Химическая кинетика. Наумов А.В. - 4 стр.

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ɳɟɫɬɜɚ ɜ ɫɢɫɬɟɦɟ ɜ ɰɟɥɨɦ, ɞɚ ɟɳɟ ɜ ɨɬɞɟɥɶɧɨ ɜɡɹɬɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ,
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɬɪɭɞɧɭɸ ɢ ɧɟɧɭɠɧɭɸ ɡɚɞɚɱɭ. Ɇɵ ɛɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ
ɬɨɥɶɤɨ
ɝɨɦɨɝɟɧɧɵɟ ɫɢɫɬɟɦɵ, ɬɨ ɟɫɬɶ ɫɢɫɬɟɦɵ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɟ ɫɨɛɨɣ
ɫɩɥóɲɧɨɟ ɬɟɥɨ, ɧɟ ɢɦɟɸɳɟɟ ɝɪɚɧɢɰ ɪɚɡɞɟɥɚ ɦɟɠɞɭ ɫɜɨɢɦɢ ɨɞɧɨɪɨɞɧɵɦɢ
ɱɚɫɬɹɦɢ. Ɍɨɝɞɚ, ɪɚɡɞɟɥɢɜ (I.3) ɧɚ ɨɛɴɟɦ ɫɢɫɬɟɦɵ
V, ɩɨɥɭɱɢɦ ɨɛɴɟɦɧɭɸ
ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ
1
i
i
C
V
Q
w
v
. (I.4)
Ɂɞɟɫɶ
C
i
= n
i
/V – ɤɨɧɰɟɧɬɪɚɰɢɹ i-ɝɨ ɜɟɳɟɫɬɜɚ – ɜɟɥɢɱɢɧɚ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ
ɢɡɦɟɪɹɟɦɚɹ
*
)
. ɉɪɢ ɷɬɨɦ ɦɵ ɩɪɢɧɢɦɚɟɦ ɨɫɧɨɜɧɨɟ ɞɨɩɭɳɟɧɢɟ, ɫɨɫɬɨɹɳɟɟ ɜ
ɬɨɦ, ɱɬɨ ɫɢɫɬɟɦɚ ɪɟɚɝɢɪɭɟɬ ɛɟɡ ɢɡɦɟɧɟɧɢɹ ɨɛɴɟɦɚ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɬɨɥɶɤɨ ɜ
ɷɬɨɦ ɫɥɭɱɚɟ ɜɟɥɢɱɢɧɚ (I.4) ɞɚɟɬ ɩɪɚɜɢɥɶɧɨɟ ɜɵɪɚɠɟɧɢɟ ɫɤɨɪɨɫɬɢ. ɂɧɚɱɟ,
ɟɫɥɢ ɫɢɫɬɟɦɚ ɪɟɚɝɢɪɭɟɬ ɧɟɢɡɨɯɨɪɧɨ (
V z const), ɩɪɨɢɡɜɨɞɧɚɹ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ
ɪɚɜɧɚ
11
ii
CnC
VV
i
V .
ȼɬɨɪɨɣ ɱɥɟɧ ɫɜɹɡɚɧ ɫ ɢɡɦɟɧɟɧɢɟɦ ɤɨɧɰɟɧɬɪɚɰɢɢ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɢɡɦɟɧɟɧɢɹ
ɨɛɴɟɦɚ, ɚ ɧɟ ɪɟɚɤɰɢɢ (ɟɝɨ ɧɚɡɵɜɚɸɬ ɢɧɨɝɞɚ ɪɚɡɛɚɜɥɟɧɢɟɦ). ȿɫɥɢ ɢɡɦɟɧɟɧɢɟ
ɨɛɴɟɦɚ ɢɡɜɟɫɬɧɨ, ɬɨ ɪɚɡɛɚɜɥɟɧɢɟ
i
CV V
ɦɨɠɧɨ ɜɩɨɫɥɟɞɫɬɜɢɢ ɢɫɤɥɸɱɢɬɶ.
