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Файл:Физическая химия — основа металлургических процессов. Учебное пособие
.pdf
K
A
K
x
x
A
Srr
= Z0ɟ
2
-E/RT
S
Ɉɛɪɚɬɢɦɵɟɪɟɚɤɰɢɢ
ɇɟɨɛɪɚɬɢɦɵɟ ɪɟɚɤɰɢɢ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɫɥɭɞɭɸɳɟɦ ɜɢɞɟ ɢ
ɨɩɢɫɚɬɶɜɵɪɚɠɟɧɢɹɦɢ
K
ɩɟɪɜɨɝɨɩɨɪɹɞɤɚ
ɝɞɟ
ɚ±ɧɚɱɚɥɶɧɚɹɤɨɧɰɟɧɬɪɚɰɢɹ
B
o
ax x
ɉɪɢɷɬɨɦɤɨɧɫɬɚɧɬɚɫɤɨɪɨɫɬɢɪɟɚɤɰɢɹɢɦɟɟɬɫɥɟɞɭɸɳɢɣɜɢɞ
t±ɜɪɟɦɹ
ɝɞɟ
ɋɬɟɩɟɧɶɩɪɟɜɪɚɳɟɧɢɹ
ɜɬɨɪɨɝɨɩɨɪɹɞɤɚ
da x dx
ax bx
dt dt
K
OQ
tax
ae
K
BP
o
Ka x
a
t
dx
dt
Kaxbx
K
ta b ab x
ba x
OQ
ɋɬɟɩɟɧɶɯɢɦɢɱɟɫɤɨɝɨɩɪɟɜɪɚɳɟɧɢɹɩɪɢɷɬɨɦ
Kta b
e
xa x ab
a
Kta b
e
b
ɑɚɫɬɨ ɪɟɚɤɰɢɢ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɧɚɡɵɜɚɸɬɫɹ ɪɟɚɤɰɢɹɦɢ ɩɫɟɜ
ɞɨɩɟɪɜɨɝɨɩɨɪɹɞɤɚɗɬɨɛɭɞɟɬɬɨɝɞɚɤɨɝɞɚɦɨɥɶɧɵɟɞɨɥɢ
ɬɨɝɞɚ
aɢbɪɚɜɧɵ
dx
K
A
K
A
K
K
x
dt
ax
Ʉ
= Ʉ2b
1
Ɍɪɟɬɶɟɝɨɩɨɪɹɞɤɚ
ªº
K
«»
ta x a taa x
¬¼
BCP
o
ax bx x
dx
dt
axbxcx
K
cx
x
ɉɨɫɥɟɢɧɬɟɝɪɢɪɨɜɚɧɢɹɷɬɨɝɨɜɵɪɚɠɟɧɢɹɩɨɥɭɱɚɟɦ
ªº
K
«»
t a ba c a x b ab c b x c ac b c x
¬¼
abc
OQ OQ OQ
ȿɫɥɢɩɪɢɧɹɬɶɱɬɨ
ɫ >> aɢc >> bɬɨɝɞɚɩɫɟɜɞɨɩɟɪɜɵɣ ɩɨɪɹɞɨɤ
ɯɢɦɢɱɟɫɤɨɣɪɟɚɤɰɢɢɛɭɞɟɬɢɦɟɬɶɜɢɞ
ba x
ɉɪɢɧɢɦɚɹɱɬɨ
dx a b x a b x
dt b b x b a x
KC
b = cɢɦɟɟɦ
Ka xbx K
OQ
OQ
ta b ab x
ta b
ªº
«»
¬¼
ȼ ɨɛɪɚɬɢɦɵɯ ɪɟɚɤɰɢɹɯ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɩɪɹɦɚɹ ɢ ɨɛɪɚɬɢɦɚɹɹɜ
