ????????? fundamental equation ?

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Thermal Equilibrium (2/4)

• ? fundamental equation ???
• ????????????????
• ?? intensive parameters

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Thermal Equilibrium (3/4)

• T??,?(??????????,???)??entropy????????
• P??,??????????????
• mi????i???????(chemical potential),????(i)???????
  ?????
• ????????????
• ??dQTdS,dWmPdV,dWcSimidNi,?????????dUdQ-dWmd
  Wc

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Thermal Equilibrium (4/4)

• ???(????)????entropy????
• ????U1U2Uconstant
• ?????????,?dSdS1dS20

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Mechanical Equilibrium

• ???????????(U1U2constant),????????????(V1V2con
  stant),???????
• U?V?????,????????T1T2, P1P2

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Matter Flow Equilibrium

• ???????????(U1U2constant),???????(N1N2constant
  ),???????
• U?V?????,????????T1T2, m1m2

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Remark

• ????intensive parameters??????????,external
  parameters???????(potential)
• ?????????
• ??????????
• ????????????
• ????????,????????????????
• ?????????????entropy????????

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Processes

• Fundamental equation UU(S,V,N),????SS(U,V,N)?
  f(U,S,V,N)0
• ???,????????U,S,V???????????
• ????????????????
• ??????????????????
• ????????????????????
• ?????????,??S?????

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Extremum Principle (1/2)

• Entropy minimum principle The equilibrium value
  of any unconstrained internal parameter is such
  as to maximize the entropy for the given value of
  the total energy.
• Energy minimum principle The equilibrium value
  of any unconstrained internal parameter is such
  as to minimize the energy for the given value of
  total entropy.
• These two principles are equivalent!

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Extremum Principle (2/2)
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Legendre Transformations

• Fundamental equation UU(S,V,N),??extensive
  paramters(S,V,N)???
• ?????????,????intensive parameters(P,T,m)???
• Why? ???,(P,T,m)?(S,V,N)???????
• Legendre transformation???extensive/intensive
  ???????

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Helmholtz Free Energy
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Enthalpy
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Gibbs Free Energy
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Grand Canonical Potential
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Now the Extremum Principles become

• Hemholtz free energy is minimized at constant
  temperature
• Enthalpy is minimized at constant pressure
• Gibbs function is minimized at constant
  temperature and constant pressure
• All these principles are equivalent!

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Stability of Thermodynamic Systems (1/3)

• Mutual stability?????????????????,???????????????
  
• Intrinsic stability????????????
• dS0,d2Slt0
• dU0,d2Ugt0

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Stability of Thermodynamic Systems (2/3)

• ?dU0?d2Ugt0???,??????????????????(uU/N,fF/N,vV/
  N,ussd2u/ds2)

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Stability of Thermodynamic Systems (3/3)

• ???????????,??????????
• ???????????,??????????
• ????????,???????????,???????(homogenous),??????(ph
  ase transition),???????????????????

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First Order Phase Transition (1/6)

• ????,fundamental equation ????????homogeneity????
• ??? equation ???????????,??????????
• ???????????????liquid-gas phase
  transition?,????????

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First Order Phase Transition (2/6)

• ????????????van der Waals equation
• ????,????(T1T6)????????????

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First Order Phase Transition (3/6)

• Gibbs-Duhem Relation
• F(T) ??????,????????

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First Order Phase Transition (4/6)
G?? G??????
mG/N
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First Order Phase Transition (5/6)

• ?????,Gibbs free energyµN??,?????B,C,D,O,Q,R??,?E
  ,F,J,K,LM,N???(?????µ)
• ??D??O??µ???
• ??????? I ? II ?????

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First Order Phase Transition (6/6)

• First order phase transition ? entropy
  ???????(latent heat)
• Latent heat LT(SD-SO)

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Summary of Part.2

• Fundamental equation of thermodynamics
• Detailed description of equilibrium
• Extremum principle and different thermodynamic
  potential
• Stability of equilibrium and phase transition

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Part.3 ????
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Ensembles (1/2)

• ??????????????,?????????????(?????????etc.),???
  ????????
• ??????????,?????????????
• Ensemble average ensemble????????????????,???????
  ????????????????

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Ensembles (2/2)

• Microcanonical ensemble ensemble ??????N, V, U??
• Canonical ensemble ensemble ??????N, V, T ??
• Grand canonical ensemble ensemble ??????µ, V, T
  ??
• ???????(constant temperature, constant
  pressureetc.)????? ensemble ?????

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Microcanonical Ensemble
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Canonical Ensemble
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Grand Canonical Ensemble
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Canonical Ensemble (1/3)

• N, V, T ??,ensemble???????A
• ????????????E1,E2
• ???????????a1, a2
• a(a1, a2) ??????????
• ??a??????W(a),???????????W(a)????
• ??

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Canonical Ensemble (2/3)

• Ensemble ????????? j ?????????
• ?????A, aj???????,?W(a)????W(a)???????W(a),a???
  ????,?? Pjaj/A
• ???????canonical ensemble average?

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Canonical Ensemble (3/3)

• ?W(a)????,??Maxwell-Boltzmann distribution
• Q???partition function?,??????

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Grand Canonical Ensemble
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Quantum Statistics (1/3)

• ????????,???????????????????????
• ??? k ??????????? ek,??????????? nk
• ???? grand canonical ensemble partition function
  ??

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Quantum Statistics (2/3)

• ??????,??? Paulis exclusion principle,nk???0?1,??
  partition function ?
• ?????,?? k ?????????
• ??? Fermi-Dirac distribution

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Quantum Statistics (3/3)

• Boson system ?? exclusion principle,?? nk ???
  0,1,28,??? partition function ?
• ??,?? k ?????????
• ??? Bose-Einstein distribution

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Summary of Part.3

• Ensembles and ensemble average
• Partition functions of ensembles
• Thermodynamic variables and the partition
  function
• Quantum statistics