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物理化学电子教案 — 第七章 PowerPoint PPT Presentation


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物理化学电子教案 — 第七章. 第七章 统计热力学基础. §7.1 概论. § 7.2 Boltzmann 统计. § 7.3 配分函数. § 7.4 各配分函数的计算. § 7.5 配分函数对热力学函数的贡献. § 7.6 单原子理想气体热力学函数的计算. § 7.7 双原子理想气体热力学函数的计算. § 7.1 概论. 一 . 统计热力学的研究方法. 二 . 统计热力学的基本任务(目的). 三 . 统计热力学的优点与不足. 四 . 定位体系和非定位体系. 五 . 独立粒子体系和相依粒子体系. 六 . 统计体系的分类.

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物理化学电子教案 — 第七章

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7.1

7.2Boltzmann

7.3

7.4

7.5

7.6

7.7


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7.1

.

.

.

.

.

.

.


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()


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.


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1.localized system


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2.non-localized system


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1.assembly of independent particles


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2.assembly of interacting particles


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Maxwell-BoltzmannBoltzmannBose-EinsteinFermi-Dirac

1900Plonck

BoltzmannBoltzmann


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1924Bose-EinsteinFermi-Dirac

Boltzmann


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2.

.

1.probability


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P

.

3.

U, V N

4.


7 2 boltzmann

7.2 Boltzmann

.

.

.

.

.

.Boltzmann

.


Boltzmann

.Boltzmann

N


Boltzmann1

.Boltzmann

469

,


Boltzmann2

(1)

.(Boltzmann)


Boltzmann3

.(Boltzmann)

mlnmln

N mPmlnm / ln

5101 1.11015 1.271014 0.112 0.9370

5102 2.710299 1.3510298 0.05 0.9904

5103 1.6103008 2.5103006 0.015 0.9987

5104 2.51030100 0.811030098 0.003 0.9998

5105 5.610301026 1.410301022 0.000025 1.0000


Boltzmann4

.Boltzmann

B

lnB=lnN!lnNi!

lnN!=NlnNN

lnB=NlnNNNilnNi+Ni

d(lnB)=0N = NiU = iNi


Boltzmann5

.Boltzmann

d(lnB)=-lnNidNi -dNi+dNi =-lnNidNi

d1=dNi

d2=idNi

-lnNidNi +dNi+idNi= 0

-lnNi ++idNi = 0

dNi0 -lnNi ++i= 0


Boltzmann6

Lagrange

.Boltzmann

Lagrange


Degeneration

.degeneration


Degeneration1

.degeneration


Degeneration2

.degeneration


Boltzmann7

.Boltzmann

N


Boltzmann8

NN1

N1

.Boltzmann


Boltzmann9

.Boltzmann


Boltzmann10

.Boltzmann

UVN


Boltzmann11

StiringLagrange

.Boltzmann


Boltzmann12

.(Boltzmann)

UVN


Boltzmann13

StiringLagrange

.(Boltzmann)


Boltzmann14

.Boltzmann

1ij


Boltzmann15

.Boltzmann

2


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1

.

Boltzmann


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.

Stiring


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2

1

.


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3

.


7 3 bose einstein fermi dirac

7.3*Bose-Einstein Fermi-Dirac

. Bose-Einstein

.Fermi-Dirac

.


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7.4

.

.

.

.


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Boltzmann

q(partition function)1 BoltzmannqBoltzmannq

.


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.

q

qqqq


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( )( )( )( )

.


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.


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.


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.


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N

1HelmholzA


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2 S


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3U


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4GibbsG


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(5)H

(6)CV


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.


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.


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AS G

.

UH CV


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7.5

.

.

.

.

.


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.


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.

sn


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.


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.

qnqn


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F, Cl

.


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.

j 2j+1


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.

j qe


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.


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m

h

.


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.


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.


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a b c

.


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N

.


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.

1Helmholtz


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.

2

-


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.

-

1mol N k = R,


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3

4


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.

5Gibbs


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.


1 helmholtz a

1HelmholtzA


1 helmholtz a1

12

1HelmholtzA


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2

-


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3


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N

4


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A

5


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5

1 mol L , Lk = R , 1 mol


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T

5


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6

AV


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1

JI r

.


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.


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I H2

.


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2 =2

3

.

2 =2


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1

=0

.


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,,

.


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=1

.


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,

.


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2

, n

(3n-5) (3n-6)

.


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.


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.

j


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1Helmholtz

.

2


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4

3

.


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.


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.

H G


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1Dulong-Petit()

2Einstein

3DebyeT

7.6*


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7.7

.

.


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.

5


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.


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.


Q e q r q t s m

.qe qr qtSm


Q e q r q t s m1

298.15 K1 molO2(g)V , , O2

.qe qr qtSm


Q e q r q t s m2

O2

.qe qr qtSm


Q e q r q t s m3

khO2,

.qe qr qtSm


Q e q r q t s m4

.qe qr qtSm


Q e q r q t s m5

.qe qr qtSm


Q e q r q t s m6

-Nk=R,

.qe qr qtSm


Q e q r q t s m7

.qe qr qtSm


Q e q r q t s m8

.qe qr qtSm


7 8 r g m

7.8 rGm


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0 K

AGHU p


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0K

free energy function


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0K


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1


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2


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3

4D


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5


Heat content function

T298.15 K

heat content function


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q

f

D + E = G

V f


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