K
B
ɥɹɸɬɫɹɬɚɤɠɟɪɟɚɤɰɢɹɦɢɩɟɪɜɨɝɨɩɨɪɹɞɤɚ
l
ax bx
K
dx
dt
ȿɫɥɢɩɪɢɧɹɬɶɱɬɨ
Ka x Kb x
aKb
D
tĺ
xe t
K
D
KK
dx
dt
ªº
D
¬¼
ɢ
D
OQ KK
tx
D
Ɍɨɝɞɚ ɜɵɯɨɞɹ ɢɡ ɤɢɧɟɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɤɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ
@
K
A
K
ɞɥɹɞɚɧɧɨɣɪɟɚɤɰɢɢɪɚɜɧɚ
A
ȿɫɥɢ
k!!ɬɨɝɞɚɛɭɞɟɬɢɞɬɢɩɪɹɦɚɹɪɟɚɤɰɢɹɞɨɤɨɧɰɚɋɯɟɦɚɬɢ
>@
>
bx K
Bax K
f
f
ɱɟɫɤɢɨɛɪɚɬɢɦɵɟɪɟɚɤɰɢɢ ɩɟɪɜɨɝɨɢɜɬɨɪɨɝɨɩɨɪɹɞɤɚ ɦɨɠɧɨɩɪɟɞɫɬɚ
ɜɢɬɶɜɫɥɟɞɭɸɳɟɦɜɢɞɟ
K
BC
l
ax x
Kx
ȿɫɥɢ ɫɢɫɬɟɦɚ ɜ ɧɚɱɚɥɟ ɫɨɫɬɨɢɬɢɡ
ɪɟɚɤɰɢɢɢɦɟɟɬɜɢɞ
dx
dt
ax Kx
Ⱥɤɨɦɩɨɧɟɧɬɚ ɬɨɝɞɚ ɫɤɨɪɨɫɬɶ
ɉɨɞɫɬɚɜɥɹɹɜɵɲɟɩɪɢɜɟɞɟɧɧɵɟɡɧɚɱɟɧɢɹɩɨɥɭɱɢɦ
ªº
axK K
K
OQ
taxKK
DD
D
x
aK
>
«»
>
«»
¬¼
KK
a
KK
ªº
«»
t
f
¬¼
D
K
D
ȼɨɡɜɨɞɹɷɬɨɜɵɪɚɠɟɧɢɟɜɤɜɚɞɪɚɬɧɚɯɨɞɢɦ
ªº
x
«»
ax K
¬¼
K
t
f
K
Ʉ
Ʉɚɬɚɥɢɬɢɱɟɫɤɢɟɪɟɚɤɰɢɢ
@
K
A
Ⱥ
K
Ʉɚɬɚɥɢɡ ± ɷɬɨ ɜɨɡɛɭɠɞɟɧɢɟ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ ɢɥɢ ɢɡɦɟɧɟɧɢɟ
ɢɯ ɫɤɨɪɨɫɬɢ ɩɨɞ ɞɚɜɥɟɧɢɟɦ ɜɟɳɟɫɬɜ ± ɤɚɬɚɥɢɡɚɬɨɪɨɜ ɦɧɨɝɨɤɪɚɬɧɨ
ɜɫɬɭɩɚɸɳɢɯ ɜ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɯɢɦɢɱɟɫɤɢɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫ ɭɱɚɫɬ
ɧɢɤɚɦɢɪɟɚɤɰɢɢɢɜɨɫɫɬɚɧɚɜɥɢɜɚɸɳɢɯɩɨɫɥɟɤɚɠɞɨɝɨɰɢɤɥɚɩɪɨɦɟɠɭ
ɬɨɱɧɵɯɜɡɚɢɦɨɞɟɣɫɬɜɢɣɫɜɨɣɯɢɦɢɱɟɫɤɢɣ ɫɨɫɬɚɜ ɂɧɵɦɢɫɥɨɜɚɦɢɤɚ
ɬɚɥɢɬɢɱɟɫɤɢɟ ɪɟɚɤɰɢɢ ɩɪɨɬɟɤɚɸɬ ɩɨ ɦɚɪɲɪɭɬɭ ɢɡ ɧɟɫɤɨɥɶɤɢɯ ɩɨɫɥɟ
