Clapeyron-クラウジウス Clausius の式の導出 kandalab/ja/lecture/glossary/clap...クラペイロンClapeyron-クラウジウスClausius…

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Clapeyron- Clausius

T P , (T, P )

()(T, P ) = ()(T, P ) (1)

1mol Gibbs GG =

i

nii,

n:G()(T, P ) = G()(T, P ) (2)

T T + T P P + P

(2)

G()(T + T, P + P ) = G()(T + T, P + P ) (3)

Taylor2

G()(T, P ) +(

G()

T

)

P

dT +(

G()

P

)

T

dP = G()(T, P ) +(

G()

T

)

P

dT +(

G()

P

)

T

dP

(4)

(4) (2)(

G()

T

)

P

dT +(

G()

P

)

T

dP =(

G()

T

)

P

dT +(

G()

P

)

T

dP (5)

(

GT

)P

(GP

)TGibbs G S

H G = H TS H = U + PV (U :V :) 2

dG = dH SdT TdS (6)dH = dU + V dP + PdV

(6)

dG = dH SdT TdS= (dU + V dP + PdV ) SdT TdS= {(TdS PdV ) + V dP + PdV } SdT TdS= V dP SdT (7)

dU = dQ PdV = TdS PdV (7) dT = 0dP = 0

(G

T

)

P

= S ,(

G

P

)

T

= V (8)

(8) (5)

S()dT + V ()dP = S()dT + V ()dPdP

dT=

S() S()

V () V ()(9)

1

S dS = dQT dS = S() S()

1mol 1mol Htrans

Htrans/T

dS = S() S() = HtransT

(10)

(10) (9)dP

dT=

HtransT

(V () V ()

) (11)

V (), V () , (11) Clapeyron - Clausius

dP

dT=

L

T(V (g) V (l)

) (12)

P LV (g), V (l)

V (g) V (l) (12) V (l)

dP

dT=

L

TV (g)

V (g) 1mol

V (g) =RT

P(R :)

1P

dP

dT=

L

RT 2

d(lnP )dT

=L

RT 2

L T

ln P = LRT

+ C (C :) (13)

log10 P = L

2.303RT+ C (C :)

log10

(P2P1

)= L

2.303R

(1T2

1T1

)

(13)

P = C exp( L

RT

)(C : )

[1] , 1999

[2] , 2000

2

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