Ɍɟɩɟɪɶ ɦɵ ɢɦɟɟɦ ɪɚɛɨɱɟɟ ɨɩɪɟɞɟɥɟɧɢɟ ɫɤɨɪɨɫɬɢ, ɤɨɬɨɪɵɦ ɢ ɛɭɞɟɦ
ɩɨɥɶɡɨɜɚɬɶɫɹ ɜ ɞɚɥɶɧɟɣɲɟɦ. Ɉɛɵɱɧɨ ɡɚ ɯɨɞɨɦ ɪɟɚɤɰɢɢ ɫɥɟɞɹɬ, ɜɵɛɢɪɚɹ
ɨɞɢɧ ɢɡ ɪɟɚɝɟɧɬɨɜ (ɫɤɚɠɟɦ, ɨɞɢɧ ɢɡ ɢɫɯɨɞɧɵɯ ɪɟɚɝɟɧɬɨɜ
A
i
) ɢ ɢɡɦɟɪɹɹ ɟɝɨ
ɤɨɧɰɟɧɬɪɚɰɢɸ ɜ ɨɬɞɟɥɶɧɵɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ. ɗɬɨɬ ɪɟɚɝɟɧɬ ɞɨɥɠɟɧ ɨɛɥɚ-
ɞɚɬɶ ɬɚɤɢɦɢ ɫɜɨɣɫɬɜɚɦɢ, ɤɨɬɨɪɵɟ ɞɟɥɚɸɬ ɜɨɡɦɨɠɧɵɦ ɢ ɭɞɨɛɧɵɦ ɚɧɚɥɢɬɢ-
ɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɟɝɨ ɤɨɧɰɟɧɬɪɚɰɢɢ. ɉɪɨɢɡɜɨɞɧɭɸ
i
C
i
v , ɜɵɱɢɫɥɹɟ-
ɦɭɸ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɤɢɧɟɬɢɱɟɫɤɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ
C
i
(W), ɧɚɡɵɜɚɸɬ
ɫɤɨɪɨɫɬɶɸ ɩɨ ɪɟɚɝɟɧɬɭ. Ⱦɥɹ ɪɚɡɧɵɯ ɭɱɚɫɬɧɢɤɨɜ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɪɟɚɤɰɢɢ
ɷɬɚ ɜɟɥɢɱɢɧɚ, ɜ ɨɬɥɢɱɢɟ ɨɬ
v, ɪɚɡɥɢɱɧɚ. ɉɨɷɬɨɦɭ ɜɨ ɜɫɟɯ ɭɪɚɜɧɟɧɢɹɯ ɯɢɦɢ-
ɱɟɫɤɨɣ ɤɢɧɟɬɢɤɢ ɫɤɨɪɨɫɬɶ ɮɢɝɭɪɢɪɭɟɬ ɜ ɜɢɞɟ (I.4) ɢɥɢ (I.3).
Ɉɩɪɟɞɟɥɟɧɢɟ (I.4) ɡɚɩɢɫɚɧɨ ɞɥɹ ɢɫɯɨɞɧɨɝɨ
i-ɝɨ ɜɟɳɟɫɬɜɚ. ȿɫɥɢ ɪɚɫɫɦɚɬ-
ɪɢɜɚɬɶ ɩɪɨɬɟɤɚɧɢɟ ɪɟɚɤɰɢɢ ɩɨ ɭɪɚɜɧɟɧɢɸ (I.1) ɫɥɟɜɚ ɧɚɩɪɚɜɨ, ɞɥɹ ɧɟɝɨ
, ɚ ɩɨɬɨɦɭ v > 0. Ɉɬɧɨɫɢɬɟɥɶɧɨ ɥɸɛɨɝɨ ɢɡ ɩɪɨɞɭɤɬɨɜ ɮɨɪɦɭɥɚ (I.4)
ɞɨɥɠɧɚ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɜ ɜɢɞɟ:
0
i
C
1
j
j
C
Q
v
.
*)
Ɉɛ ɨɞɧɨɦ ɢɡ ɫɩɨɫɨɛɨɜ ɟɟ ɢɡɦɟɪɟɧɢɹ ɪɟɱɶ ɛɭɞɟɬ ɢɞɬɢ ɧɢɠɟ, ɜɨ II ɱɚɫɬɢ ɧɚɲɟɝɨ ɩɨ-
ɫɨɛɢɹ.