ɞɨɜɚɬɟɥɶɧɵɯɢɥɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɩɚɪɚɥɥɟɥɶɧɵɯɫɬɚɞɢɣɜɪɟɡɭɥɶɬɚɬɟ
ɤɨɬɨɪɵɯ ɤɚɬɚɥɢɡɚɬɨɪ ɪɟɚɥɢɡɭɟɬɫɹ ɜɩɟɪɜɨɣ ɫɬɚɞɢɢ ɢ ɜɧɨɜɶ ɪɟɝɟɧɟɪɢ
ɪɭɟɬɫɹɜɩɨɫɥɟɞɧɟɣ>@
ɋɯɟɦɚɬɢɱɟɫɤɢɷɬɨɦɨɠɧɨɩɪɟɞɫɬɚɜɢɬɶɫɥɟɞɭɸɳɢɦɨɛɪɚɡɨɦ
K
SE PEo
vKSE
p
ªº
>@
¬¼
K
SE PEo
vKSE
E
>@>@
ªº
SE
>
¬¼
ɉɪɢ ɷɬɨɦ ɫɤɨɪɨɫɬɶ ɯɢɦɢɱɟɫɤɨɝɨ ɩɪɟɜɪɚɳɟɧɢɹ ɜ ɤɢɧɟɬɢɱɟɫɤɨɣ
ɫɢɫɬɟɦɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɭɦɦɨɣ ɤɚɬɚɥɢɬɢɱɟɫɤɨɣ ɢ ɧɟɤɚɬɚɥɢɬɢɱɟɫɤɨɣ
ɪɟɚɤɰɢɣ
dx
rdt
ɉɭɫɬɶ
ɝɞɟr = r
+ r
0
K
ȼɛɨɥɶɲɢɧɫɬɜɟɫɥɭɱɚɟɜɤɚɬɚɥɢɬɢɱɟɫɤɢɣɷɮɮɟɤɬɨɱɟɧɶɜɟɥɢɤ ɩɨ
r
ɷɬɨɦɭ
ɩɨɫɪɚɜɧɟɧɢɸɫrɄɨɱɟɧɶɦɚɥɨ
0
Ⱦɥɹɪɟɚɤɰɢɢɩɟɪɜɨɝɨɩɨɪɹɞɤɚɦɨɠɧɨɡɚɩɢɫɚɬɶ
K
P o
ɬɚɤɤɚɤ
Ʉ
ɋɊɋo
dx
dt
ax Kcax
Ʉ = constɩɨɫɥɟɢɧɬɟɝɪɢɪɨɜɚɧɢɹɩɨɥɭɱɚɟɦ
A
K
K
K
K
K
KKc K
Ʉɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ
OQ
ax
a
ɨɩɵɬ
Ʉ
ɤɨɬɨɪɭɸ ɨɩɪɟɞɟɥɹɸɬ ɷɤɫɩɟ
ɨɩɵɬ.
ɪɢɦɟɧɬɚɥɶɧɨɢɡɦɟɧɹɟɬɫɹ ɥɢɧɟɣɧɨɫɤɨɧɰɟɧɬɪɚɰɢɟɣɤɚɬɚɥɢɡɚɬɨɪɚȾɥɹ
ɧɚɯɨɠɞɟɧɢɹ
ɱɟɧɢɸɫɨɫɶɸɨɪɞɢɧɚɬɧɚɯɨɞɹɬ
Ʉ
ɢɄ2ɫɬɪɨɹɬ ɝɪɚɮɢɤɄ
1
ɨɩɵɬ.
Ʉ
ɚɩɨɭɝɥɭɧɚɤɥɨɧɚɄ2
1
Ⱦɥɹɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɣɪɟɚɤɰɢɢ
KK
nn
BCo o
ɝɞɟ ɢɫɯɨɞɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɦɨɥɟɤɭɥɵ
ɩɪɟɞɫɬɚɜɢɬɶɜɜɢɞɟ
dn
ɉɪɢɧɢɦɚɹ ɱɬɨ
dn
dt
nne
Kn
dt
nKn
t
ɢ ɩɨɞɫɬɚɜɥɹɹ ɟɝɨ ɜ ɩɪɟɞɵɞɭɳɟɟ
ɭɪɚɜɧɟɧɢɟɩɨɥɭɱɢɦ
dn
Kn Kne
dt
