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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


7.1

.

.

.

.

.

.

.


.

()


.


.


.

1.localized system


.

2.non-localized system


.

1.assembly of independent particles


.

2.assembly of interacting particles


.

Maxwell-BoltzmannBoltzmannBose-EinsteinFermi-Dirac

1900Plonck

BoltzmannBoltzmann


.

1924Bose-EinsteinFermi-Dirac

Boltzmann


2.

.

1.probability


P

.

3.

U, V N

4.


7.2 Boltzmann

.

.

.

.

.

.Boltzmann

.


.Boltzmann

N


.Boltzmann

469

,


(1)

.(Boltzmann)


.(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


.Boltzmann

B

lnB=lnN!lnNi!

lnN!=NlnNN

lnB=NlnNNNilnNi+Ni

d(lnB)=0N = NiU = iNi


.Boltzmann

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

d1=dNi

d2=idNi

-lnNidNi +dNi+idNi= 0

-lnNi ++idNi = 0

dNi0 -lnNi ++i= 0


Lagrange

.Boltzmann

Lagrange


.degeneration


.degeneration


.degeneration


.Boltzmann

N


NN1

N1

.Boltzmann


.Boltzmann


.Boltzmann

UVN


StiringLagrange

.Boltzmann


.(Boltzmann)

UVN


StiringLagrange

.(Boltzmann)


.Boltzmann

1ij


.Boltzmann

2


1

.

Boltzmann


.

Stiring


.


2

1

.


3

.


7.3*Bose-Einstein Fermi-Dirac

. Bose-Einstein

.Fermi-Dirac

.


7.4

.

.

.

.


Boltzmann

q(partition function)1 BoltzmannqBoltzmannq

.


.

q

qqqq


( )( )( )( )

.


.


.


.


.

N

1HelmholzA


.

2 S


.

3U


.

4GibbsG


.

(5)H

(6)CV


.


.


AS G

.

UH CV


7.5

.

.

.

.

.


.


.

sn


.


.

qnqn


F, Cl

.


.

j 2j+1


.

j qe


.


m

h

.


.


.


a b c

.


N

.


.

1Helmholtz


.

2

-


.

-

1mol N k = R,


.

3

4


.

5Gibbs


.


1HelmholtzA


12

1HelmholtzA


2

-


3


N

4


A

5


5

1 mol L , Lk = R , 1 mol


T

5


6

AV


1

JI r

.


.


I H2

.


2 =2

3

.

2 =2


1

=0

.


,,

.


=1

.


,

.


2

, n

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

.


.


.

j


1Helmholtz

.

2


4

3

.


.


.

H G


1Dulong-Petit()

2Einstein

3DebyeT

7.6*


7.7

.

.


.

5


.


.


.qe qr qtSm


298.15 K1 molO2(g)V , , O2

.qe qr qtSm


O2

.qe qr qtSm


khO2,

.qe qr qtSm


.qe qr qtSm


.qe qr qtSm


-Nk=R,

.qe qr qtSm


.qe qr qtSm


.qe qr qtSm


7.8 rGm



0 K

AGHU p



0K

free energy function


0K


1


2


3

4D



5


T298.15 K

heat content function


q

f

D + E = G

V f



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