7
ɉɨɤɚ ɦɵ ɫɨɯɪɚɧɹɟɦ ɹɜɧɨɟ ɪɚɡɥɢɱɢɟ ɦɟɠɞɭ ɢɫɯɨɞɧɵɦɢ ɜɟɳɟɫɬɜɚɦɢ ɢ ɩɪɨ-
ɞɭɤɬɚɦɢ, ɯɨɬɹ ɜɩɨɫɥɟɞɫɬɜɢɢ ɭɜɢɞɢɦ, ɱɬɨ ɷɬɨ ɜɨɩɪɨɫ ɫɨɝɥɚɲɟɧɢɹ.
3. Ɂɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ
ȼ ɫɚɦɨɦ ɧɚɱɚɥɟ ɦɵ ɭɩɨɦɹɧɭɥɢ ɨɛ ɨɫɧɨɜɧɨɣ ɡɚɞɚɱɟ ɮɨɪɦɚɥɶɧɨɣ ɤɢɧɟ-
ɬɢɤɢ. Ɍɟɩɟɪɶ ɟɟ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: ɞɥɹ ɞɚɧɧɨɣ
ɪɟɚɤɰɢɢ ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɡɚɤɨɧ
C
k
(W), ɩɨ ɤɨɬɨɪɨɦɭ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɫɟɯ
ɭɱɚɫɬɧɢɤɨɜ ɪɟɚɤɰɢɢ ɢɡɦɟɧɹɸɬɫɹ ɜɨ ɜɪɟɦɟɧɢ. ȼɜɢɞɭ ɫɨɨɬɧɨɲɟɧɢɹ (I.2) ɹɫ-
ɧɨ, ɱɬɨ ɛɭɞɟɬ ɞɨɫɬɚɬɨɱɧɨ ɫɞɟɥɚɬɶ ɷɬɨ ɞɥɹ ɨɞɧɨɝɨ ɢɡ ɪɟɚɝɟɧɬɨɜ; ɞɥɹ ɜɫɟɯ ɨɫ-
ɬɚɥɶɧɵɯ ɡɚɜɢɫɢɦɨɫɬɢ ɜɵɱɢɫɥɹɸɬɫɹ ɩɨ ɫɬɟɯɢɨɦɟɬɪɢɢ. Ɏɭɧɤɰɢɹ
C
k
(W) ɧɚɡɵ-
ɜɚɟɬɫɹ
ɤɢɧɟɬɢɱɟɫɤɢɦ ɡɚɤɨɧɨɦ ɪɟɚɤɰɢɢ.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɫɥɟɞɭɟɬ ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ ɡɧɚɬɶ, ɤɚɤɢɦ ɨɛɪɚ-
ɡɨɦ ɫɤɨɪɨɫɬɶ ɫɜɹɡɚɧɚ ɫ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ ɜɟɳɟɫɬɜ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟ-
ɧɢ. ȿɫɥɢ ɬɚɤɭɸ ɫɜɹɡɶ ɭɞɚɫɬɫɹ ɧɚɣɬɢ ɜ ɹɜɧɨɦ ɜɢɞɟ, ɬɨ ɡɚɞɚɱɚ ɫɜɟɞɟɬɫɹ ɤ ɪɟ-
ɲɟɧɢɸ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ

1
1
(), , ()
i
iN
CfC C
Q
W
W
.
ɍɫɬɚɧɨɜɢɬɶ ɡɚɜɢɫɢɦɨɫɬɶ
f, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɦɨɠɧɨ ɥɢɛɨ ɷɦɩɢɪɢɱɟɫɤɢɦ ɩɭ-
ɬɟɦ, ɥɢɛɨ ɧɚ ɨɫɧɨɜɚɧɢɢ ɦɨɞɟɥɢ, ɨɩɪɟɞɟɥɟɧɧɵɦ ɨɛɪɚɡɨɦ ɬɨɥɤɭɸɳɟɣ ɦɟɯɚ-
ɧɢɡɦ ɪɟɚɤɰɢɢ.