ɉɨɫɥɟɢɧɬɟɝɪɢɪɨɜɚɧɢɹ
K
nn e e
KK
± ɤɨɧɰɟɧɬɪɚɰɢɹɢɩɨɩɟɪɟɫɟ
n
Ⱥ ɪɚɜɧɚ n
tKt
ɫɤɨɪɨɫɬɶ ɦɨɠɧɨ
0
t
ɂɫɯɨɞɹɢɡɪɟɚɤɰɢɢ
nn e
Ʉ2 >> Ʉ
ȿɫɥɢ
ɬɨɝɞɚ
1
ɫɹɩɟɪɜɨɣɤɨɧɫɬɚɧɬɨɣ
n
= n1+ n
0
ªº
«»
KK
¬¼
nn e
Ʉ
1
+ n
2
3
KK
Kt
KKe
t
ɬɟɫɤɨɪɨɫɬɶɨɩɪɟɞɟɥɹɟɬ
Kt
Ʉɨɝɞɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɤɨɦɩɥɟɤɫɚ ɩɨɪɹɞɤɚ n2
K
dn
ɢɫɥɟɞɭɟɬɱɬɨ
ɫɬɚɰɢɨɧɚɪɧɚɬɨɝɞɚ
dt
Kn Kne
t
ɇɚɨɫɧɨɜɚɧɢɢɜɵɲɟɩɪɟɞɨɫɬɚɜɥɟɧɧɨɝɨɦɨɠɧɨɨɩɪɟɞɟɥɢɬɶ
tKtK
eeKnKnKn
tK
eKnKn
tK
eKnn
tKtKtK
eeKnKnenK
n
2
ɉɪɢɧɢɦɚɹɱɬɨ
Ʉ2n2 – Ʉ1n1 = 0ɬɨɝɞɚ
K
nn
n
K
nK
nK
tKtK
enKenK
K
K
tK
e
ɉɪɢɦɟɪɨɦɬɚɤɨɣɪɟɚɤɰɢɢɦɨɠɟɬɫɥɭɠɢɬɶɪɟɚɤɰɢɹɪɚɞɢɨɚɤɬɢɜɧɨɝɨ
ɪɚɫɩɚɞɚ
ooo
KKK
ȽCBA
Ⱥɞɢɚɛɚɬɢɱɟɫɤɢɟɢɧɟɚɞɢɚɛɚɬɢɱɟɫɤɢɟɪɟɚɤɰɢɢ
Ɍɪɚɧɫɦɢɫɫɢɨɧɧɵɣɤɨɷɮɮɢɰɢɟɧɬ
Ⱥɞɢɚɛɚɬɢɱɟɫɤɢɟ ɪɟɚɤɰɢɢ ± ɷɬɨ ɩɪɨɰɟɫɫɵ ɩɨɥɧɨɫɬɶɸ ɩɪɨɬɟɤɚɸ
ɳɢɟɧɚ ɨɞɧɨɣɩɨɜɟɪɯɧɨɫɬɢ ɧɟɚɞɢɚɛɚɬɢɱɟɫɤɢɟɤɨɝɞɚɢɦɟɟɬɫɹɜɨɡɦɨɠ
ɧɨɫɬɶɩɟɪɟɯɨɞɚɫɨɞɧɨɣɩɨɜɟɪɯɧɨɫɬɢɧɚɞɪɭɝɭɸ
ɉɪɟɞɩɨɥɨɠɢɦ ɱɬɨ ɜ ɧɟɤɨɬɨɪɨɣ ɚɞɢɚɛɚɬɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɢɫɯɨɞ
ɧɵɟɜɟɳɟɫɬɜɚɢɩɪɨɞɭɤɬɵɪɟɚɤɰɢɢɧɚɯɨɞɹɬɫɹɜɩɨɥɧɨɦɬɟɩɥɨɜɨɦ ɪɚɜ
ɧɨɜɟɫɢɢȼɷɬɨɦɫɥɭɱɚɟɫɢɫɬɟɦɚɧɚɯɨɞɢɬɫɹɧɚɜɟɪɲɢɧɟɷɧɟɪɝɟɬɢɱɟɫɤɨ
U
U
U
U
f
U
U
ɝɨ ɛɚɪɶɟɪɚ Ʌɢɲɶ ɧɟɤɨɬɨɪɚɹ ɞɨɥɹ
ɯ ɦɨɠɟɬ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɩɨɤɢɧɭɬɶ
ɢɫɯɨɞɧɨɟɫɨɫɬɨɹɧɢɟɢɩɟɪɟɣɬɢɤ ɤɨɧɟɱɧɨɦɭ ɧɟ ɜɨɡɜɪɚɳɚɹɫɶ ɤ ɢɫɯɨɞ
ɧɨɦɭ ɗɬɚ ɞɨɥɹ
