:

:::-::::

: :()()() (): ()():

.1:2:,

1.:,,,,,.2.:, .

localized system

non-localized system

. ... ..

.UVNi

N1, N2, , Ni

(3.1) (3.2) (3.3)(3.4)(3.4),tmtm

N(3.5),,,: (3.5)(3.6):1., . 2.(3.6) ,.

. : *i =N(3.6)(3.7)(3.7)

:S=kN=ktm,(3.6)(3.7):S=kNi-ku (3.8)(UN),S(NUV),(3.8),S[NU(UV)]N,:(3.8):

:dU=TdS-PdV,1/T: =-1/kT (3.9)(3.7): (3.10)(3.9)(3.8): S=kN-i/kT+U/T(3.11)

F=U-TS=-NkT-i/kT : (3.11)(3.12) ,i ,F(T VN),(3.12) F.(3.12)

.1.,,.:

nx,ny,nzx,y,zgi=1nx ny nz1 1 2 1 2 12 1 1 gi=3

(3.13):

UVN(3.14)tm,

,Nitm,Ni*,S,F: S=kNgi-i/kT +U/T (3.16) F=-NkTgi-i/kT (3.17) (3.15)

2. (3.14)N!.(3.18),, Ni*,S,F: (3.18)N,:

(3.20) SF (3.19)(3.21)

. ,,:1.,(3.19):(3.22)

2.0N0,(3.21): Ni=N0-i/kT (3.23)i=i-0i.,.,: P=P0-mgh/kT (3.24)Ph,P0(h=0),g,m,(3.23)0hT.

.,:(1),,.(2),,,...,(3.13):

,.NiNi,tt,NiNi+Ni,tt+t, (t+t)=NN-N+(Ni+Ni)gi --(Ni+Ni)(Ni+Ni)+(Ni+Ni) (3.26)(3.26)(3.25)::

Ni,,N,Ni=0.,t. t=0: (1+x)=x-x2/2+x3/3-

(3.27)

(3.28): :(3.28),,tm(tm+t).Ni,.

,. 1%, ,, () ,? (3.28) Ni=3*1019.cm-3,Ni/Ni=0.01 : :

,Ni,.tm,.,,.. U,V,N,,.t.,,P: P=/(a)

(a),(b)..tx,: Px=tx/,,.,.: P=1/(b)

. . U,V,N,1,2,,ig1,g2,,gi,:N1,N2,,Ni

(t1):(3.29)(3.31)(3.30): (3.30),.,:

(3.31)(3.32): S=k{gi(1+Ni*/gi)+ Ni*(1+gi/Ni*)} (3.33):,,.(3.32)

.,,,,.iNigi,giNi,,,.giNi:

,::(3.34)(3.35)

:(3.36),: S=k{Ni*(gi/Ni*-1)-gi(1-Ni*/gi)} (3.38).(3.37)

::+1,giNi, gi/Ni ,:::

...

,,.

e --i -1e --ie --i +1

Boltzmann. : 1.,gie -i/kT .(3.39)

2. ,.3.,,q ,.:(3.41),q . (3.39):(3.40)(3.41)

.

1.(N) HelmholzF S(3.42)

: (3.43)(3.20): (3.44)

3U(3.45)

4GibbsGdF=-SdT-PdV,G=F+pV,(3.46)(5)H(3.47)

(6)CV(3.48) 2. ,

F()=-kTq(3.49)(3.50)(3.51)(3.52)

(3.53)(3.54): ,U,H,CV, F,S,G. .

.(r )(v )(e )(n )

i(3.55)4.2*10-21,r(42-420)J/mol,v(4.2-42)kJ/mol, e, n.

(3.56)

(3.57)=qt*q():qt,qr,qV,qe,qn , ,,, .qq=gexp(-i/kT)i.

: ,: F()= -NkTq =-NkTqt -NkTqr -NkTqv -NkTqe -NkTqn = Ft+Fr+Fv+Fe+Fn (3.58) : F()= -kTqN/N! = -kTqtN/N! -NkTqr -NkTqv -NkTqe -NkTqn

:, kTN!,.= Ft+Fr+Fv+Fe+Fn (3.59)

......