Ɋɚɫɫɦɨɬɪɢɦ ɜ ɤɚɱɟɫɬɜɟ ɬɚɤɨɣ ɦɨɞɟɥɢ ɪɟɚɝɢɪɭɸɳɭɸ ɫɦɟɫɶ ɢɞɟɚɥɶɧɵɯ
ɝɚɡɨɜ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɩɪɨɢɡɨɲɟɥ ɚɤɬ ɩɪɟɜɪɚɳɟɧɢɹ, ɨɧɢ
ɞɨɥɠɧɵ ɫɛɥɢɡɢɬɶɫɹ ɩɨ ɦɟɧɶɲɟɣ ɦɟɪɟ ɧɚ ɪɚɫɫɬɨɹɧɢɟ, ɫɪɚɜɧɢɦɨɟ ɫ ɢɯ ɫɨɛɫɬ-
ɜɟɧɧɵɦɢ ɪɚɡɦɟɪɚɦɢ. ɗɬɭ ɫɢɬɭɚɰɢɸ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɦɨɠɧɨ ɫɱɢɬɚɬɶ
ɭɞɚɪɨɦ. ȼ ɬɚɤɨɦ ɫɥɭɱɚɟ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɛɭɞɟɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɱɚɫɬɨɬɟ
ɫɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰ, ɩɪɢɱɟɦ ɧɚɫ ɭɫɬɪɚɢɜɚɸɬ ɧɟ ɤɚɤɢɟ ɭɝɨɞɧɨ ɫɬɨɥɤɧɨɜɟ-
ɧɢɹ, ɚ ɬɨɥɶɤɨ ɜ ɞɚɧɧɨɣ ɤɨɦɛɢɧɚɰɢɢ. ɂɦɟɟɬɫɹ ɜ ɜɢɞɭ, ɱɬɨ ɜ ɤɚɠɞɨɦ ɚɤɬɟ
ɞɨɥɠɧɵ ɩɪɢɣɬɢ ɜ ɫɨɭɞɚɪɟɧɢɟ ɧɭɠɧɵɟ ɦɨɥɟɤɭɥɵ ɜ ɧɭɠɧɨɦ ɱɢɫɥɟ ɜ ɫɨɨɬɜɟɬ-
ɫɬɜɢɢ ɫɨ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɭɪɚɜɧɟɧɢɟɦ.
ɑɚɫɬɨɬɚ ɩ ɚ ɪ ɧ ɵ ɯ ɫɨɭɞɚɪɟɧɢɣ
z ɨɞɢɧɚɤɨɜɵɯ ɱɚɫɬɢɰ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ
ɤɜɚɞɪɚɬɭ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ:

1
2
22
16
2
A
ɤT
rN C S
SP
z
2
, (I.5)
ɝɞɟ
r – ɪɚɞɢɭɫ ɱɚɫɬɢɰɵ; P – ɟɟ ɦɚɫɫɚ; N
A
– ɱɢɫɥɨ Ⱥɜɨɝɚɞɪɨ; ɤ – ɩɨɫɬɨɹɧɧɚɹ
Ȼɨɥɶɰɦɚɧɚ. ɗɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɬɟɦ, ɱɬɨ ɩɚɪɧɨɟ ɫɨɭɞɚɪɟɧɢɟ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɵɦ
ɫɨɛɵɬɢɟɦ, ɢ ɟɝɨ ɦɨɠɧɨ ɩɪɨɤɨɦɦɟɧɬɢɪɨɜɚɬɶ ɬɚɤ. ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɧɚɪɭɠɢɬɶ
ɱɚɫɬɢɰɭ ɜ ɦɚɥɨɦ ɨɛɴɟɦɟ (ɩɨɪɹɞɤɚ
r
3
), ɨɤɪɭɠɚɸɳɟɦ ɜɵɞɟɥɟɧɧɭɸ ɬɨɱɤɭ
ɩɪɨɫɬɪɚɧɫɬɜɚ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ
C. ɋɬɨɥɤɧɨɜɟɧɢɟ – ɟɫɬɶ ɫɨɛɵɬɢɟ, ɫɨɫɬɨɹ-
ɳɢɟ ɜ ɩɨɩɚɞɚɧɢɢ ɫɪɚɡɭ 2-ɯ ɱɚɫɬɢɰ ɜ ɷɬɨɬ ɨɛɴɟɦ, ɢ ɜɟɪɨɹɬɧɨɫɬɶ ɟɝɨ ɪɚɜɧɚ
ɩɪɨɢɡɜɟɞɟɧɢɸ ɷɥɟɦɟɧɬɚɪɧɵɯ ɜɟɪɨɹɬɧɨɫɬɟɣ, ɬɨ ɟɫɬɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ
C
2
.