ɯ ± ɟɫɬɶ ɬɪɚɧɫɦɢɫɫɢɨɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɉɭɫɬɶ Ⱥ±
ɱɢɫɥɨ ɫɢɫɬɟɦ ɞɨɫɬɢɝɚɸɳɢɯ ɜɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɚɤɬɢɜɢɪɨɜɚɧɧɨɝɨ ɫɨ
ɫɬɨɹɧɢɹ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɢɡ ɢɫɯɨɞɧɨɝɨ ɫɨɫɬɨɹɧɢɹ
ȼ±ɱɢɫɥɨɫɢɫɬɟɦ
ɩɪɢɯɨɞɹɳɢɯɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɢɡɤɨɧɟɱɧɨɝɨɫɨɫɬɨɹɧɢɹ
ɢ
ɜɟɪɨɹɬɧɨɫɬɢɨɬɪɚɠɟɧɢɹɫɥɟɜɚɧɚɩɪɚɜɨɢɧɚɨɛɨɪɨɬ
i
f
ɑɢɫɥɨɩɟɪɟɯɨɞɨɜɱɟɪɟɡɚɤɬɢɜɢɪɨɜɚɧɧɨɟɫɨɫɬɨɹɧɢɟɫɥɟɜɚɧɚɩɪɚɜɨ
ɢɫɩɪɚɜɚɧɚɥɟɜɨ
erNo
NA B
er i f i f i i f i f
o
UU U U U UU U U
NA B
re f i f i f i f i f
o
U UUUU UUUU
ɉɪɢɬɟɩɥɨɜɨɦɪɚɜɧɨɜɟɫɢɢ
N
re
o
N
o
BABA
er
AB
UUU
iif
AB
UUU
fif
reN
o
UUUUUU
fiffii
ɉɨɞɫɬɚɜɥɹɹɜɜɵɪɚɠɟɧɢɟ
BA
erNo
BA
ɩɨɥɭɱɢɦ
if
i
AN
U
ire
ɑɢɫɥɨ ɫɢɫɬɟɦ ɩɨɤɢɞɚɸɳɢɯ ɢɫɯɨɞɧɨɟ ɫɨɫɬɨɹɧɢɟ ɢɞɨɫɬɢɝɚɸɳɢɯ
fNio
ɢɫɯɨɞɧɨɝɨɫɨɫɬɨɹɧɢɹ
ɛɟɡɜɨɡɜɪɚɬɚɤɧɚɱɚɥɶɧɨɦɭ
U
U
U
U
U
UiU
U
UiU
A
A1 –
U
UiU
1 –
f
f
U
f
A
A
U
A
U
1 –
U
f
i
2
A
UiU
1 –
U
f
i
f
UfU
A
i
2
A
U
U
f
i
A
B1±
U
f
B
1 –
f
f
ɂɫɯɨɞɧɨɟ
ɫɨɫɬɨɹɧɢɟ
ɉɨɨɩɪɟɞɟɥɟɧɢɸ
x
ɂɡɡɚɜɢɫɢɦɨɫɬɢɫɥɟɞɭɟɬɱɬɨɩɪɢ
B
U
i
B
f
2
B
U
U
i
f
Ⱥɤɬɢɜɢɪɨɜɚɧɧɨɟ
ɫɨɫɬɨɹɧɢɟ
NNxo
refi
UU
if
UU
if
ɯĺɟɫɥɢ
AAN
B
Ʉɨɧɟɱɧɨɟ
ɫɨɫɬɨɹɧɢɟ
ɢ
i
B
U
1 –
i
2
B
i
UUUUUUUU
fiffififfi
Ⱦɥɹɧɟɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨɩɪɨɰɟɫɫɚɪɚɫɫɦɨɬɪɢɪɟɚɤɰɢɸ
B
