Фізична та колоїдна хімія
.pdfD ; |
$ V, T = const, |
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(3.18) " |
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WMAX/ WMAX , |
(3.30) |
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pdV = 0 (V = const). $ $( |
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, / (3.22) (3.23), " : |
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WMAX/ |
(U TS) . |
(3.31) |
0 ($ ) ' ) -$ ; " - / $ #$: F = U – TS. $ -$ ( :
U F TS , |
(3.32) |
" $, ; $ -. ! , , F " % ) %, /" + . < - % ) % TS " ’ % ) % + - /" . J ) (3.31) (3.32) "
F WMAX/ , |
(3.33) |
" ) % ' ) , – %% -
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> i-i i i i i e-! i i : i ! i i.
’ (3.32) (3.24) - :
dF * SdT pdV , |
(3.34) |
) , ; , -, " - ( F = f(V, T), -) , $( ) . ! , +$ $ -$ dF = 0, +$ – dF < 0. 0 / $ $ .
C , $ $, - $ $ (p, T = onst), (3.22) (3.23):
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WMAX/ (U TS pV ) , |
(3.35) |
0 ($ (U + pV–TS = H – TS) ' ++ / ) "/, $ # G:
G H TS , |
(3.36) |
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WMAX/ G . |
(3.37) |
" $ $( +- ) .
> i-i i e !: ! -
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D ; , ) ; , ( ( (3.24) (3.32)) - :
dG * SdT Vdp , |
(3.38) |
G =f(p,T); (dG)p,T ‚ 0 , ; +-$ +- $ dG = 0, +$ – dG < 0.
?$ $+ ) ( . 7) ( . %] " + ) ) - , ]; – , ] – % - % ) , ) ( .
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; . 7. -" !" !"!? ' " *! ( !" # , ! * # )
C ; -$ :
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dU * TdS pdV |
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dH * TdS Vdp |
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dF * SdT pdV . |
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(3.39) |
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dG * SdT Vdp |
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% + ) $ |
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+ .3. |
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' 3. |
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-" !" "$# ) !" # " *! |
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#"#$ !" % $* |
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E - |
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V, |
S |
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dS = 0 |
dS > 0 |
dS > 0 |
dS < 0 |
dS = 0 |
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U = const |
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S = Smax |
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d2S < 0 |
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g ? |
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S, V = const |
U |
dU = 0 |
dU < 0 |
dU < 0 |
dU > 0 |
dU = 0 |
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- |
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U = Umin |
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- |
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d2U > 0 |
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S, p = const |
H |
dH = 0 |
dH < 0 |
dH < 0 |
dH > 0 |
dH = 0 |
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H = Hmin |
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d2H > 0 |
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T, V = const |
F |
dF = 0 |
dF < 0 |
dF < 0 |
dF > 0 |
dF = 0 |
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F = Fmin |
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d2F > 0 |
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T, p = const |
G |
dG = 0 |
dG < 0 |
dG < 0 |
dG > 0 |
dG = 0 |
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G = Gmin |
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d2G > 0 |
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3.4. ; ) ) F ?? #–F! ' *# |
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$ $ $ - |
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( . 3.3) , ; $ $ |
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( ( 4) // -
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. & $ ($. |
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0 , ; F = f(V, T). ! : |
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F |
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F |
dV ; (3.39) dF = – SdT – pdV |
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dF |
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dT |
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T V |
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V T |
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F |
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p . |
(3.40) |
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S; |
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T |
V |
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V T |
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0 , ;
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G |
dG |
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p T |
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G = f(p, T); :
G
dp dT ; (3.39) dG = –SdT +Vdp
T p
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G |
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G |
S; |
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V; |
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(3.41) |
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T p |
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p |
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T |
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& + ) )$ $ $ $ $ , " :
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U f (S,V ); |
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U |
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U |
dV; |
dU TdS pdV , |
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dU |
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dS |
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S |
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U |
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p . |
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(3.42) |
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V |
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S V |
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S |
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% H = f(S, p); |
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dS |
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dp; dH TdS Vdp |
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dH |
H |
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S P |
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p S |
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T; |
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(3.43) |
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S P |
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p S |
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/ ($ -$ $ $ $ , ' ++ ' ) , ( ) , +. ) $ - % – ) ' ) F ) ' ++ G:
F U TS; G H TS . |
(3.44) |
& S, %% $ (3.40) (3.41), " :
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F |
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F U T |
;G H T |
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0 , ; F F2 F1; G G2 G1. 0$/ |
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$ ( F) |
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' G H T |
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"P |
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(3.45)
(3.46)
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+ $ )
WMAX/ ( F)V ,T ; WMAX/ ( G) p,T ;
0$/ , (3.46) ( -) :
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'WMAX/ |
U T $ |
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MAX |
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(3.47) |
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'WMAX/ |
H T $ |
MAX |
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? (3.47) % $% -# –#$ ; ’ / -+ + ) (Qp = H)$) (QV = U) .