8
ɳɟɫɬɜɚ ɜ ɫɢɫɬɟɦɟ ɜ ɰɟɥɨɦ, ɞɚ ɟɳɟ ɜ ɨɬɞɟɥɶɧɨ ɜɡɹɬɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ,                     ɉɨɤɚ ɦɵ ɫɨɯɪɚɧɹɟɦ ɹɜɧɨɟ ɪɚɡɥɢɱɢɟ ɦɟɠɞɭ ɢɫɯɨɞɧɵɦɢ ɜɟɳɟɫɬɜɚɦɢ ɢ ɩɪɨ-
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɬɪɭɞɧɭɸ ɢ ɧɟɧɭɠɧɭɸ ɡɚɞɚɱɭ. Ɇɵ ɛɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ                   ɞɭɤɬɚɦɢ, ɯɨɬɹ ɜɩɨɫɥɟɞɫɬɜɢɢ ɭɜɢɞɢɦ, ɱɬɨ ɷɬɨ ɜɨɩɪɨɫ ɫɨɝɥɚɲɟɧɢɹ.
ɬɨɥɶɤɨ ɝ ɨ ɦ ɨ ɝ ɟ ɧ ɧ ɵ ɟ ɫɢɫɬɟɦɵ, ɬɨ ɟɫɬɶ ɫɢɫɬɟɦɵ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɟ ɫɨɛɨɣ
ɫɩɥóɲɧɨɟ ɬɟɥɨ, ɧɟ ɢɦɟɸɳɟɟ ɝɪɚɧɢɰ ɪɚɡɞɟɥɚ ɦɟɠɞɭ ɫɜɨɢɦɢ ɨɞɧɨɪɨɞɧɵɦɢ                                            3. Ɂɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ
ɱɚɫɬɹɦɢ. Ɍɨɝɞɚ, ɪɚɡɞɟɥɢɜ (I.3) ɧɚ ɨɛɴɟɦ ɫɢɫɬɟɦɵ V, ɩɨɥɭɱɢɦ ɨɛɴɟɦɧɭɸ
ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ                                                                           ȼ ɫɚɦɨɦ ɧɚɱɚɥɟ ɦɵ ɭɩɨɦɹɧɭɥɢ ɨɛ ɨɫɧɨɜɧɨɣ ɡɚɞɚɱɟ ɮɨɪɦɚɥɶɧɨɣ ɤɢɧɟ-
                                        w            1                                ɬɢɤɢ. Ɍɟɩɟɪɶ ɟɟ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: ɞɥɹ ɞɚɧɧɨɣ
                                   v                   Ci .                   (I.4)   ɪɟɚɤɰɢɢ ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɡɚɤɨɧ Ck(W), ɩɨ ɤɨɬɨɪɨɦɭ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɫɟɯ
                                        V            Qi
                                                                                       ɭɱɚɫɬɧɢɤɨɜ ɪɟɚɤɰɢɢ ɢɡɦɟɧɹɸɬɫɹ ɜɨ ɜɪɟɦɟɧɢ. ȼɜɢɞɭ ɫɨɨɬɧɨɲɟɧɢɹ (I.2) ɹɫ-
Ɂɞɟɫɶ Ci = ni/V – ɤɨɧɰɟɧɬɪɚɰɢɹ i-ɝɨ ɜɟɳɟɫɬɜɚ – ɜɟɥɢɱɢɧɚ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ                ɧɨ, ɱɬɨ ɛɭɞɟɬ ɞɨɫɬɚɬɨɱɧɨ ɫɞɟɥɚɬɶ ɷɬɨ ɞɥɹ ɨɞɧɨɝɨ ɢɡ ɪɟɚɝɟɧɬɨɜ; ɞɥɹ ɜɫɟɯ ɨɫ-
ɢɡɦɟɪɹɟɦɚɹ ) . ɉɪɢ ɷɬɨɦ ɦɵ ɩɪɢɧɢɦɚɟɦ ɨɫɧɨɜɧɨɟ ɞɨɩɭɳɟɧɢɟ, ɫɨɫɬɨɹɳɟɟ ɜ
            *

                                                                                       ɬɚɥɶɧɵɯ ɡɚɜɢɫɢɦɨɫɬɢ ɜɵɱɢɫɥɹɸɬɫɹ ɩɨ ɫɬɟɯɢɨɦɟɬɪɢɢ. Ɏɭɧɤɰɢɹ Ck(W) ɧɚɡɵ-
ɬɨɦ, ɱɬɨ ɫɢɫɬɟɦɚ ɪɟɚɝɢɪɭɟɬ ɛɟɡ ɢɡɦɟɧɟɧɢɹ ɨɛɴɟɦɚ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɬɨɥɶɤɨ ɜ               ɜɚɟɬɫɹ ɤɢɧɟɬɢɱɟɫɤɢɦ ɡɚɤɨɧɨɦ ɪɟɚɤɰɢɢ.
