Sotnikov_Vatolin_vce
.pdf1.2.$1 * 1% 2$.. (%$ 4 0 53$ 4. -$
+, *01%$ % 6$ /
6 0 0,
/ 0
( , ) 1 2
. . 0 0 , . .
, 1 ". *
0 0,
0, .
-0 0 . ' .
cp ,
cp = |
Qp |
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H |
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= |
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T2 |
− T1 |
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T p, |
(1.8) |
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0 1
2. ) p , 0
. +0 , 0
, .
6 0 0 0
. * /
cp = |
δ Qp |
∂ H |
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= |
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d T |
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∂ T p, |
(1.9) |
δQp − , (
) +d ; dH –
. 0 . !
1 2
. 0, , , /
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T2 |
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H = HT |
− HT |
= cp dT = Qp . |
(1.10) |
2 |
1 |
T1 |
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, 0 / (1.10),
0 0 p . - $ ,
. 0, . * 0
.
cp = a + bT + cT 2 , |
(1.11) |
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cp = a + bT + c′ / T 2 , |
(1.12) |
.$$ a, b, c, c′ , |
0 |
. 0 p
. , p=1
( ), . .$$
. * 0
( cp0 ) .
) 0 . 0 cp0 (1.12), /
$ (1.10) 0, 0 . 0
.
, 298 " (
)
HT0 = H2980 + T cp0dT = H2980 + a(T − 298) + b2 (T 2 − 2982 ) −
298
(1.13)
− c′(T −1 − 298−1 ) .
! H2980 , .
, 0 /
$ (1.13) 0 0 |
HT0 |
− HT0 |
, Qp . , |
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1 |
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2 0 0 1, Qp
/ / 0 ( ).
, 2 < 1 (/) /, Qp <0, . .
.
, 0 Qp , /
0 0 p
0 0 p, ,
. - (1.10)
Qp = H ≈c0p 298 (T2−T1) |
(1.14) |
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Qp ≈c0p(298.) (T2 −T1). |
(1.15) |
! / 0
$ , /
, ,
/ ,
/ . )
. 0 . .$$
( , .). !
$ (1.10) 0 /. ,
1 , 2
( ) ( ),
/ 0 1 , ,
, / ,
( ) 2:
HT0 ( ) |
= HT0 ( ) + |
T |
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T |
(1.16) |
c0p |
( )dT + H 0 + |
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c0p ( )dT + |
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2 |
1 |
T1 |
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T |
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T2
+ΔH 0 + cp0( ) dT .
T
#, ,
700 " 1800 ".
+
=1728 ", 0 /
cp0 ( ) =38,4 //0·", 0
c0p( ) = 25,1 + 7,53×10−3 T |
//0·", |
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H 0 =17,7 //0. |
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. + (1.16) |
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1728 |
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1800 |
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H18000 ( ) = H7000 ( ) + |
(25,1+ 7,53×10−3 T)dT +17700+ |
38,4dT . |
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700 |
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1728 |
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! , |
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H 0( ) = H |
0( ) |
+ 55700 //0. |
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1800 |
700 |
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- |
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(Q |
p |
= DH 0 = H 0( ) - H |
0( ) = 55,7 |
//0) |
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1800 |
700 |
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55,7 //0, |
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/ (Qp = DH 0 = H7000( ) - H18000( ) = |
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=55,7 //0) / .
1.3. $1 *$7++$ * 0 ) -$. 0%$ 2 /
7 /
. - .$$
,
- P, T=const (Qp)
V, T=const (Qv). " , 0 .$$
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P, T=const, . 0 ( H ) 0
. - $ 0,
0 .
! . 0 0 ,
/
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.$$ 0 %,
.$$ (Qp Qv)
, 0 0
. 3 % /
(1.6) (1.7), 0 .
* 0 0 0
0 0 .
, H2980(Fe2O3 )
.$$ ( QP )
Fe2O3 /
(T=298K )
3
2Fe+ 2 O2 =Fe2O3
& .
' 0 0 .$$
CO+3Fe2O3 =CO2 +2Fe3O4 |
(1.17) |
//0 CO2 T=298K. ' 0 0 %, /
, , .
+ / (0 CO 3 Fe2O3 )
(0 C , 5 O2 , 6 Fe). 3
(0 CO2 , 2 Fe3O4 ). *
.$$ /
/ :
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o |
= |
o(CO2 ) |
o(Fe3O4 ) |
− |
o(CO) |
o(Fe2O3 ) |
. |
(1.18) |
H298 |
H298 |
+ 2 H298 |
H298 |
− 3 H298 |
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!
