2012 年度前期課程 熱力学 例題3nt1.c.u-tokyo.ac.jp/~tmatsui/course/therm12/ . (Clapeyron-Clausius…

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2012 3 7 3: I 10, 12, 16, 18, 21, 33

1. T p V1 n1 V2 n2 V = V1 + V2

2. HelmholtzV n1n2 T

3. van der Waals p = RTV b a

V 2 1T V1 V2 van der Waals HelmholtzF = U TS[dF = SdT pdV ]

4. Legendre1 f(x) = x2 + x 1 Legendre (v) = f(x) vx v y = f(x) v = f (x)(v) y (v) Legendre f(x)

5. LegendreMaxwelldU = TdSpdV Legendre F = U TSG = H TSH = U + pV 4MaxwellMaxwell(

U

V

)T

= T(

p

T

)V

p, (1)(H

p

)T

= T(

V

T

)p

+ V (2)

6. MaxwellpVTS 2 2Maxwell (

S

V

)T

=(

p

T

)V

(3)

7. GibbGibbsG T pN GN T pG(T, p, N) = G(T, p,N)G =

(GN

)T,pG = N

8. Gibbs-DuhemG U

U = TS pV + N (4)

dU = TdS pdV + dN Gibbs-Duhem

SdT V dp + Nd = 0 . (5)

9. Gibbs-Duhem (5) (T, p) (

T

)p

= S/N, (6)(

p

)T

= V/N, (7)

10. Helmholtz Helmholtz f = F/N f = pv(

f

v

)T

= p, (8)

v = V/N

11. 2 Clapeyron-ClausiusA B

A(T, p) = B(T, p)

dp

dT=

lABT (vA vB)

(9)

Gibbs-Duhem (5) lAB A B vAvB

12. Clapeyron-Clausius (10) 0.2 100 540cal/g V = 0.6Kg/m3 L = 0.96 103Kg/m3

13. Clapeyron-Clausius 2 Clapeyron-Clausius

dp

dT=

lp

RT 2(10)

l0.2 100 540cal/g

14. van der WaalsMaxwellvan der Waals p = RTV b a

V 2 2pV p = peq. 2

15. Gibbskf = 2 f + k

16. Stefan-Boltzmann N = 0 u = U/V p = u/3p u T Gibbs-Duhem (5) Stefan-Boltzmann

u = T 4

Gibbs-Duhem (5) s = S/V

s =43T 3

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