ɷɬɨɦ ɫɥɭɱɚɟ ɜɟɥɢɱɢɧɚ (I.4) ɞɚɟɬ ɩɪɚɜɢɥɶɧɨɟ ɜɵɪɚɠɟɧɢɟ ɫɤɨɪɨɫɬɢ. ɂɧɚɱɟ,                      Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɫɥɟɞɭɟɬ ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ ɡɧɚɬɶ, ɤɚɤɢɦ ɨɛɪɚ-
ɟɫɥɢ ɫɢɫɬɟɦɚ ɪɟɚɝɢɪɭɟɬ ɧɟɢɡɨɯɨɪɧɨ (V z const), ɩɪɨɢɡɜɨɞɧɚɹ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ              ɡɨɦ ɫɤɨɪɨɫɬɶ ɫɜɹɡɚɧɚ ɫ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ ɜɟɳɟɫɬɜ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟ-
ɪɚɜɧɚ                                                                                  ɧɢ. ȿɫɥɢ ɬɚɤɭɸ ɫɜɹɡɶ ɭɞɚɫɬɫɹ ɧɚɣɬɢ ɜ ɹɜɧɨɦ ɜɢɞɟ, ɬɨ ɡɚɞɚɱɚ ɫɜɟɞɟɬɫɹ ɤ ɪɟ-
                                        1      1                                       ɲɟɧɢɸ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ
                                 C i     ni  CiV .
                                        V      V                                                                 1 
ȼɬɨɪɨɣ ɱɥɟɧ ɫɜɹɡɚɧ ɫ ɢɡɦɟɧɟɧɢɟɦ ɤɨɧɰɟɧɬɪɚɰɢɢ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɢɡɦɟɧɟɧɢɹ                                               Ci  f C1 (W),, C N (W) .
                                                                                                                 Qi
ɨɛɴɟɦɚ, ɚ ɧɟ ɪɟɚɤɰɢɢ (ɟɝɨ ɧɚɡɵɜɚɸɬ ɢɧɨɝɞɚ ɪɚɡɛɚɜɥɟɧɢɟɦ). ȿɫɥɢ ɢɡɦɟɧɟɧɢɟ
                                                                                       ɍɫɬɚɧɨɜɢɬɶ ɡɚɜɢɫɢɦɨɫɬɶ f, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɦɨɠɧɨ ɥɢɛɨ ɷɦɩɢɪɢɱɟɫɤɢɦ ɩɭ-
ɨɛɴɟɦɚ ɢɡɜɟɫɬɧɨ, ɬɨ ɪɚɡɛɚɜɥɟɧɢɟ Ci V V ɦɨɠɧɨ ɜɩɨɫɥɟɞɫɬɜɢɢ ɢɫɤɥɸɱɢɬɶ.                  ɬɟɦ, ɥɢɛɨ ɧɚ ɨɫɧɨɜɚɧɢɢ ɦɨɞɟɥɢ, ɨɩɪɟɞɟɥɟɧɧɵɦ ɨɛɪɚɡɨɦ ɬɨɥɤɭɸɳɟɣ ɦɟɯɚ-
     Ɍɟɩɟɪɶ ɦɵ ɢɦɟɟɦ ɪɚɛɨɱɟɟ ɨɩɪɟɞɟɥɟɧɢɟ ɫɤɨɪɨɫɬɢ, ɤɨɬɨɪɵɦ ɢ ɛɭɞɟɦ                     ɧɢɡɦ ɪɟɚɤɰɢɢ.