wx + yz = xy + wz
Ɋɚɫɩɪɟɞɟɥɟɧɢɟɫɜɹɡɟɣɜɧɚɱɚɥɶɧɵɯɢɤɨɧɟɱɧɵɯɫɨɫɬɨɹɧɢɹɯɦɨɠɧɨ
f
1 –
f
U
f
f
ɩɪɟɞɫɬɚɜɢɬɶɫɥɟɞɭɸɳɢɦɢɜɚɥɟɧɬɧɵɦɢɫɯɟɦɚɦɢ
w – x y – z x – y w – z
$ %
ɗɧɟɪɝɢɹ ɷɬɨɣ ɫɢɫɬɟɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɟɲɟɧɢɟɦ ɜɨɥɧɨɜɨɝɨ ɭɪɚɜ
x
ɧɟɧɢɹɂɡɩɨɫɥɟɞɧɟɝɨɜɵɬɟɤɚɟɬɮɨɪɦɭɥɚɅɨɧɞɨɧɚɧɚɨɫɧɨɜɚɧɢɢɤɨɬɨ
ɪɨɣɫɬɪɨɢɬɫɹɩɨɥɧɚɹɩɨɜɟɪɯɧɨɫɬɶɩɨɬɟɧɰɢɚɥɶɧɨɣɷɧɟɪɝɢɢ
ȿɫɥɢɫɨɛɫɬɜɟɧɧɵɟɮɭɧɤɰɢɢ
ij
ɢijȼɜɡɧɚɱɢɬɟɥɶɧɨɣɦɟɪɟɩɟɪɟɤɪɵ
Ⱥ
ɜɚɸɬɫɹ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ
ɨɛɦɟɧɧɵɟɢɧɬɟɝɪɚɥɵ ɱɬɨɩɪɢɜɨ
B
A
ɞɢɬ ɤ ɡɚɤɪɭɝɥɟɧɢɸ ɩɨɜɟɪɯɧɨɫɬɢ
ɜɛɥɢɡɢɢɯɩɟɪɟɫɟɱɟɧɢɹ
ɍɦɟɧɶɲɟɧɢɟ ɷɧɟɪɝɢɢ ɚɤɬɢ
2E
AB
ɜɚɰɢɢɡɚɫɱɟɬɩɟɪɟɤɪɵɜɚɧɢɹɪɚɜ
ɧɨ ɪɟɡɨɧɚɧɫɧɨɣ ɢɥɢ ɨɛɦɟɧɧɨɣ
ɷɧɟɪɝɢɢ ɜ ɚɤɬɢɜɢɪɨɜɚɧɧɨɦ ɫɨ
A
B
ɫɬɨɹɧɢɢ ɗɬɨ ɭɦɟɧɶɲɟɧɢɟ ɜɨɡ
ɧɢɤɚɟɬ ɜɫɥɟɞɫɬɜɢɟ ɜɵɪɨɠɞɟɧɢɹ
ɫɢɫɬɟɦɵ ɜ ɬɨɱɤɟ ɩɟɪɟɫɟɱɟɧɢɹ ɜ
ɤɨɬɨɪɨɣɫɢɫɬɟɦɚɢɦɟɟɬɞɜɟɫɨɛɫɬɜɟɧɧɵɟɮɭɧɤɰɢɢ
ij
ɢijȼɧɨɪɚɜɧɵɦɢ
Ⱥ
ɷɧɟɪɝɢɹɦɢ
ȿɫɥɢɪɟɡɨɧɚɧɫɧɚɹɷɧɟɪɝɢɹɜɚɤɬɢɜɢɪɨɜɚɧɧɨɦɫɨɫɬɨɹɧɢɢɧɟɜɟɥɢɤɚ
ɬɨɜɟɪɯɧɹɹɢɧɢɠɧɹɹɩɨɜɟɪɯɧɨɫɬɢɪɚɫɩɨɥɨɠɟɧɵɛɥɢɡɤɨ ɞɪɭɝ ɤ ɞɪɭɝɭ
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɢɦɟɟɬɫɹ ɫɪɚɜɧɢɬɟɥɶɧɨ ɛɨɥɶɲɚɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɟɪɟɯɨɞɚ
ɚɤɬɢɜɢɪɨɜɚɧɧɨɝɨɤɨɦɩɥɟɤɫɚɧɚɜɟɪɯɧɸɸɩɨɜɟɪɯɧɨɫɬɶ ɇɟɚɞɢɚɛɟɬɢɱɟ
ɫɤɢɟɪɟɚɤɰɢɢ ɩɪɨɬɟɤɚɸɬɨɛɵɱɧɨ ɤɨɝɞɚɪɟɚɤɰɢɹɫɨɩɪɨɜɨɠɞɚɟɬɫɹɷɥɟɤ
ɬɪɨɧɧɵɦɩɟɪɟɯɨɞɨɦ
