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Файл:Элементы теории образования электрического тока в грунтовых и водных средах (проводниках второго рода). Монография
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Ʉɚɤ ɩɪɚɜɢɥɨ, ɷɬɢ ɱɚɫɬɢ ɡɚɪɹɠɟɧɵ ɜɡɚɢɦɧɨ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦɢ ɡɚɪɹɞɚɦɢ ɢ ɩɨɞ
HCl
l
l
HCl
HCl
ɩɚɞɚɸɬ ɩɨɞ ɞɟɣɫɬɜɢɟ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɉɨɷɬɨɦɭ ɧɚɱɢɧɚɸɬ
, ɬ.ɟ.
ɞɜɢɝɚɬɶɫɹ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɫɬɨɪɨɧɵ
ɫɬɚɧɨɜɹɬɫɹ ɢɨɧɚɦɢ
.
-
ɂɬɚɤ, ɫɨɝɥɚɫɧɨ Ʉɥɚɭɡɢɭɫɭ
3.
ɞɢɫɫɨɰɢɢɪɨɜɚɧɧɵɟ
ɧɟ ɬɪɟɛɭɟɬɫɹ
4.
».
Ⱥɪɪɟɧɢɭɫ ɫɨɜɟɪɲɟɧɧɨ ɢɡ ɞɪɭɝɢɯ ɫɨɨɛɪɚɠɟɧɢɣ ɩɪɢɲɟɥ ɤ ɬɚɤɨɦɭ ɠɟ ɜɵ
,
ɢ ɩɨɷɬɨɦɭ ɧɢɤɚɤɨɣ ɧɨɜɨɣ ɷɧɟɪɝɢɢ ɧɚ ɢɯ ɪɚɡɥɨɠɟɧɢɟ ɛɨɥɟɟ
, «
ɜ ɷɥɟɤɬɪɨɥɢɬɟ ɦɵ ɢɦɟɟɦ ɦɨɥɟɤɭɥɵ, ɱɚɫɬɶɸ
ɜɨɞɭ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɡ ɝɢɩɨɬɟɡɵ Ʉɥɚɭɡɢɭɫɚ–Ⱥɪɪɟɧɢɭɫɚ ɦɨɠɧɨ ɡɚɤɥɸɱɢɬɶ, ɱɬɨ
ɷɥɟɤɬɪɨɥɢɬɵ ɩɪɢ ɬɨɣ ɠɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢɦɟɸɬ ɛɨɥɶɲɟɟ ɨɫɦɨɬɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ
ɱɟɦ ɧɟ ɷɥɟɤɬɪɨɥɢɬɵ. ɗɬɨ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɢ ɨɩɵɬɨɦ
Ɉɞɧɚɤɨ ɡɚɦɟɬɢɦ, ɱɬɨ ɪɟɡɭɥɶɬɚɬɵ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɞɢɫɫɨɰɢɚɰɢɢ ɧɟ ɜɫɟɝɞɚ
5.
ɨɞɢɧɚɤɨɜɵ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɪɚɫɩɚɞɟɧɢɹ ɦɨɥɟɤɭɥɵ ɨɬ ɞɪɭɝɢɯ ɩɪɢɱɢɧ
ɯɥɨɪɢɫɬɵɣ ɚɦɦɨɧɢɣ
,
ɬɨɝɞɚ ɤɚɤ ɜ ɪɚɫɬɜɨɪɟ ɨɧ ɪɚɫɩɚɞɚɟɬɫɹ ɧɚ
ɦɟɪɟ
NH
ɡɚɪɹɠɟɧ ɩɨɥɨɠɢɬɟɥɶɧɨ ɢ ɢɝɪɚɟɬ ɪɨɥɶ ɦɟɬɚɥɥɚ, ɚ
4
ClNH
ɩɪɢ ɜɵɫɨɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɞɢɫɫɨɰɢɢɪɭɟɬ ɧɚ
4
NH
.
,
ɧɚɩɪɢɦɟɪ
NH
3
ɢ
C
.
4
ȼɩɪɢɜɟɞɟɧɧɨɦ ɩɪɢ
C
ɡɚɪɹɠɟɧ ɨɬɪɢɰɚ
-
,
,
ɢ
-
-
ɬɟɥɶɧɨ. ɉɚɪɵ ɠɟ
ɬɨɤɚ ɧɟ ɩɪɨɜɨɞɹɬ
6.
ɇɢ Ƚɪɨɬɝɭɫ, ɧɢ Ʉɥɚɭɡɢɭɫ, ɧɢ Ⱥɪɪɟɧɢɭɫ ɧɟ ɜɵɹɜɢɥɢ ɥɨɝɢɱɟɫɤɭɸ ɫɜɹɡɶ
,
ɦɟɠɞɭ ɨɫɦɨɬɢɱɟɫɤɢɦ ɞɚɜɥɟɧɢɟɦ ɢ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶɸ ɪɚɫɬɜɨɪɨɜ
ClNH
,
4
ɞɢɫɫɨɰɢɢɪɨɜɚɧɧɵɟ ɧɚ
ɢɦɨɥɟɤɭɥɵ
NH
NH
ɢ
3
ɥɢɲɟɧɵ ɡɚɪɹɞɨɜ
ɢ
3
,
ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ
.
.
Ɉɞɧɚɤɨ ɤɢ
ɧɟɬɢɱɟɫɤɢɟ ɜɨɡɡɪɟɧɢɹ Ʉɥɚɭɡɢɭɫɚ, ɱɬɨ «ɜɫɟ ɦɨɥɟɤɭɥɵ ɜ ɪɚɫɬɜɨɪɟ ɩɨɫɬɨɹɧɧɨ
»,
ɪɚɡɴɟɞɢɧɹɸɬɫɹ ɧɚ ɢɨɧɵ ɢ ɜɧɨɜɶ ɫɨɟɞɢɧɹɸɬɫɹ
,
ɡɚɤɨɧ
ɰɢɢɪɨɜɚɧɚ. Ɉɬ ɜɟɥɢɱɢɧɵ
ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ
ɤɨɬɨɪɵɣ ɫɜɹɡɵɜɚɟɬ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ ɢ ɤɨɧɰɟɧɬɪɚɰɢɸ ɪɚɫɬɜɨɪɚ
7.
