現代物理化学 1-1(4)16.ppt
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3 1-1-2 EU E = K E + P E + U ΔE K E = 0P E ΔE = ΔU U U = εn ΔU ΔU = Q + W, du = d 'Q + d 'W Q, d Q Q, d Q W, d W W, d W ΔUΔU 1-1-3
4 1-1-4 PV d 'W = P e dv ( d 'W = P e dv ) dx P (as) A P e 2.2(P > P e ) d W d 'W = F e dx = (AP e )dx = P e (Adx) = P e dv P e dv = Adx PVPdV P 1,, TP 2,, T P > P e = 0 W = d'w = P e dv = 0 P > P e = W = d'w = P e P P e dv = P e dv = P e ( ) = P e ΔV W r = d'w r = P e dv = P dv r : reversible,
5 nrt W r = d'w r = P e dv = P dv = V dv (P = nrt / V ) T nrt W r = d'w r = P e dv = P dv = V dv = nrt ln P e ~ V P + a n 2 V V nb ( ) = nrt P = nrt V nb a n 2 V W r = P e dv = P dv = nrt / (V nb) a(n / V ) 2 dv = nrt ln nb nb + 1 an d W P e [N m ] dv [m ] P e dv γ [N m ] da [m ] γ da f [N] dl [m] fdl Δφ [V] dq [C] Δφ dq H [A m ] dm [Wb m] HdM
6 -2-1 µ (T, P 0 ) < µ l (T, P 0 ) l [G m (T, P0 ) < G m (T, P 0 )] P V µ (T, P) = µ l (T, P) [G m (T, P) = l Gm (T, P)] P V 4-a. G m (T, P) = l Gm (T, P) T, V da=(µ µ l )dn < 0 da = 0 T, PdG=(µ µ l )dn < 0 dg = 0 P e = P ± dpt e = T ± dt T 2-2 (a) (b) P e < P (c) P e = P dp 1
7 2-3 (P a, V a )(P b, V b )(P a, V a ) ΔU = µ (T, P 0 ) < µ l (T, P 0 ) l [G m (T, P0 ) < G m (T, P 0 )] P V µ (T, P) = µ l (T, P) [G m (T, P) = l Gm (T, P)] P V 4-a. G m (T, P) = l Gm (T, P) W 1 = 0, Q 1 = ΔU v Δ P e = P (Δ = Δ < 0) W 2 = P e Δ > 0, Q 2 = ΔH v < 0 ΔU = Q + W = 0 Q = W = W 1 + W 2 Q [= (Q 1 + Q 2 )] Q = W 1 + W 2 = P e Δ = P e Δ > 0 P e = P W 1 = PΔ > 0, Q 1 = ΔH v > 0 P e = P (Δ = Δ < 0) W 2 = PΔ > 0, Q 2 = ΔH v < 0 ΔU = Q + W = 0 Q = W = W 1 + W 2 Q [= (Q 1 + Q 2 )] Q = W 1 + W 2 = PΔ PΔ = 0 2
8 T, V ldn l > 0dn () n = n l + n, dn = dn l + dn = 0, dn l = dn = dn(l ) > α α β β da = µ i dni + µ i dni +, 0α µ i (T, P) = 0α Gi,m (T, P) α α Gm (T, P) = Gm da = G l A ( m G m )dn(l ) = (Δ l Gm )dn(l ) = n(l ) dn(l ) T,V da < 0, G m G m l ( ) l < 0 G m (T, P0 ) < G m (T, P 0 ) 4-b. A, G VP T PG m G m dg m = G m P dp = V m dp T V l ( m >> V m > 0) da = G l ( m G m )dn(l ) = (Δ l Gm )dn(l ) = P (G l G m < G m ) l m G m AA G m (T, P) = Gm l (T, P) PT 3
9 2-7 G m = H m TS m H m S m = H l l ( m TS m ) ( H m TS m ) ( ) T S l ( m S m ) = Δ l Hm T Δ l Sm Δ l Gm = G m G m l = H m H m l Δ l Hm > 0, Δ l Sm > 0, but Δ l Gm < 0 T Δ l Sm > Δ l Hm Δ l Hm Δ l Sm Δ l Gm = Δ l Hm T Δ l Sm = 0 [i.e., G m (T, P) = Gm l (T, P)] Δ l Sm = Q r / T t = Δ l Hm / T t 2-8 P, T G dg = 0 µ (T, P 0 ) < µ l (T, P 0 ) l [G m (T, P0 ) < G m (T, P 0 )] P V µ (T, P) = µ l (T, P) [G m (T, P) = l Gm (T, P)] P V 4-a. G m (T, P) = l Gm (T, P) dg = (µ µ l )dn(l ) = (G m l Gm)dn(l ) = 0 G m (T, P) = l Gm (T, P) G = A+PV 4-b. A, G 4
