現代物理化学 2-1(9)16.ppt

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1 --- S A, G U S S ds = d 'Q r / ΔS = S S = ds =,r,r d 'Q r r S -- ds = d 'Q r / ΔS = S S = ds =,r,r d 'Q r r d Q r e = P e = P ΔS d 'Q / e (d'q / e )

2 --3,e Q W Q (> 0),e e ΔU = Q + W = (Q + Q ) + W = 0 W = Q + Q (Q < 0) e = W Q = Q + Q Q --4 = e P = P e,e,e n P,V, P,V, ΔU = 0 Q,r = W,r = nr ln(v / V ) P,V, P 3,V 3, Q,r = 0 W,r = ΔU = nc V,m ( ) [ / = (V / V 3 ) γ ] (Q, r )

3 P 3,V 3, P 4,V 4, ΔU 3 = 0 Q 3,r = W 3,r = nr ln(v 4 / V 3 ) ( Q, r ) --5 P 4,V 4, P,V, Q 4,r = 0 W 4,r = ΔU 4 = nc V,m ( ) = W,r [ / = (V / V 4 ) γ ] V / V 3 = V / V 4 V / V = V 3 / V 4 ΔU = ΔU + ΔU + ΔU 3 + ΔU 4 = 0 W r = (W,r + W,r + W 3,r + W 4,r ) = (W,r + W 3,r ) = nr ln(v / V ) + nr ln(v 4 / V 3 ) = nr( )ln(v / V ) W e r Q 3,r Q,r e r = W r / Q,r = (Q,r + Q,r ) / Q,r = ( ) / [= (,e,e ) /,e ] e r = (Q,r + Q,r ) / Q,r = ( ) / + Q,r / Q,r = / Q,r / Q,r = / Q,r / + Q,r / = 0 d Q / e = d Q r / d 'Q r = d 'Q r + d 'Q r I + d 'Q r II + III IV d 'Q = r + d 'Q r I = Q,r + Q,r = 0 III ΔS ΔS = (S,final S, initial ) = S ds = 0 ds = d 'Q r d 'Q r =

4 e r,e,e,e,e e ir e r e ir < e r Q W e ir = W ir Q,r W ir < W r ΔU = 0, Q + W = 0, W = Q W ir = Q,r + Q ' < Q,r + Q,r = W r i.e., Q ' < Q,r < 0, Q ' > Q,r = Q,r + Q ' <,e,e = W r = e r Q,r,e Q,r --7 Q,r + Q ' Q,r <,e,e,e + Q ' Q,r <,e,e Q ' Q,r <,e,e (Q,,e > 0) Q,r,e + Q ',e < d Q / e d 'Q ir = e d 'Q r d 'Q + r d 'Q + I e II e + III e IV d 'Q r e d 'Q = r d 'Q Q + =,r I e + Q ' < 0 III e,e,e d Q = d Q r, e = d 'Q ir < 0 e d 'Q 0 e 4

5 P e = P ± dp e = ± d --9 (a) (b) P e < P (c) P e = P dp --0 (P a, V a ) (P b, V b ) (P a, V a ) ΔU = 0 5

6 --- Clausius d 'Q d 'Q = ir d 'Q e + r e d 'Q = ir d 'Q r e < 0 d 'Q r d 'Q = r, d 'Q ir e d 'Q ir e d 'Q ir < e d 'Q r d 'Q ΔS = S S = ds = r > d 'Q ir e -- ΔS = ds d 'Q e ds d 'Q e ds e, ΔS e d Q d Q ( d 'Q) ds + = ds + ds e 0 e d 'Q ΔS + ΔS e = ds + ds e = r ( d 'Q) + 0 e

7 --3 ΔS d 'Q r = du d 'W r = du + PdV = dh VdP ds = d 'Q r du + PdV dh VdP = = ΔS ds = dh / = nc P,m d / ΔS = S( ) S( ) = nc P,m d / = nc P,m ln ds = du / = nc V,m d / ΔS = S( ) S( ) = nc V,m d / = nc V,m ln --4 ΔS t, P β α Δ α S β β Δ α S = n β Sm α ( Sm ) = ds = Δ α β H m t n=n dn n=0 = d 'Q r = d'q r t = n=n β Δ α Hm dn n=0 t = n Δ α β H m t β Δ α Sm = Δ β α Hm t per mol ΔS P,V, P,V, 3 a b c S ΔS