ɉɭɫɬɶ ɜ ɞɚɧɧɨɦ ɪɚɫɬɜɨɪɟ ɱɚɫɬɶaɜɫɟɝɨ ɪɚɫɬɜɨɪɟɧɧɨɝɨ ɜɟɳɟɫɬɜɚ ɞɢɫɫɨ
a
ɛɭɞɟɬ ɡɚɜɢɫɟɬɶ ɤɚɤ ɨɫɦɨɬɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ, ɬɚɤ ɢ
.
ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɤɨɷɮɮɢɰɢɟɧɬaɛɭɞɟɬ ɡɚɜɢɫɟɬɶ ɨɬ ɬɟɦɩɟɪɚ
ɩɨɡɜɨɥɢɥɢ Ɉɫɬɜɚɥɶɞɭ ɨɬɤɪɵɬɶ
.
ɬɭɪɵ, ɨɬ ɫɜɨɣɫɬɜ ɪɚɫɬɜɨɪɢɬɟɥɹ, ɚ ɬɚɤɠɟ ɨɬ ɤɨɥɢɱɟɫɬɜɚ ɪɚɫɬɜɨɪɟɧɧɨɝɨ ɜɟɳɟɫɬɜɚ
-
-
-
.
51
Ⱦɥɹ ɪɚɜɧɨɜɟɫɢɹ, ɬ.ɟ. ɞɥɹ ɧɟɢɡɦɟɧɧɨɫɬɢ ɫɨɫɬɨɹɧɢɹ ɪɚɫɬɜɨɪɚ, ɨɱɟɜɢɞɧɨ, ɧɟɨɛɯɨ
P
-
ɞɢɦɨ, ɱɬɨɛɵ ɢɨɧɢɡɚɰɢɹ ɪɚɜɧɹɥɚɫɶ ɦɨɥɢɡɚɰɢɢ
()
2
()( )()
ɝɞɟ
n –
ɱɢɫɥɨ ɦɨɥɟɤɭɥ ɪɚɫɬɜɨɪɟɧɧɨɝɨ ɜɟɳɟɫɬɜɚ ɜ ɤɚɠɞɨɦ ɤɭɛɢɱɟɫɤɨɦ ɫɚɧɬɢɦɟɬ
ɪɟ ɪɚɫɬɜɨɪɚ
ɥɟɤɭɥɵ, ɧɚɯɨɞɹɳɢɟɫɹ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɜ ɫɜɹɡɚɧɧɨɦ ɫɨɫɬɨɹɧɢɢ
ɟɧɬ ɢɨɧɢɡɚɰɢɢ
ɳɢɯɫɹ
).
; na ⋅ –
;
ɱɢɫɥɨ ɦɨɥɟɤɭɥ ɞɢɫɫɨɰɢɢɪɨɜɚɧɧɨɝɨ ɪɚɫɬɜɨɪɚ
22
naQ ⋅⋅ –
ɱɢɫɥɨ ɦɨɥɟɤɭɥ ɦɨɥɢɡɢɪɭɸɳɢɯɫɹ (ɜɧɨɜɶ ɫɨɟɞɢɧɹɸ
:
22
,1
naQ=naP ⋅⋅⋅−⋅
nQP=aa /1/1/
⋅− , (52)
;
()
; P–
na ⋅−1–
ɦɨ
ɤɨɷɮɮɢɰɢ
ɗɬɚ ɮɨɪɦɭɥɚ ɢ ɜɵɪɚɠɚɟɬ ɡɚɤɨɧ Ɉɫɬɜɚɥɶɞɚ, ɤɨɬɨɪɵɣ ɫɜɹɡɵɜɚɟɬ ɤɨɷɮɮɢɰɢ
ɟɧɬaɫɱɢɫɥɨɦnɦɨɥɟɤɭɥ ɪɚɫɬɜɨɪɟɧɧɨɝɨ ɜɟɳɟɫɬɜɚ, ɩɪɢɯɨɞɹɳɢɯɫɹ ɧɚ ɤɚɠɞɵɣ
3
ɫɦ ɪɚɫɬɜɨɪɚ, ɬ.ɟ. ɫ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɪɚɫɬɜɨɪɚ ɨɬɧɨɲɟɧɢɟ
QP/
ɞɥɹ ɞɚɧɧɨɝɨ ɪɚɫ
-
-
-
-
-
-
ɬɜɨɪɚ ɜɟɥɢɱɢɧɚ ɩɨɫɬɨɹɧɧɚɹ, ɨɞɧɚɤɨ ɞɥɹ ɪɚɡɧɵɯ ɪɚɫɬɜɨɪɨɜ ɢ ɪɚɡɧɵɯ ɬɟɦɩɟɪɚɬɭ
ɪɵ ɢ ɞɚɜɥɟɧɢɹ ɤɚɤ
,
ɬɚɤ ɢ
Q
ɛɭɞɭɬ ɪɚɡɧɵɟ. ɉɨɷɬɨɦɭ ɡɚɤɨɧ Ɉɫɬɜɚɥɶɞɚ ɧɟ ɜɫɟ
ɝɞɚ ɫɩɪɚɜɟɞɥɢɜ ɞɥɹ ɜɫɟɯ ɫɥɭɱɚɟɜ. Ɋɚɡɧɨɝɥɚɫɢɹ ɬɟɨɪɢɢ ɫ ɨɩɵɬɨɦ ɯɚɪɚɤɬɟɪɧɵ ɞɥɹ
ɫɢɥɶɧɨ ɞɢɫɫɨɰɢɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɥɢɬɨɜ
ɂɫɩɨɥɶɡɭɹ ɡɚɤɨɧɵ ɷɥɟɤɬɪɨɥɢɬɢɱɟɫɤɨɣ ɞɢɫɫɨɰɢɚɰɢɢ, Ƚɢɬɬɨɪɮ ɫɞɟɥɚɥ
8.