%, .$$
:
H298o = νi H298o(i) − |
νi H298o(i) , |
(1.19) |
i |
i |
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! |
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ν i − .$$ .
+ .$$
H298o
( HTo ), .
(1.17) T .$$
HT = HT(CO2 ) + 2HT(Fe3O4 ) − HT(CO) − 3HT(Fe2O3 ) . |
(1.20) |
/ . 0 /
T 0 0 (1.13). -
HT0,CO
HT0,CO = H298,CO0 |
+ |
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T |
c0p,COdT = H298,CO0 |
+ aCO (T − 298) + |
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298 |
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+ |
bCO |
(T |
2 |
− |
298 |
2 |
′ |
−1 |
− 298 |
−1 |
) . |
(1.21) |
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) − cCO (T |
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& ,
HT0,i / (1.20). - 0
/ .$$
0 :
HT0 = H2980 + a(T − 298) + |
b |
(T 2 |
− 2982 ) − c′(T −1 − 298−1) , |
(1.22) |
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a, b, c′ ,
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b = bCO |
2 |
+ 2bFe O |
4 |
− bCO − 3bFe |
O |
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(1.23) |
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2 |
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( / 0 0 . !
b
b = νibi − |
νibi . |
(1.24) |
i |
i |
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' a ,
c′ .
' .$$ (1.17)
1000 ". + H2980 , 0
/ (1.18)
:
H298o = H298o(CO2 ) + 2 H298o(Fe3O4 ) − H298o(CO) − 3 H298o(Fe2O3 ) =
= −393,51 + 2 (−1117,13) − (−110,53) − 3 (−822,16) = −50,76 //0.
3 .$$ a , b, c′ :
a= aCO2 + 2aFe3O4 − aCO − 3aFe2O3 =
=44,14 + 2·86,27 − 28,41 − 3·97,74 = − 104,95;
b = bCO2 + 2bFe3O4 − bCO − 3bFe2O3 =
=(9,04 + 2·208,92 − 4,1 − 3·72,13)·10-3 = 0,206;
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c′ = c′ |
+ 2c′ |
− c′ |
− 3c′ |
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CO2 |
Fe3O4 |
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CO |
Fe2O3 |
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= [−8,54 + 2·0 − (−0,46) − 3 (−12,89)]·105 = 30,59·105. |
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* 0 $ (1.22) H |
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1000 |
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H 0 |
= H 0 |
+ a(1000 − 298) + |
b |
(10002 |
− 2982 ) − |
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1000 |
298 |
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2 |
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− c′(1000−1 − 298−1) = −50760 −104,95·702 |
+0,103·9,11·105 − |
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− 30,59·105 ·(−235,5 ·10-5) = −23400 //0 = −23,4 //0.
- ,
(1.19) (1.22) 0
.$$ / , 0
.
. 0 (
, .$$ ),
.
! .$$
, . !
, . 0
. '
2. - / . /
.$$ .
1.4. % /, $%) 3 ). $%( 4 &&.
2 / 0,
0 0
.
. 0 ,
( 0)
- . ! 0,
0 . , 0
, 0 . ) 0
$ ,
“0 0
”.
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0 − .
$0 . !- ,
0 0 ., . ,
.0; /
, 0 . . ;
.
!- , 0 0
. ,
0 .
+ 0 ( )
. ' / ,
" " ,
. !
.
) , 0 (>105-106 .)
0 , . . 0
, 0 , 0
, 0 / .
/ . .
" / .
(S, //0·"). * / . +
0 / 0
$
dS ³ |
δQ |
. |
(1.25) |
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T |
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3 0 , . .
,
. ! (0)
δQ
. 0 ( T ).
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' .
$
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∂ S |
= |
cp |
, |
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(1.26) |
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∂ T p |
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T |
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cp – 0 p=const. .
S = H /T ; S = H /T , (1.27)
.
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* - ,
0 ( 0 0 .
0 .),
0 (>1020 ). , P,T=const ( ), . 0
0 – . % (G),
G = H − TS . |
(1.28) |
0, (1.6) (1.25)
( P,T=const),
dH − TdS ≤ 0. |
(1.29) |
" , 0 / (1.29) |
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$$ . % (G) P,T=const. |
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, P,T=const
,
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G = G − G < 0 . |
(1.30) |
! . % 0, |
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0
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