8 du = nc V,m d, dh = nc P,m d, V γ = const. --5 ΔS V V P P ΔS P P ds = (du + PdV ) / = n(c V,m d / + RdV / V ) { } ΔS = ΔS + ΔS = n C V,m ln( / ) + Rln(V / V ) ΔS 3 P P V V ΔS 4 V V ds = (dh VdP) / = n(c P,m d / RdP / P) { } ΔS = ΔS 4 + ΔS 3 = n C P,m ln( / ) Rln(P / P ) ΔS 5 V V P P ΔS 6 V V ΔS 6 = d'q r / = 0 ds = (du + PdV ) / = n(c V,m d / + RdV / V ) nrdv / V ΔS = ΔS 5 + ΔS 6 = nrln(v "/ V ) = n Rln(V / V ) + [ R / (γ ) ]ln( / ) V " (γ ) γ = V /(γ ), V " = ( / ) ( ) V (a), (b), (c) ΔS { } A, B ΔS () A, B V f V f = V A + V B () Δ mix S () A, B --6 ΔS = ΔS A + ΔS B = n A Rln V A + V B V A + n B Rln V A + V B V B = R(n A ln x A + n B ln x B ) () A, B ΔU = 0, W r = 0, Q r = ΔU W r = 0 ΔS = Q r / = 0 Δ mix S = ΔS + ΔS = R(n A ln x A + n B ln x B ) 3

9 --7 Δ mix S Δ mix S = R n i ln x i S Δ mix S = S (n A S A,m + n B S B,m ) = R(n A ln x A + n B ln x B ) S = (n A S A,m + n B S B,m ) + Δ mix S = n A (S A,m Rln x A ) + n B (S B,m Rln x B ) S S = n i (S i,m Rln x i ) A, B Δ mix S () V f Δ mix S = n A Rln(V f / V A ) + n B Rln(V f / V B ) 3 3. ΔS --8 ΔS = n{ C V,m ln( / ) + Rln(V / V )}, ΔS = n C P,m ln( / ) Rln(P / P ) H O 0 C 00 C Δ α β S = n Δα β Hm / t ΔS { } ΔS = n C V,m ln( / ) + Rln(V / V ) { } ds = dh / = nc P,m d /, ΔS = S( ) S( ) = nc P,m d / 4

10 --9 S W Boltzmann S = k B lnw (k B = k : Boltzmann constant) S Boltzmann S = k ln W M. Plank S lim S = 0 (S = k B lnw, W = ) 0 α mol 0. MPa S m ( ) ΔS m = S m g ( ) S m s (0) = S m g ( ) 5

11 ΔS = ds d 'Q e --3- A, G e PV work e e = ΔS d'q e = Q, e = > 0 () e e ΔS = ΔS Q () ΔS Q () Q = ΔU W (= 0) = ΔU (3) -3- () (3) ΔU ΔS 0 () Q = ΔU ΔU ΔS = (U S ) (U S ) = A A = ΔA 0 A = U S Helmholtz P e P = P e Q = ΔU W = ΔU + PΔV = (U + PV ) (U + PV ) = H H = ΔH (4) () (4) ΔH ΔS 0 () Q = ΔH ΔH ΔS = (H S ) (H S ) = G G = ΔG 0 G = H S Gibbs

12 (a), (b), (c) (a) e e = (5) Q () : ΔS d'q e = Q, e = > 0 () e e ΔS = ΔS Q () Q = ΔU W (5) ΔU ΔS W A U S, ΔU ΔS = ΔA W, ΔA W W da d 'W ΔA W ΔA HelmholtzA -3-3 (b) W V PV W net W = W V + W net W V = 0, ΔA W = W net, ΔA W net -3-4 da d 'W net PV W net = 0 (d W net = 0 ) ΔU ΔS = ΔA 0, da 0 (c) W V = P e dv = P e ΔV = PΔV ΔU ΔS = ΔA W = W V + W net = PΔV + W net ΔU ΔS + PΔV = ΔA + PΔV = ΔH ΔS = ΔG W net, ΔG W net dg d 'W net (G U S + PV = A + PV = H S) PV W net = 0 (d W net = 0 ) ΔH ΔS = ΔG 0, dg 0