.
ɫɥɟɞɭɸɳɢɟ ɫɭɳɟɫɬɜɟɧɧɵɟ ɜɵɜɨɞɵ ɨ ɞɜɢɠɟɧɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɜ ɷɥɟɤɬɪɨ
ɥɢɬɚɯ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɉɪɢ ɩɪɨɯɨɠɞɟɧɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨ
ɝɨ ɬɨɤɚ ɱɟɪɟɡ ɠɢɞɤɨɫɬɶ ɜ ɧɟɣ ɜɨɡɧɢɤɚɟɬ ɨɞɧɨɜɪɟɦɟɧɧɨɟ, ɭɩɨɪɹɞɨɱɟɧɧɨɟ, ɩɪɨɬɢ
ɜɨɩɨɥɹɪɧɨɟ ɞɜɢɠɟɧɢɟ ɢɨɧɨɜ. ɉɨɥɨɠɢɬɟɥɶɧɵɟ ɢɨɧɵ ɩɟɪɟɦɟɳɚɸɬɫɹ ɩɨ ɧɚɩɪɚɜ
ɥɟɧɢɸ ɬɨɤɚ ɤ ɤɚɬɨɞɭ, ɚ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɢɨɧɵ
–
ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɤ ɚɧɨɞɭ. ɂɡ
ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɪɚɡɥɢɱɧɵɯ ɫɤɨɪɨɫɬɟɣ ɞɜɢɠɟɧɢɹ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢ ɨɬɪɢɰɚɬɟɥɶ
ɧɵɯ ɢɨɧɨɜ, ɢɡɦɟɪɹɹ ɤɨɧɰɟɧɬɪɚɰɢɸ ɪɚɫɬɜɨɪɨɜ ɩɨɫɥɟ ɷɥɟɤɬɪɨɥɢɡɚ ɭ ɤɚɬɨɞɚ ɢ ɚɧɨ
-
-
-
-
-
-
-
-
ɞɚ, Ƚɢɬɬɨɪɮ ɨɛɧɚɪɭɠɢɥ, ɱɬɨ ɜ ɫɨɥɹɧɨɣ ɤɢɫɥɨɬɟ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɢɨɧɚ ɜɨɞɨ
ɪɨɞɚ ɩɨɱɬɢ ɜ
5
ɪɚɡ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɯɥɨɪɚ. Ɉɩɵɬɵ Ƚɢɬɬɨɪɮɚ ɩɨɡɜɨ
52
-
-
ɥɢɥɢ ɨɩɪɟɞɟɥɹɬɶ ɨɬɧɨɲɟɧɢɟ ɫɤɨɪɨɫɬɟɣ ɨɬɞɟɥɶɧɵɯ ɢɨɧɨɜ, ɧɨ ɧɟ ɢɯ ɚɛɫɨɥɸɬɧɵɟ
F
E
ɫɤɨɪɨɫɬɢ
ɨɛɨɢɯ ɢɨɧɨɜ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɢ ɷɥɟɤɬɪɨɥɢɬɚ
ɪɚɡɨɦ, ɡɧɚɹ ɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɫɤɨɪɨɫɬɹɦɢ ɢɨɧɨɜ ɢɡ ɨɩɵɬɨɜ Ƚɢɬɬɨɪɮɚ, ɚɫɭɦɦɭ
ɫɤɨɪɨɫɬɟɣ ɢɡ ɨɩɵɬɨɜ Ʉɚɥɶɪɚɭɲɚ
ɢɨɧɨɜ
ɧɨɦ ɧɚɩɪɹɠɟɧɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɟ ɦɟɧɹɟɬɫɹ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɫɤɚɤɢɦ
ɞɪɭɝɢɦ ɢɨɧɨɦ ɞɚɧɧɵɣ ɢɨɧ ɧɚɯɨɞɢɬɫɹ ɜ ɪɚɫɬɜɨɪɟ
ɬɜɟɪɠɞɚɟɬ ɝɢɩɨɬɟɡɭ Ⱥɪɪɟɧɢɭɫɚ, ɱɬɨɢɨɧɵɜɷɥɟɤɬɪɨɥɢɬɟɧɟɫɜɹɡɚɧɵɞɪɭɝɫɞɪɭ
ɝɨɦ, ɚ ɞɢɫɫɨɰɢɢɪɨɜɚɧɵ, ɩɨɫɤɨɥɶɤɭ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɧɟɡɚɜɢɫɢɦɵ ɞɪɭɝ ɨɬ ɞɪɭ
ɝɚ. Ɉɧ ɬɚɤɠɟ ɩɨɤɚɡɚɥ, ɱɬɨ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɜ ɷɥɟɤɬɪɨɥɢɬɟ ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ ɫɤɨ
ɪɨɫɬɢ ɢɨɧɨɜUɢVɢ ɱɟɪɟɡ ɤɨɧɰɟɧɬɪɚɰɢɸ ɪɚɫɬɜɨɪɚȘɮɨɪɦɭɥɨɣ
.
Ɋɚɡɜɢɜɚɹ ɭɱɟɧɢɟ Ƚɢɬɬɨɪɮɚ, Ʉɚɥɶɪɚɭɲ ɩɨɤɚɡɚɥ, ɱɬɨ ɫɭɦɦɭ ɫɤɨɪɨɫɬɟɣ
9.
.
Ɍɚɤɢɦ ɨɛ
,
ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢ ɚɛɫɨɥɸɬɧɵɟ ɫɤɨɪɨɫɬɢ
.
Ɉɩɵɬɵ Ʉɚɥɶɪɚɭɲɚ ɩɨɤɚɡɚɥɢ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɤɚɤɨɝɨ-ɧɢɛɭɞɶ ɢɨɧɚ ɩɪɢ ɞɚɧ
.
Ɍɚɤ Ʉɚɥɶɪɚɭɲ ɟɳɟ ɪɚɡ ɩɨɞ
-
-
-
-
-
-
()
Ș
⋅⋅ , (53)
ɝɞɟ
=
96500.
ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɩɨ ɡɚɤɨɧɭ Ɉɦɚ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ
V+UaF=i
k=i ⋅ , (54)
ɝɞɟ
k –
ɭɞɟɥɶɧɚɹ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ
ɉɨɷɬɨɦɭ
Ɉɫɨɛɨ ɨɛɪɚɬɢɦ ɜɧɢɦɚɧɢɟ ɧɚ ɫɥɟɞɭɸɳɢɟ ɩɨɥɨɠɟɧɢɹ ɞɚɥɶɧɟɣɲɟɝɨ ɢɫ
10.
ɬɨɪɢɱɟɫɤɨɝɨ ɪɚɡɜɢɬɢɹ ɬɟɨɪɢɢ ɩɪɨɯɨɠɞɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ
ɚ) ɨɬɧɨɲɟɧɢɟ ɭɞɟɥɶɧɨɣ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɢ ɤ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɤɨɧɰɟɧɬɪɚ
ɰɢɢ ɪɚɫɬɜɨɪɟɧɧɨɝɨ ɬɟɥɚ Ʉɚɥɶɪɚɭɲ ɧɚɡɜɚɥ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶɸ
ɬ. ɟ
.
Ȝ
;
Ș
/ =k
.
()
Ș
Ek=V+UaF ⋅⋅⋅
.
(55)
-
:
-
,
ɛ) ɨɬɧɨɲɟɧɢɟ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɢ ɤ ɫɬɟɩɟɧɢ ɞɢɫɫɨɰɢɚɰɢɢ
⋅
/ =a=hak
Ȝ
Ȝ
/
ɬɨɥɶɤɨ ɩɪɢ ɛɟɫɤɨɧɟɱɧɨɦ ɪɚɡɪɹɠɟɧɢɢ, ɬ.ɟ. ɩɪɢ
∞
53
1=a ;
ɜ) ɫɤɨɪɨɫɬɢ ɢɨɧɨɜ
E
U
ɢ
V
0
0
ɩɪɢ
1=
,
ɫɦȼ
/
,
Ʉɚɥɶɪɚɭɲ ɧɚɡɜɚɥ ɩɨɞɜɢɠɧɨ
-
ɫɬɹɦɢ ɢɨɧɨɜ, ɬ. ɟ
.
Ȝ
=F=F
VU
00
.
Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɫɭɦɦɚ ɩɨɞɜɢɠɧɨɫɬɟɣ ɨɛɨ
∞
ɢɯ ɢɨɧɨɜ ɪɚɜɧɚ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɢ ɩɪɢ ɛɟɫɤɨɧɟɱɧɨɦ ɪɚɡɪɹɠɟ
ɧɢɢ. Ɂɧɚɹ∞Ȝ ɢ ɢɡɦɟɪɹɹ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ ɪɚɫɬɜɨɪɚ Ȝ
ɩɟɧɶ ɞɢɫɫɨɰɢɚɰɢɢ
ɞɥɹ ɟɺ ɜɵɱɢɫɥɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɬɶ
ɥɚ ɧɚɯɨɞɢɬɫɹ ɜ
ɰɢɚɰɢɢ
a .
⋅⋅
ȜȘ
a=k ,
∞
1
ɫɦ3ɪɚɫɬɜɨɪɚ, ɬ.ɟ. ɤɨɧɰɟɧɬɪɚɰɢɸ ɪɚɫɬɜɨɪɚ Ș ɢ ɫɬɟɩɟɧɶ ɞɢɫɫɨ
Ɍɨɥɶɤɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɞɟɥɶɧɚɹ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ
ɚ ɭɞɟɥɶɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ
Ȝ
/
Ȝ
=a .
∞
ɑɬɨ ɠɟ ɤɚɫɚɟɬɫɹ ɭɞɟɥɶɧɨɣ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɢ, ɬɨ
,
ɫɤɨɥɶɤɨ ɝɪɚɦɦ-ɷɤɜɢɜɚɥɟɧɬɨɜ ɞɚɧɧɨɝɨ ɬɟ
: .
ȡ
/1/1
, ɦɨɠɧɨ
ȜȘ
⋅⋅a=k=
∞
ɨɩɪɟɞɟɥɢɬɶ ɫɬɟ
ɇɟɬɪɭɞɧɨ ɡɚɦɟɬɢɬɶ
ɱɬɨ ɷɤɜɢɜɚɥɟɧɬɧɚɹ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ ɬɟɦ ɛɨɥɶɲɟ, ɱɟɦ ɫɥɚɛɟɟ ɪɚɫɬɜɨɪ. ɑɬɨ ɠɟ
,
ɤɚɫɚɟɬɫɹ ɭɞɟɥɶɧɨɣ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɢ
Ș
⋅a ,
ɬɨ ɩɪɢ ɪɚɡɛɚɜɥɟɧɢɢ ɪɚɫɬɜɨɪɚ ɨɧɚ ɞɨɫɬɢɝɚɟɬ ɧɟɤɨɬɨɪɨɝɨ ɦɚɤɫɢɦɭɦɚ, ɚ ɡɚɬɟɦ
ɩɪɢ ɟɳɟ ɛɨɥɶɲɟɦ ɪɚɡɛɚɜɥɟɧɢɢ ɭɦɟɧɶɲɚɟɬɫɹ
ɤɨɬɨɪɚɹ ɡɚɜɢɫɢɬ ɟɳɟ ɢ ɨɬ ɩɪɨɢɡɜɟɞɟɧɢɹ
(
ɬɚɤ ɤɚɤ ɭɦɟɧɶɲɚɟɬɫɹ Ș
).
Ʉɥɚɫɫɢ
-
-
-
-
-
:
,
-
ɱɟɫɤɢɦ ɩɪɢɦɟɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɢɡɜɟɫɬɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɭɞɟɥɶɧɨɣ ɩɪɨɜɨɞɢɦɨ
ɫɬɢ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜ ɜɨɞɧɨɦ ɪɚɫɬɜɨɪɟ ɫɟɪɧɨɣ ɤɢɫɥɨɬɵ, ɝɞɟ ɦɚɤɫɢɦɚɥɶɧɚɹ
ɭɞɟɥɶɧɚɹ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ ɞɨɫɬɢɝɚɟɬɫɹ ɞɥɹ
, ɬ.ɟ.