.

(3.60)(3.61) sn

,.:1.,, (3.45)(3.47)(3.48)(),qn, .,,

[(3.42)(3.43)(3.44)(3.46) ],qn.:

. 2., , qn,, qn . .3.,.

e,1-e,0=400kJ/moF, Cl ,:, -j+(2j+1), (2j+1).

j,,:Ue=He=Cve=0 (3.62)Fe=-NkTqe (3.63)Ge=-NkTqe (3.64)Se=Nkqe (3.65)

:,, ,qe . .

.1.ma*b*c(3.66)h, 1,2

(3.67)(3.68)

0gitqt,

(3.69)

2.1Helmholtz

2(3.70)

(3.71)(Sackur-Tetrode),.,:

(3) U=F+TS (3.72)4(3.73)

5GibbsP=-(F/V)T,NUt,Ft

. , ,,.1.(F): (3.21), F=-kTqN/N! =(N0n+N0e)-NkTg0ng0e-NkT(2mkT)3/2/h3 -NkTV+NkTN-NkT (3.74)

..,,.

2.: S=-(F/T)V,N =Nk[g0ng0e+(2mk/h2)3/2+V-N +(3/2)T+5/2] (3.75) , .

3. U=NkT2(q/T)V,N=(3/2)NkT (3.76) 4.CV CV=(U/T)V,N=(3/2)Nk (3.77)5.: =(F/N)T,V =(0n+0e) -kTg0ng0e -kT(2kT)3/2/h3 -kTkT + kTp (V=NkT/p) (3.78)

,N=L,: =L (0n+0e)-RTg0ng0e -RT(2kT)3/2/h3 -RTkT+ RTp (3.79)

p,:

,, (T),(3.78)(3.79),: = (T) + RTp/p (3.81)6.: p=-(F/V)T,N=NkT/V (3.82) .

.qr qr

1 qr JIm1,m2 r

(3.83)

:r qr Ir H2 r,r /T

2qr(360o (3.85)(3.86)

3qr.1.vgi,v=1(3.87)

vv=0,v,0 (3.87)

Qv=hv/k,Qv,,,Qv,qv (3.88)

QvQv=310kv=1, Qv/T >>1exp(-Qv/T)

, v,0=(1/2)hv=0,2.ft, frn(3.90)

qv qv(3n-5) (3n-6)3.(3.91)

I v j

1HelmholtzFr,Fv2Sr=-(Fr/T)v,NSv=-(Fv/T)v,N(3.92)(3.93)(3.94)(3.95)

3Ur,Uv4CV,r,CV,v(3.96)(3.97)

(3.99)

H G .(3.100)

298.15 K1 molO2(g)Vgn,o=3,n,o=0,O2r=1.207*10-10mqnqv

O2qe,qrqt

khO2=2,

Sm,tSackur-TetrodeNk=R,

.,(1/2)kT,(1/2)kT.,:=3* [(1/2)kT+ (1/2)kT]=3kT,U=L*3kT=3RT,:Cv,m=-(U/T)v=3R=24.94J/(k*mol)(3.101)

.:1..2..3.. 3.,N,3N. :qv=giv e-(v+)h/kT

3N,:=(3/2)Nh+3NkT(1-e -h/kT)3N(3.102)(3.103)

U=F+TS =(3/2)Nh+3Nh:S,F,Uv,,,,.:, Cv,(3.104)(3.105)

(3.105),h/kT=v/T =X,N=L,:(3.106)XX/(ex-1)1/(ex-1)2.:(1) : X=v/T 0,ex1+x,Cv,m3R(1+v/T)3R

(2) 0k: v>>T ,X(3),,:(3.107)

:Cv,m=233.702R(T/D) =*TD,D=hm/k, m. (3.108)(3.109)(3.110)

q=giexp(-i/kT)= qnqeqtqrqv(3.111)

1.q=*2.q=**(3.112)(3.113)

3.q=** 4.(3.114)

,,,..F=-kTqNF=-kT()()(3.115)