& (3.47) " ( -
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WMAX |
WhMAX > – H, |
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1. D ; |
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> 0, |
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, " ) - / ) ; .
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WMAX |
WhMAX < – H, |
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2. D ; |
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< 0, |
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) % $ + , - ) % /" ; .
3. D ; $ /" /, WƒMAX = – H;+ " , ; - + ( " %.
& + . I % ) % ' ) ) U = F + TS + ( + + , ; ) " : ) / F, $ % ( + , « ’ » ) / TS, " - ) ( / + .
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’ ) ( %, ) + , / ( ( / ’ % ) % .
J . C ( + )% . ( , ; ) " $ – % ’ %. C ( / , ; + - ) " ) % ' ) ,( + /, ( ) %, + ’ %% .
3.5. , ! * #
, $ $ , ( -$ , " , ; $ % + " + ) "/, / ( ). C- , ; $" / ) "/,( : U = f(S,V,n), n – - .
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U |
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dni . |
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(3.48) |
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ni |
S,V,nj 1 |
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U
nj–1 $ ", ;
ni S,V,nj 1
/" ni -) , -
$ $( %
U
$% ni ( " / /.
D ; + " $ , ; $/(S, V ( ) ),% ) % / ) :
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U |
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U |
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U |
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U |
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dU |
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dS |
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dV |
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dn1 |
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n2 |
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S V,n |
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V S,n |
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S,V,nj 1 |
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S,V,nj 1 |
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U |
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dn3 |
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dni |
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n3 S,V,nj 1 |
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ni S,V,nj 1 |
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+ ; ) :
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U |
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dni . |
dU |
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dS |
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dV |
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V,nj |
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S,nj |
i 1 |
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ni S,V,nj 1 |
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? " i = 1 i = j.
dn2
(3.49)
(3.50)
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i - |
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ni |
S,V,nj 1 |
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/ . M ) ( -$ % (U, H, F, G). , , ; $ $ $ -( ) $ $ -$ // :
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i .(3.51) |
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ni |
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S,V,nj 1 |
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S,p,nj 1 |
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ni V,T,nj 1 |
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p,T,nj 1 |
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& ) " $) - .
ji i i – , i ! i K (U, H, F, G), -i i i i i (UqS, V, nj-1; HqS, p, nj-1; FqT, V, nj-1;G qT, p, nj-1) 1 - -.
0$/ (3.39), $ $( :
dU * TdS pdV + idni
dH * TdS + Vdp + idni
(3.52)
dF * SdT pdV + idni dG * SdT + Vdp + idni
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? (3.39) (3.52) " , ; / ) $ " :
i dni 0 , |
(3.53) |
($ , $ ) " ).
J ) $( $ -
$ ( |
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idni < 0. |
(3.54) |
, + ) $% % +- |
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i i0 RT ln pi ; |
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i i0 RT ln Ci ; |
(3.55) |
i i0 RT ln ai , |
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i0 – $ -) $ |
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( + pi, Ci, i ‡ 1).
-" # ) ! 3
1.< / + + ? )+ ) ?
2.C / ) ) .
3.? / – %% -. .
4.0 ) ) +-$ +$ .
5.0 % " " - ) ? & $ ) /%?
6.$ $ -$ . -$ .
59
7.& $ $ % + / -$ ? D" ?
8.C , $$ " p, ' ; V ,T ?
9.C , $$ " V , S ; p, S ?
10.< $ %, ) % ' )- , ) % ' ++ +$ $ / , +$ ?
11.D % /, ; $ -$ V , T ; p, T ?
12.& $ ) ( ( " ? D /"$( ) $ ?
13.0 % ) ) / $ .
14.0 $ $ -$ .
15.0 ' ++-' ) . %$ .
16.J ) " ( $ -? C + ( $ - ) .
17.0 $ % -
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18.D % ) - ?
19.) + ( " ) + ( +- / ) ?
20.D /" %% ) ? &- + / ( ) .
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