ɜ ɜɨɞɟ
ɱɢɫɬɚɹ ɜɨɞɚ ɢ ɱɢɫɬɚɹ ɫɟɪɧɚɹ ɤɢɫɥɨɬɚ ɩɨɱɬɢ ɧɟ ɩɪɨɜɨɞɹɬ ɬɨɤ
30%-
ɝɨ ɪɚɫɬɜɨɪɚ ɫɟɪɧɨɣ ɤɢɫɥɨɬɵ
;
ɝ) ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɷɥɟɤɬɪɨɥɢɬɨɜ Ʉɚɥɶɪɚɭɲ ɢɫɩɨɥɶɡɨɜɚɥ
,
ɢɫɬɨɱɧɢɤ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ
ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɞɥɹ ɬɟɯ ɠɟ ɷɥɟɤɬɪɨɥɢɬɨɜ
ɩɨ ɫɟɣ ɞɟɧɶ
;
ɱɬɨ ɧɟ ɪɚɜɧɨɡɧɚɱɧɨ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɢɫɬɨɱɧɢɤɚ
.
Ɉɞɧɚɤɨ ɷɬɨɬ ɦɟɬɨɞ ɢɫɩɨɥɶɡɭɟɬɫɹ ɢ
ɞ) ɨɩɵɬɵ Ʉɚɥɶɪɚɭɲɚ ɢ Ƚɟɣɞɜɟɣɥɟɪɚ ɩɪɨɜɨɞɢɥɢɫɶ ɫɨ ɫɩɟɰɢɚɥɶɧɨ ɩɪɢɝɨɬɨɜ
ɥɟɧɧɨɣ ɱɢɫɬɨɣ ɜɨɞɨɣ ɢ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ
,
ɛɵɥɨ ɩɨɤɚɡɚɧɨ
ɱɬɨ ɞɢɫɫɨɰɢɚɰɢɹ ɜɨɞɵ ɨɱɟɧɶ ɫɥɚɛɚɹ. Ɉɞɧɚɤɨ ɧɚɪɹɞɭ ɫɨ ɫɥɚɛɨɣ
18°ɋ.
ȼɷɬɢɯɭɫɥɨɜɢɹɯ
ɞɢɫɫɨɰɢɚɰɢɟɣ ɫɨɛɫɬɜɟɧɧɵɯ ɦɨɥɟɤɭɥ ɜɨɞɚ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɨɦ ɫɢɥɶɧɨ ɞɢɫɫɨ
ɰɢɢɪɨɜɚɬɶ ɪɚɫɬɜɨɪɟɧɧɵɟ ɜ ɧɟɣ ɬɟɥɚ ɢ ɨɛɪɚɡɨɜɵɜɚɬɶ ɷɥɟɤɬɪɨɥɢɬɵ. ɗɬɭ ɨɫɨɛɟɧ
-
-
-
-
54
ɧɨɫɬɶ, ɫɜɨɣɫɬɜɟɧɧɭɸ ɜɨɞɟ, ɚ ɡɚɬɟɦ ɢ ɞɪɭɝɢɦ ɠɢɞɤɨɫɬɹɦ, ɜɵɹɜɢɥɢ ɇɟɪɧɫɬ ɢ Ⱦɠ
HCl
.
Ɍɨɦɫɨɧ
;
ɟ) ɨɧɢ ɨɛɪɚɬɢɥɢ ɜɧɢɦɚɧɢɟ, ɱɬɨ «ɞɢɫɫɨɰɢɢɪɭɸɳɚɹ ɫɢɥɚ» ɪɚɡɥɢɱɧɵɯ ɠɢɞɤɨ
ɫɬɟɣ «ɟɫɥɢ ɢ ɧɟ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ, ɬɨ ɩɪɚɤɬɢɱɟɫɤɢ ɢɞɟɬ ɩɚɪɚɥɥɟɥɶɧɨ ɫ ɜɟɥɢɱɢɧɨɣ
».
ɢɯ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɨɫɬɨɹɧɧɨɣ
ɡɨɥɚ
81
İ
= .
ɧɟ ɩɪɨɜɨɞɢɬ ɬɨɤɚ
2,5
İ
= ,
ɷɮɢɪɚ
4,1
İ
= ,
ɚɥɤɨɝɨɥɹ25İ
ȼ ɬɚɤɨɦ ɠɟ ɩɨɪɹɞɤɟ ɢɞɭɬ ɢ ɢɯ ɞɢɫɫɨɰɢɢɪɭɸɳɢɟ ɫɢɥɵ. ɋɨɥɹɧɚɹ ɤɢɫɥɨɬɚ
,
ɪɚɫɬɜɨɪɟɧɧɚɹ ɜ ɜɨɞɟ
.
Ⱥɧɚɥɢɡɢɪɭɹ ɩɪɨɰɟɫɫɵ ɪɚɫɬɜɨɪɢɦɨɫɬɢ ɢ ɞɢɫɫɨɰɢɚɰɢɢ, Ɇ. Ɏɚ
, –
ɯɨɪɨɲɢɣ ɩɪɨɜɨɞɧɢɤ, ɬɨɝɞɚ ɤɚɤ ɜ ɷɮɢɪɟ ɨɧɚ ɩɨɱɬɢ
ɇɚɩɪɢɦɟɪ, ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɛɟɧ
= ,
ɦɭɪɚɜɶɢɧɨɣ ɤɢɫɥɨɬɵ62İ
= ,
ɜɨɞɵ
ɪɚɞɟɣ ɩɨɤɚɡɚɥ, ɱɬɨ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ «ɤɚɠɞɵɣ ɝɪɚɦɦ-ɷɤɜɢɜɚɥɟɧɬ ɪɚɫɬɜɨɪɟɧɧɨɝɨ
ɜɟɳɟɫɬɜɚ ɧɟɫɟɬ ɧɚ ɫɟɛɟ
,
ɞɨɤɚɡɚɥ
ɱɬɨ ɫɢɥɚ, ɫ ɤɨɬɨɪɨɣ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɞɟɣɫɬɜɭɟɬ ɧɚ ɨɞɢɧ ɝɪɚɦɦ
96.500
ɷɤɜɢɜɚɥɟɧɬ ɥɸɛɨɝɨ ɢɨɧɚ, ɫɨɫɬɚɜɥɹɟɬ
ɤɭɥɨɧɨɜ ɩɪɢ ɧɚɩɪɹɠɟɧɢɢ 1ȼ
: ,100,9810981/)109650(
».