10 G m G m = U m + PV m TS m = H m TS m = A m + PV m dg m = du m + d(pv m ) d(ts m ) = (TdS m PdV m ) + (PdV m + V m dp) (TdS m + S m dt ) = S m dt + V m dp = G m / T ( ) P = S m S l m >> S m ( G m / P) T = V m V l m >> V m G m / T ( ) P dt + ( G m / P) T dp ( > 0) > 0 ( ) 2-9 G m dg m = S m dt G m dg m = V m dp G m G m (T, P) = l Gm (T, P) G m (T + dt, P + dp) = l Gm dg l m = dg m (T + dt, P + dp) 2-10 dg l m = dg m and dg m = S m dt + V m dp S S m dt + V m dp = S l m dt + V l m, V m (T, P) m dp dp dt = S m l S m V l m V m = Δ l S m = Δ l Hm Δ l Vm T Δ l Vm (Δ l Vm = V l m V m dp dt = Δ l Hm = Δ l H m TV m RT 2 P dp P = Δ l Hm RT 2 dt, P dp = P 0 P (Δ l Hm = constant) ln P P 0 = Δ l H m R 1 T 1 T 0, V m = RT / P) T T 0 Δ l Hm RT 2 dt ln P = Δ l H m RT + C ( P vs t ) 5
11 2-11 P = A exp Δ l Hm RT ln P = Δ l Hm RT + C ( P vs t ) 2-12 T b P e P e T b 1 atm (0.1 MPa) T b0 ln P e 1 = Δ l Hm 1 1 R T 0, b T b ln P e = Δ l Hm + C RT b Δ l Hm RT b = Δ l Sm R PDF 6
12 PT -3-1 dp dt = S β m α Sm β V m α = Δ β α Sm = Δ β α Hm β β Vm Δ αvm T Δ αvm - P P e l s s l α β β β Δ α Hm > 0, Δ αvm > 0, dp / dt > 0 PT Δ l s V m < 0 Δ l s V m 0 ln P P 0 = Δ α β H m R 1 T 1 T 0, lnp = Δ α β H m RT + C CO 2 H 2 O S 3-2 T c P c V c T c P c CO 2 PV m
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14 T, P T, PG m T, P dn (> 0) αβ dg = (G m β Gm α )dn 3-5 dg < 0, dg = 0, i.e., G m β < Gm α i.e., G m β = Gm α β G m dg m = G m T dt + G m P P dp = S m dt + V m dp T G m G m T = S m < 0 S l m >> S m > S s m > 0 P ( ) G m G m P ( ) = V m > 0 V l m >> V m > V s m > 0 T 3-6 P P G m T G m P ( ) = S m < 0 P S l m >> S m > S s m > 0 = V m > 0 T V l m >> V m > V s m > 0 ( ) T, PG m 2
1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2
2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
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1 Physical Chemistry I (Basic Chemical Thermodynamics) [I] [II] [III] [IV] Introduction Energy(The First Law of Thermodynamics) Work Heat Capacity C p and C v Adiabatic Change Exact(=Perfect) Differential
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3 3.1 [ ]< 85, 86 > ( ) ds > 0. (1) dt ds dt =0, S = S max. (2) ( δq 1 = TdS 1 =0) (δw 1 < 0) (du 1 < 0) (δq 2 > 0) (ds = ds 2 = TδQ 2 > 0) 39 3.2 [ ]< 86, 87 > ( ) T = U V,N,, du = TdS PdV + µdn +, (3)
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5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â = Tr Âe βĥ Tr e βĥ = dγ e βh (p,q) A(p, q) dγ e βh (p,q) (5.2) e βĥ A(p, q) p q Â(t) = Tr Â(t)e βĥ Tr e βĥ = dγ() e βĥ(p(),q())
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