ȼɟɪɨɹɬɧɨɫɬɶɩɟɪɟɯɨɞɚɫɨɞɧɨɣɩɨɜɟɪɯɧɨɫɬɢɧɚɞɪɭɝɭɸ
§·
H[S
ݱɪɟɡɨɧɚɧɫɧɚɹɷɧɟɪɝɢɹɚɤɬɢɜɢɪɨɜɚɧɧɨɝɨɫɨɫɬɨɹɧɢɹ
ɝɞɟ
SH
¨¸
©¹
hv
SS
if
ɯ
v±ɫɤɨɪɨɫɬɶɫɤɨɬɨɪɨɣɫɢɫɬɟɦɚɩɪɨɯɨɞɢɬɪɚɫɫɬɨɹɧɢɟɦɟɠɞɭɩɨ
P
x
U
ɜɟɪɯɧɨɫɬɹɦɢ
ʜ
Si – S
ʜ ± ɚɛɫɨɥɸɬɧɚɹ ɜɟɥɢɱɢɧɚ ɪɚɡɧɨɫɬɢ ɭɝɥɨɜɵɯ ɤɨɷɮɮɢɰɢɟɧ
f
ɬɨɜ ɞɜɭɯ ɤɚɫɚɬɟɥɶɧɵɯ ɤ ɧɚɱɚɥɶɧɨɣ ɢ ɤɨɧɟɱɧɨɣ ɩɨɜɟɪɯɧɨɫɬɹɦ ɜ
ɬɨɱɤɟɢɯɩɟɪɟɫɟɱɟɧɢɹ
v
H
ɍɪɚɜɧɟɧɢɟ ɫɩɪɚɜɟɞɥɢɜɨ ɞɥɹ ɫɥɭɱɚɹ
ȝ±ɩɪɢɜɟɞɟɧɧɚɹ
ɦɚɫɫɚɫɢɫɬɟɦɵȼɟɪɨɹɬɧɨɫɬɶɬɨɝɨɱɬɨɫɢɫɬɟɦɚɨɫɬɚɟɬɫɹɧɚɧɢɠɧɟɣɩɨ
ɜɟɪɯɧɨɫɬɢ
USH
ªº
H[S
¬¼
hv S S
if
Ɇɟɬɨɞɚɤɬɢɜɢɪɨɜɚɧɧɨɝɨɤɨɦɩɥɟɤɫɚȼɵɪɚɠɟɧɢɟɤɨɧɫɬɚɧɬɵ
ɫɤɨɪɨɫɬɢɱɟɪɟɡɫɬɚɬɢɫɬɢɱɟɫɤɢɟɫɭɦɦɵ
ȼɥɸɛɨɦ ɩɪɨɰɟɫɫɟɜ ɤɨɬɨɪɨɦɩɪɢɧɢɦɚɸɬ ɭɱɚɫɬɢɟɚɬɨɦɵ ɢɥɢɦɨ
ɥɟɤɭɥɵɢɤɨɬɨɪɵɣɬɪɟɛɭɟɬɷɧɟɪɝɢɢɚɤɬɢɜɚɰɢɢɬɟɫɤɨɪɨɫɬɶɤɨɬɨɪɨɝɨ
TeD
ɡɚɜɢɫɢɬ ɨɬ ɦɧɨɠɢɬɟɥɹ
ɚɬɨɦɵ ɢɥɢɦɨɥɟɤɭɥɵ ɞɨɥɠɧɵ ɫɧɚɱɚɥɚ
ɫɛɥɢɡɢɬɶɫɹɞɥɹɨɛɪɚɡɨɜɚɧɢɹɚɤɬɢɜɢɪɨɜɚɧɧɨɝɨɤɨɦɩɥɟɤɫɚɢɥɢɩɟɪɟɣɬɢ
ɜɚɤɬɢɜɢɪɨɜɚɧɧɨɟɫɨɫɬɨɹɧɢɟȺɤɬɢɜɢɪɨɜɚɧɧɵɣɤɨɦɩɥɟɤɫɧɚɯɨɞɢɬɫɹɧɚ
ɜɟɪɲɢɧɟ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ
Z
A – X – Z
ɛɚɪɶɟɪɚ
ɋɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɨɩ
ɪɟɞɟɥɹɟɬɫɹɫɤɨɪɨɫɬɶɸɫ
ɤɨɪɨɣɚɤɬɢɜɢɪɨɜɚɧɧɵɣɤɨɦ
ɩɥɟɤɫ ɩɟɪɟɯɨɞɢɬ ɱɟɪɟɡ ɜɟɪ
ɲɢɧɭɛɚɪɶɟɪɚ
A Z
X
Ʉɨɧɮɢɝɭɪɚɰɢɹ ɚɤɬɢ
ɜɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɨɛ
X
ɥɚɞɚɟɬ ɜɫɟɦɢ ɫɜɨɣɫɬɜɚɦɢ
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