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɨɧ
638
⋅⋅⋅ =
ɤɝ
.
-
-
-
-
ȼɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɦɚɬɟɪɢɟɣ (ɫɪɟɞɨɣ) ɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɨɛɭ
ɫɥɚɜɥɢɜɚɟɬɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ, ɧɟɡɚɜɢɫɢɦɨ ɪɚɫɩɪɟɞɟ
ɥɟɧɧɵɦɢ ɜ ɬɟɥɟ ɢɥɢ ɫɜɹɡɚɧɧɵɦɢ ɜ ɞɢɩɨɥɢ. ɗɬɨ ɡɚɤɥɸɱɟɧɢɟ ɫɞɟɥɚɥɢ ɗɣɧɲɬɟɣɧ ɢ
Ʌɚɭɛ ɜ ɫɜɨɟɣ ɡɧɚɦɟɧɢɬɨɣ ɪɚɛɨɬɟ
ɧɚɩɢɫɚɧɧɨɣ ɜ
1908
ɝɨɞɭ. ɉɨɷɬɨɦɭ ɫɢɥɚ, ɞɟɣɫɬ
,
ɜɭɸɳɚɹ ɜ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɧɚ ɷɥɟɦɟɧɬ ɨɛɴɟɦɚ ɦɚɬɟɪɢɢ, ɹɜɥɹɟɬɫɹ ɪɟɡɭɥɶ
ɬɢɪɭɸɳɟɣ ɩɨɧɞɟɪɨɦɚɬɨɪɧɵɯ ɫɢɥ, ɤɨɬɨɪɵɟ ɞɟɣɫɬɜɭɸɬ ɜ ɷɬɨɦ ɩɨɥɟ ɧɚ ɜɫɟ ɧɚɯɨ
ɞɹɳɢɟɫɹ ɜ ɞɚɧɧɨɦ ɷɥɟɦɟɧɬɟ ɨɛɴɟɦɚ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɢ ɦɚɝɧɢɬɧɵɟ ɷɥɟɦɟɧɬɚɪɧɵɟ
.
ɱɚɫɬɢɰɵ
ȼ ɩɨɬɟɧɰɢɚɥɶɧɨɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɩɪɨɹɜɥɹɸɬɫɹ ɬɨɥɶɤɨ ɫɢɥɵ, ɢɫ
ɩɵɬɵɜɚɟɦɵɟ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɡɚɪɹɞɨɦ, ɚɬɚɤɠɟɫɢɥɵ, ɢɫɩɵɬɵɜɚɟɦɵɟ ɞɢɩɨɥɹɦɢ
.
ɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɜɟɳɟɫɬɜɚ
ɉɪɨɢɡɜɟɞɟɧɢɟ ɷɬɨɣ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɷɥɟɦɟɧ
ɬɚɪɧɵɣ ɡɚɪɹɞ, ɧɚ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ ɩɨɥɭɱɚɟɬɫɹ ɜɫɟɝɞɚ ɨɞɢɧɚɤɨɜɵɦ
,
ɢ ɞɚɟɬ ɷɧɟɪɝɢɸ
ɡɚɜɢɫɢɬ ɨɬ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ
ɩɟɪɟɞɚɜɚɟɦɭɸ ɡɚɪɹɞɭ, ɤɨɬɨɪɚɹ ɨɫɬɚɟɬɫɹ ɜɫɟɝɞɚ ɩɨɫɬɨɹɧɧɨɣ ɢ ɧɟ
.
ɗɧɟɪɝɢɹ, ɫɨɨɛɳɚɟɦɚɹ ɷɥɟɦɟɧɬɚɪɧɨ
-
-
-
-
-
-
-
-
ɦɭ ɡɚɪɹɞɭ, ɧɟ ɡɚɜɢɫɢɬ ɢ ɨɬ ɜɟɥɢɱɢɧɵ ɫɢɥɵ ɬɨɤɚ
55
.
ɉɨɫɤɨɥɶɤɭ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɥɸɛɨɣ ɫɪɟɞɨɣ ɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɦ ɩɨ
E
V
F
E
E
-
ɥɟɦ ɨɛɭɫɥɚɜɥɢɜɚɟɬɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ, ɧɟɡɚɜɢɫɢɦɨ ɪɚɫ
ɩɪɟɞɟɥɟɧɧɵɦɢ ɜ ɬɟɥɟ ɢɥɢ ɫɜɹɡɚɧɧɵɦɢ ɜ ɞɢɩɨɥɢ, ɪɚɫɫɦɨɬɪɢɦ ɦɟɯɚɧɢɡɦ ɩɨɜɟɞɟ
ɧɢɹ ɩɨɥɨɠɢɬɟɥɶɧɨ ɢ ɨɬɪɢɰɚɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ
ɧɚɩɪɢɦɟɪ, ɜ ɫɢɫɬɟɦɟ ɤɚɬɨɞɧɨɣ ɡɚɳɢɬɵ
Ⱦɜɢɠɟɧɢɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ ɜ ɭɫɤɨɪɹɸɳɟɦɫɹ ɩɨɥɟ
.
(
ɪɢɫ
. 9).