13 (b), (c) ΔA W net, da d 'W net : ΔA 0, da 0 ΔG W net, dg d 'W net : ΔG 0, dg PV work A G da < 0, dg < 0 A, G da = 0, dg = 0 A, G da = 0, dg = 0 da = 0, dg = 0 dg = d'w net = (ΔG)dξ = ( nfδe)dξ, ΔE = ΔE Θ (R / nf)lnπq i, ΔG = ΔG Θ + R lnπq i ΔG = 0 ΔE Θ = (R / nf)ln K ΔG < 0 3 ( ) 0 C, atm 0 C, atm K ( ) mol (0 C, atm) 73. K ( ) mol ΔH (0 C, atm), ΔS ΔG = ΔH ΔS = 0 ΔH, ΔS 63. K ( ) mol ( 0 C, atm) ΔH 3, ΔS K ( ) mol ΔH ( 0 C, atm) m, ΔS m ( =63. K, P= atm) ΔH m = ΔH + ΔH + ΔH 3 ΔS m = ΔS + ΔS + ΔS 3 ΔH m ΔS m ΔG = ΔH ΔS (ΔG m = ΔH m ΔS m ) ΔH m = 5.63 kj mol, ΔS m = 0.6 J K mol, = 63. K ΔG m = 0. kj mol < 0 3

14 -3-7 PV work ΔU, ΔH, ΔA, ΔG U, H, A, G du = d 'Q r + d 'W r,v = ds PdV H = U + PV, A = U S, G = H S, dh = ds + VdP da = Sd PdV dg = Sd + VdP dg(,p,n) = Sd + VdP + µdn, µ = ( G / n),p µ S,V const., (du) S,V = 0 S,P const., (dh ) S,P = 0,V const., (da),v = 0,P const., (dg),p = 0 4

15 --4- G G A dg = ( G / ) P d + ( G / P) dp = Sd + VdP G ( G / ) P = S, ( G / P) = V da = ( A / ) V d + ( A / V ) dv = Sd PdV ( A / ) V = S, ( A / V ) = P (a) G ( G / P) = V P P ΔG = G() G() = dg = ( G / P) dp = V dp P P (b) molv m P P ΔG m = G m (P ) G m (P ) = V m dp V P m dp = V P m (P P ) = V m ΔP (c) molv m ΔG m = G m (P ) G m (P ) = P P R P dp P dp = R = R ln(p P / P ) P P = P = atm (0.35 kpa 0. MPa) -4- P atm ΔG m R G m (P) = G m (P ) + R ln(p / P ) = G m + R ln(p / atm) P f (d) G III ΔG = G(P, products) G(R, reactants) ΔG P = { G(P) G(R) } P = V (P) V (R) = ΔV K G Δ r G* = R ln K

16 -4-3 G Gibbs-Helmholtz (a) G ( G / ) P = S (b) ( G / ) P = S = (G H ) / G = G P + G P = G P G P G P = H (c) G III ΔG = G(P, products) G(R, reactants) ΔG ( / ) G(P) = P ΔG G(R) = H (P) P H (R) = ΔH = ΔH (Δ r G* = R ln K, Δ r G * / = Rln K) P Maxwell (a) z z dz = 0 dz = X(x, y)dx + Y (x, y)dy dz = (X dx + Y dy) = σ Y ( x )y X y dxdy x -4-4 Y x = X y y, (i.e.) x z x y = z x y x y y x (b) da = Sd PdV, ( S / V ) = ( P / ) V dg = Sd + VdP, ( S / P) = ( V / ) P du = ds PdV, U V = S V P = P P V dh = ds + VdP, H P = S P + V = V + V P

17 Joul U V = P V P = nr V P = 0 H P = V + V = nr P P + V = 0 van der Waals' equation : P + a n V V nb P / ( ) V = nr / (V nb) U V = P P = a n V V (> 0) ( U / V ) ( ) = nr van der Waals V U U(V, ) U(V, ) = ΔU = du = V dv V = a n V V dv = an V V V -4-5 ds = (du + PdV ) / = (dh VdP) / -4-6 van der Waals ( ) V d + ( U / V ) dv = nc V,m d + ( P / ) V P ( ) V dv du = U / ds = (du + PdV ) / = nc V,m d / + P / nc ΔS = V,m d + van der Waals' equation : V P dv V V ( P / ) V = nr / (V nb) dv nc ΔS = V,m V nr d + V nb dv = n C V V,m ln + Rln V nb V nb C P C V = P + U V V = P V P V P van der Waals U V ( ) 3

18 Duet 4

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