ɩɨɥɶɡɨɜɚɬɶɫɹ ɜ ɞɚɥɶɧɟɣɲɟɦ. Ɉɛɵɱɧɨ ɡɚ ɯɨɞɨɦ ɪɟɚɤɰɢɢ ɫɥɟɞɹɬ, ɜɵɛɢɪɚɹ                         Ɋɚɫɫɦɨɬɪɢɦ ɜ ɤɚɱɟɫɬɜɟ ɬɚɤɨɣ ɦɨɞɟɥɢ ɪɟɚɝɢɪɭɸɳɭɸ ɫɦɟɫɶ ɢɞɟɚɥɶɧɵɯ
ɨɞɢɧ ɢɡ ɪɟɚɝɟɧɬɨɜ (ɫɤɚɠɟɦ, ɨɞɢɧ ɢɡ ɢɫɯɨɞɧɵɯ ɪɟɚɝɟɧɬɨɜ Ai) ɢ ɢɡɦɟɪɹɹ ɟɝɨ                ɝɚɡɨɜ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɩɪɨɢɡɨɲɟɥ ɚɤɬ ɩɪɟɜɪɚɳɟɧɢɹ, ɨɧɢ
ɤɨɧɰɟɧɬɪɚɰɢɸ ɜ ɨɬɞɟɥɶɧɵɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ. ɗɬɨɬ ɪɟɚɝɟɧɬ ɞɨɥɠɟɧ ɨɛɥɚ-                    ɞɨɥɠɧɵ ɫɛɥɢɡɢɬɶɫɹ ɩɨ ɦɟɧɶɲɟɣ ɦɟɪɟ ɧɚ ɪɚɫɫɬɨɹɧɢɟ, ɫɪɚɜɧɢɦɨɟ ɫ ɢɯ ɫɨɛɫɬ-
ɞɚɬɶ ɬɚɤɢɦɢ ɫɜɨɣɫɬɜɚɦɢ, ɤɨɬɨɪɵɟ ɞɟɥɚɸɬ ɜɨɡɦɨɠɧɵɦ ɢ ɭɞɨɛɧɵɦ ɚɧɚɥɢɬɢ-                    ɜɟɧɧɵɦɢ ɪɚɡɦɟɪɚɦɢ. ɗɬɭ ɫɢɬɭɚɰɢɸ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɦɨɠɧɨ ɫɱɢɬɚɬɶ
ɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɟɝɨ ɤɨɧɰɟɧɬɪɚɰɢɢ. ɉɪɨɢɡɜɨɞɧɭɸ vi C i , ɜɵɱɢɫɥɹɟ-                  ɭɞɚɪɨɦ. ȼ ɬɚɤɨɦ ɫɥɭɱɚɟ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɛɭɞɟɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɱɚɫɬɨɬɟ
                                                                                       ɫɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰ, ɩɪɢɱɟɦ ɧɚɫ ɭɫɬɪɚɢɜɚɸɬ ɧɟ ɤɚɤɢɟ ɭɝɨɞɧɨ ɫɬɨɥɤɧɨɜɟ-
ɦɭɸ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɤɢɧɟɬɢɱɟɫɤɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ Ci(W), ɧɚɡɵɜɚɸɬ
                                                                                       ɧɢɹ, ɚ ɬɨɥɶɤɨ ɜ ɞɚɧɧɨɣ ɤɨɦɛɢɧɚɰɢɢ. ɂɦɟɟɬɫɹ ɜ ɜɢɞɭ, ɱɬɨ ɜ ɤɚɠɞɨɦ ɚɤɬɟ
ɫɤɨɪɨɫɬɶɸ ɩɨ ɪɟɚɝɟɧɬɭ. Ⱦɥɹ ɪɚɡɧɵɯ ɭɱɚɫɬɧɢɤɨɜ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɪɟɚɤɰɢɢ
                                                                                       ɞɨɥɠɧɵ ɩɪɢɣɬɢ ɜ ɫɨɭɞɚɪɟɧɢɟ ɧɭɠɧɵɟ ɦɨɥɟɤɭɥɵ ɜ ɧɭɠɧɨɦ ɱɢɫɥɟ ɜ ɫɨɨɬɜɟɬ-
ɷɬɚ ɜɟɥɢɱɢɧɚ, ɜ ɨɬɥɢɱɢɟ ɨɬ v, ɪɚɡɥɢɱɧɚ. ɉɨɷɬɨɦɭ ɜɨ ɜɫɟɯ ɭɪɚɜɧɟɧɢɹɯ ɯɢɦɢ-
                                                                                       ɫɬɜɢɢ ɫɨ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɭɪɚɜɧɟɧɢɟɦ.