ɉɭɫɬɶ
ɨɬɪɢɰɚɬɟɥɶɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɱɚɫɬɢɰɚ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɫ
ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ
(
ɫɨɨɪɭɠɟɧɢɹ
ɋ)ɤ ɚɧɨɞɧɨɦɭ ɡɚɡɟɦɥɟɧɢɸ
ɧɚɱɢɧɚɟɬ ɞɜɢɝɚɬɶɫɹ ɫ ɦɚɥɨɣ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ
ɱɚɫɬɢɰɭ ɞɟɣɫɬɜɭɟɬ ɩɨɫɬɨɹɧɧɚɹ ɫɢɥɚ ɩɨɥɹ
ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ
:
.).(
ɁȺ
.
ȼɷɬɨɦɫɥɭɱɚɟ, ɨɱɟɜɢɞɧɨ, ɧɚ ɷɬɭ
,
ɪɚɜɧɚɹ ɩɪɨɢɡɜɟɞɟɧɢɸ ɡɚɪɹɞɚeɧɚ
0=
ɨɬ
V
.
e=Ee=F ⋅ (56)
d
ɇɚɩɪɹɠɟɧɢɟ ɫɢɥɵ ɩɨɥɹ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɩɨɥɹ ɩɪɢ ɨɬɪɢɰɚ
-
-
,
-
ɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɟ ɢ, ɧɚɨɛɨɪɨɬ, ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɩɨɥɹ ɩɪɢ ɩɨɥɨɠɢɬɟɥɶ
ɧɨ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɟ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɣ ɫɢɥɵ ɬɚ ɢɥɢ ɢɧɚɹ ɱɚɫɬɢɰɚ, ɤɚɤ ɷɬɨ
,
ɲɢɪɨɤɨ ɢɡɜɟɫɬɧɨ
ɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɟ ɦɚɫɫɟ ɬɟɥɚ
ɝɞɟ
e
⋅ m–
11
⋅≈ –
ɩɨɥɭɱɚɟɬ ɭɫɤɨɪɟɧɢɟ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɟ ɜɟɥɢɱɢɧɟ ɫɢɥɵ ɢ ɨɛ
:
m
=
eV
md
,
),
ɪɚɜɧɚɹ
eE
F
=
=a (57)
m
19
−
;101,6
Ʉɥ=e
ɤɝɄɥ
/101,76
ɦɚɫɫɚ ɱɚɫɬɢɰɵ (ɨɬɪɢɰɚɬɟɥɶɧɨɣ
ɨɬɧɨɲɟɧɢɟ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ ɤ ɟɝɨ ɦɚɫɫɟ
31
−
⋅
ɤɝ
m
Ⱦɜɢɠɟɧɢɟ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɱɚɫɬɢɰɵ
,
ɩɨɥɟ ɛɭɞɟɬ ɭɫɤɨɪɹɸɳɢɦ
ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɫɢɥɵ
ɬɚɤ ɤɚɤ ɧɚɩɪɚɜɥɟɧɢɟ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ
F.
(
ɧɚɩɪɢɦɟɪ, ɷɥɟɤɬɪɨɧɚ) ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ
V
ɫɨɜɩɚɞɚɟɬ
0
-
-
;109,1
56
Ɋɢɫ. 9. Ɉɬɪɢɰɚɬɟɥɶɧɚɹ ɱɚɫɬɢɰɚ ɜ ɭɫɤɨɪɹɸɳɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ
Ɂ
Ɂ
Ⱥ
F
Ⱦɜɢɝɚɹɫɶ ɪɚɜɧɨɭɫɤɨɪɟɧɧɨ, ɷɥɟɤɬɪɨɧ, ɩɪɨɣɞɹ ɩɭɬɶ
ɧɨɝɨ ɷɥɟɤɬɪɨɞɚ
..
Ⱥ
ɫɨ ɫɤɨɪɨɫɬɶɸVɢ ɛɭɞɟɬ ɨɛɥɚɞɚɬɶ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ
2
mV
=W
k
.
(58)
2
ɉɪɢ ɷɬɨɦ ɪɚɛɨɬɚ, ɫɨɜɟɪɲɟɧɧɚɹ ɫɢɥɚɦɢ ɩɨɥɹ ɧɚ ɩɭɬɢ
eV=eEd=Fd=A
.
d ,
ɞɨɫɬɢɝɧɟɬ ɩɨɥɨɠɢɬɟɥɶ
d
,
ɫɨɫɬɚɜɥɹɟɬ
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ ɪɚɜɧɚ ɪɚɛɨɬɟ ɫɢɥ ɩɨɥɹ ɧɚ ɩɭɬɢ ɷɥɟɤɬɪɨ
ɧɚ ɫ ɪɚɡɧɨɫɬɶɸ
(U)
ɩɨɬɟɧɰɢɚɥɨɜ
mV
:
2
.
eU=
2
Ɍɨɝɞɚ, ɩɪɢɧɹɜ ɡɚɪɹɞ ɷɥɟɤɬɪɨɧɚ ɡɚ ɟɞɢɧɢɰɭ ɩɪɢ ɪɚɡɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɨɜ
1
ȼ
=U
,
ɫɥɟɞɭɟɬ
ɩɨɥɭɱɢɦ ɟɞɢɧɢɰɭ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ
,
ɱɬɨ
1
ɷɥɟɤɬɪɨɧ-ȼɨɥɶɬ
(ɷȼ).
-
(59)
-
(60)
ɂɡ ɷɬɨɝɨ
1919
101,61
ȼ
−−
⋅⋅⋅
Ⱦɠ=Ʉɥ=ɷȼ
Ⱦɜɢɠɟɧɢɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ ɜ ɬɨɪɦɨɡɹɳɟɦ ɩɨɥɟ
ɪɢɰɚɬɟɥɶɧɚɹ ɱɚɫɬɢɰɚ ɞɜɢɝɚɟɬɫɹ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ
..
