o
3 3
−11
o
• • • • • • •
X A = 5 mm X B = 10 10 mm mm C A = 1, 2 kg/m3 C B = 0, 8 kg/m3 D = 3 × 10−11 m2 /s J dC/dx J = −D
J = −D J = 2, 4 × 10−9 kg/m2 s
dC ∆C C A − C B = −D = −D dx ∆x xA − xB
C A − C B 1, 2 − 0, 8 = −3 × 10−11 xA − xB (5 − 10) × 10−3
2
o
−9
• • • • • • • •
2
o
= 2 mm
C C A = 0, 015% p C C B = 0, 0068% p J = 7, 36 × 10−9 kg/m2 s
ρF e = 7, 87 g/cm3 ρC = 2, 25 g/cm3
⇒ J = −D
C A − C B xA − xB
D D =
xA − xB −J C − C A
B
D C A
C B
kg/m3
kg/m3
C ” (1)
C kg/m3
C 1” =
C 1 ρ1
C 1 + C ρ
2
2
× 103 kg/m3
A
B
A
B
” C C
A
” C C
B
C 1 + C 2 = 100 C C + C F e = 100
” C C
A
= =
C C A + C ρ
C CA ρC
Fe
Fe
0, 015 0,015 + 997,,985 2,25 87
× 103
× 103
= 1, 18 kg/m3
” C C
B
= =
C C B + C ρ
C CB ρC
Fe
Fe
× 103
0, 0068 + 997,,9932 87
0,0068 2,25
× 103
= 0, 53 kg/m3 ” C C
A
” C C
xA
B
D
D
=
xA − xB −J C − C A
= D = 2, 27 × 10−11 m2 /s
B
−7, 36 × 10−9
(0 − 2) × 10−3 1, 18 − 0, 53
xB
J
2 −8
• • • • • • • •
o
2
o
= 6 mm = 0, 25 m 2
C H A = 2, 0 kg/m3 C H B = 0, 4 kg/m3 D = 1, 7 × 10−8 m2 /s t = 1 h
⇒ J = −D
C A − C B xA − xB
J
M A
t M = J At
J =
M At
M
J
J =
C H B −D C HxA − −x A
= = M
B
−8
2, 0 − 0, 4 (0 − 6) × 10−3
−1, 7 × 10 4, 533 × 10−6 kg/m2 s
J
t
M = J × A × t
= 4, 533 × 10−6 × 0, 25 × 3600
M = 4, 1 × 10−3 kg/h
A
4
o
−11
t
• • • • • • •
%C (x = 0, 5 mm) = 0, 80% p
o
4
C C 0 = 0, 25% p C C S = 1, 20% p C C x = 0, 80% p
x
x = 0, 5 mm
D = 1, 6 × 10−11 m2 /s
C x − C 0 x = 1 − erf √ C s − C 0 2 Dt
t
C x − C 0 C s − C 0 C C x − C C 0 C C s − C C 0
0, 80 − 0, 25 1, 20 − 0, 25
= 1 = 1 = 1
√ − √ − × × − √
0, 4211 = erf
x 2 Dt x erf 2 Dt erf
erf
10−4
5
2 1, 6
10−11 t
62, 50 t
√
erf (x/2 Dt) (1)
2
√
x/2 Dt
z
z (1)
z
y = mx + b
m = tgα = xm xm =
∆y y2 − y1 ym − y1 = = ∆x x2 − x1 xm − x1 ym − y1 (x2 − x1 ) + x1 y2 − y1 z = x m z
erf (z)
x
y
x1
y1
xm
z
ym
x2
z
y2
ym − y1 (x2 − x1 ) + x1 y2 − y1 0, 4211 − 0, 3794 = (0, 40 − 0, 34) + 0, 35 0, 4284 − 0, 3794 = 0, 3926 =
z
=
0, 3926 =
√ x
2 Dt 62, 50 √ t
t
62, 50 t = 0, 3926 = 25343 s = 7, 0397 h t = 7 h
2
erf (z) = 0, 4210
o
−11
γ
t
• • • • • • •
%C (x = 4 mm) = 0, 30% p
o
C C 0 = 0, 10% p C C S = 0, 90% p C C x = 0, 30% p
x
x = 4 mm
D = 5, 3 (1)
× 10−11
2
m2 /s
γ
o
⇒ ⇒ C x − C 0 C s − C 0 C C x − C C 0 C C s − C C 0
0, 30 − 0, 10 0, 90 − 0, 10
= 1 = 1 = 1
√ − √ − × × − √
0, 7500 = erf
x2
z
erf
4
2 5, 3
10
−3
10−11 t
274, 7211 t
z
erf (z)
x
y
x1 xm
x 2 Dt x erf 2 Dt erf
y1 z
ym y2
ym − y1 (x2 − x1 ) + x1 y2 − y1 0, 7500 − 0, 7421 = (0, 85 − 0, 80) + 0, 80 0, 7707 − 0, 7421 = 0, 8138 =
z
=
0, 8138 =
t =
√ x
2 Dt 274, 7211 √ t
274, 7211 0, 8138
2
= 1, 1396 × 105 s = 31, 6553 h t = 31, 7 h
o
D0
Qd
R
1, 2 × 10−4 m2 /s o
• • • •
o
D0 = 1, 2 × 10−4 m2 /s Qd = 131 kJ/mol R = 8, 31 J/mol − K D
D = D 0 exp
− Qd RT
D0
Qd
(1)
R
D
− × −
= D0 exp = 1, 2
D = 5, 76 × 10−13 m2 /s
10
Qd RT
−4
exp
131 × 103 8, 31 × (550 + 273)
2, 6 × 10−16 m2 /s D = 2, 6 × 10−16 m2 /s
• • • • •
D = 2, 6 × 10−16 m2 /s D0 = 2, 4 × 10−5 m2 /s Qd = 189 kJ/mol R = 8, 31 J/mol − K D = D0 exp
ln D = ln D0 −
T =
Qd R
1 T
Qd R(ln D0 − ln D)
Qd R(ln D0 − ln D) 189 × 103 = 8, 31(ln(2, 4 × 10−5 ) − ln(2, 6 × 10−16 )) = 900, 7972K
T =
= 627, 7972o C T = 628o C
− Qd RT