ɱɟɫɤɨɣ ɤɢɧɟɬɢɤɢ ɫɤɨɪɨɫɬɶ ɮɢɝɭɪɢɪɭɟɬ ɜ ɜɢɞɟ (I.4) ɢɥɢ (I.3).                                ɑɚɫɬɨɬɚ ɩ ɚ ɪ ɧ ɵ ɯ ɫɨɭɞɚɪɟɧɢɣ z ɨɞɢɧɚɤɨɜɵɯ ɱɚɫɬɢɰ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ
     Ɉɩɪɟɞɟɥɟɧɢɟ (I.4) ɡɚɩɢɫɚɧɨ ɞɥɹ ɢɫɯɨɞɧɨɝɨ i-ɝɨ ɜɟɳɟɫɬɜɚ. ȿɫɥɢ ɪɚɫɫɦɚɬ-
                                                                                       ɤɜɚɞɪɚɬɭ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ:
ɪɢɜɚɬɶ ɩɪɨɬɟɤɚɧɢɟ ɪɟɚɤɰɢɢ ɩɨ ɭɪɚɜɧɟɧɢɸ (I.1) ɫɥɟɜɚ ɧɚɩɪɚɜɨ, ɞɥɹ ɧɟɝɨ                                                                  1
C i  0 , ɚ ɩɨɬɨɦɭ v > 0. Ɉɬɧɨɫɢɬɟɥɶɧɨ ɥɸɛɨɝɨ ɢɡ ɩɪɨɞɭɤɬɨɜ ɮɨɪɦɭɥɚ (I.4)                                         z       2
                                                                                                                      2Sr N
                                                                                                                            16ɤT  2   2
                                                                                                                                          C2,               (I.5)
                                                                                                                                  A
ɞɨɥɠɧɚ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɜ ɜɢɞɟ:                                                                                                 SP
                                                1                                     ɝɞɟ r – ɪɚɞɢɭɫ ɱɚɫɬɢɰɵ; P – ɟɟ ɦɚɫɫɚ; NA – ɱɢɫɥɨ Ⱥɜɨɝɚɞɪɨ; ɤ – ɩɨɫɬɨɹɧɧɚɹ
                                        v          Cj .
                                                                                       Ȼɨɥɶɰɦɚɧɚ. ɗɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɬɟɦ, ɱɬɨ ɩɚɪɧɨɟ ɫɨɭɞɚɪɟɧɢɟ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɵɦ
                                                Qj
                                                                                       ɫɨɛɵɬɢɟɦ, ɢ ɟɝɨ ɦɨɠɧɨ ɩɪɨɤɨɦɦɟɧɬɢɪɨɜɚɬɶ ɬɚɤ. ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɧɚɪɭɠɢɬɶ
                                                                                       ɱɚɫɬɢɰɭ ɜ ɦɚɥɨɦ ɨɛɴɟɦɟ (ɩɨɪɹɞɤɚ r3), ɨɤɪɭɠɚɸɳɟɦ ɜɵɞɟɥɟɧɧɭɸ ɬɨɱɤɭ
   *)
      Ɉɛ ɨɞɧɨɦ ɢɡ ɫɩɨɫɨɛɨɜ ɟɟ ɢɡɦɟɪɟɧɢɹ ɪɟɱɶ ɛɭɞɟɬ ɢɞɬɢ ɧɢɠɟ, ɜɨ II ɱɚɫɬɢ ɧɚɲɟɝɨ ɩɨ-   ɩɪɨɫɬɪɚɧɫɬɜɚ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ C. ɋɬɨɥɤɧɨɜɟɧɢɟ – ɟɫɬɶ ɫɨɛɵɬɢɟ, ɫɨɫɬɨɹ-
ɫɨɛɢɹ.                                                                                 ɳɢɟ ɜ ɩɨɩɚɞɚɧɢɢ ɫɪɚɡɭ 2-ɯ ɱɚɫɬɢɰ ɜ ɷɬɨɬ ɨɛɴɟɦ, ɢ ɜɟɪɨɹɬɧɨɫɬɶ ɟɝɨ ɪɚɜɧɚ
                                                                                       ɩɪɨɢɡɜɟɞɟɧɢɸ ɷɥɟɦɟɧɬɚɪɧɵɯ ɜɟɪɨɹɬɧɨɫɬɟɣ, ɬɨ ɟɫɬɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ C2.
                                            7                                                                                 8

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