ɚɧɨɞɧɨɝɨ ɡɚɡɟɦɥɟɧɢɹ
c
,
ɬɨ ɫɢɥɚ ɩɨɥɹ
ɩɨɥɸ ɢ
,
ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɚ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ, ɤɨɬɨɪɚɹ
,
ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɷɬɭ ɱɚɫɬɢɰɭ, ɧɚɩɪɚɜɥɟɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ
ɢ ɞɜɢɠɟɬɫɹ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɡɚɳɢɳɚɟɦɨɝɨ ɫɨɨɪɭɠɟɧɢɹ
ɬɨɪɦɨɡɢɬɫɹ ɫɢɥɨɣ ɩɨɥɹ ɢ ɞɜɢɠɟɬɫɹ ɪɚɜɧɨɦɟɪɧɨ ɡɚɦɟɞɥɟɧɧɨ
57
.101,61
(
ɪɢɫ
. 10).
V
ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ
0
ȿɫɥɢ ɨɬ
-
.
Ɋɢɫ. 10. Ɉɬɪɢɰɚɬɟɥɶɧɚɹ ɱɚɫɬɢɰɚ ɜ ɬɨɪɦɨɡɹɳɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ
Ɂ
F
Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜ ɬɨɪɦɨɡɹɳɟɦ ɩɨɥɟ
ɫɨɫɬɚɜɥɹɟɬ
:
2
mV
0
.
=W
0
(61)
2
ɉɨɫɤɨɥɶɤɭ ɷɧɟɪɝɢɹ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɱɚɫɬɢɰɵ ɫ ɦɨɦɟɧɬɚ ɜɵɥɟɬɚ ɫ ɩɨɜɟɪɯɧɨ
ɫɬɢ ɫɨɨɪɭɠɟɧɢɹ ɋ ɫɪɚɡɭ ɠɟ ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɧɚ ɩɪɟɨɞɨɥɟɧɢɟ ɫɢɥɵ ɩɨɥɹ, ɬɨ ɷɧɟɪɝɢɹ
W
ɭɦɟɧɶɲɚɟɬɫɹ. ɉɨɷɬɨɦɭ ɟɫɥɢ ɧɚɱɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ
0
ɝɢɢ, ɤɨɬɨɪɭɸ ɧɚɞɨ ɡɚɬɪɚɬɢɬɶ ɧɚ ɟɟ ɞɜɢɠɟɧɢɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ
,
eU=W>W
0
ɬɨ ɱɚɫɬɢɰɚ, ɩɪɨɣɞɹ ɪɚɫɫɬɨɹɧɢɟ
. ɂ,
ɤɚɬɨɞɚ
ɧɚɨɛɨɪɨɬ, ɟɫɥɢ ɧɚɱɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ, ɤɨɬɨɪɭɸ
d
ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ, ɨɛɹɡɚɬɟɥɶɧɨ ɞɨɫɬɢɝɧɟɬ
ɧɚɞɨ ɡɚɬɪɚɬɢɬɶ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ ɤɚɬɨɞɚ
0
(62)
,
ɚɢɦɟɧɧɨ
,
eU=W<W
(63)
:
W
ɛɨɥɶɲɟ ɷɧɟɪ
0
..
Ⱥ
ɢɋ, ɬ. ɟ
.:
-
-
ɬɨ ɱɚɫɬɢɰɚ, ɧɟ ɞɨɫɬɢɝɧɭɜ ɤɚɬɨɞɚ, ɢɡɪɚɫɯɨɞɭɟɬ ɜɫɸ ɫɜɨɸ ɷɧɟɪɝɢɸ ɢ ɧɚ ɤɚɤɨɣ-ɬɨ
,
ɦɨɦɟɧɬ ɨɫɬɚɧɨɜɢɬɫɹ
ɥɟɧɢɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ ɩɨɥɹ
ɩɨɥɭɱɚɟɬ ɨɬ ɧɟɝɨ ɷɧɟɪɝɢɸ, ɡɚɬɪɚɱɟɧɧɭɸ ɱɚɫɬɢɰɟɣ ɞɨ ɦɨɦɟɧɬɚ ɨɫɬɚɧɨɜɤɢ
ɡɚɬɟɦ ɧɚɱɧɟɬ ɪɚɜɧɨɭɫɤɨɪɟɧɧɨ ɞɜɢɝɚɬɶɫɹ ɜ ɨɛɪɚɬɧɨɦ ɧɚɩɪɚɜ
.
ɑɚɫɬɢɰɚ, ɞɜɢɠɭɳɚɹɫɹ ɜ ɭɫɤɨɪɹɸɳɟɦɫɹ ɩɨɥɟ
.
58
-
,
Ⱦɜɢɠɟɧɢɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ ɜ ɩɨɩɟɪɟɱɧɨɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ
(
ɪɢɫ
. 11).
Ⱦɨɩɭɫɬɢɦ, ɨɬɪɢɰɚɬɟɥɶɧɚɹ ɱɚɫɬɢɰɚ ɞɜɢɝɚɟɬɫɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɷɥɟɤ
-
ɬɪɢɱɟɫɤɨɦɭ ɩɨɥɸ ɢ ɩɨɩɚɞɚɟɬ ɜ ɧɟɝɨ ɫɨ ɫɤɨɪɨɫɬɶɸ
ɭɠɟ ɪɚɫɫɦɨɬɪɟɥɢ
(
ɪɢɫ
. 9 ɢ 10),
ɫɢɥɚ ɩɨɥɹ
,
F
ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɷɥɟɤɬɪɨɧ, ɧɚɩɪɚɜ
V
.
ȼɷɬɨɦɫɥɭɱɚɟ, ɤɚɤ ɦɵ
0
ɥɟɧɚ ɜ ɫɬɨɪɨɧɭ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɧɚɩɪɚɜɥɟɧɢɸ ɩɨɥɹ. Ɍɨɝɞɚ ɨɬɪɢɰɚɬɟɥɶɧɚɹ
.
ɱɚɫɬɢɰɚ ɞɜɢɠɟɬɫɹ ɜ ɞɜɭɯ ɜɡɚɢɦɧɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ
Ɉɞɧɨ ɧɚ
ɩɪɚɜɥɟɧɢɟ ɩɨ ɢɧɟɪɰɢɢ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɨɥɸ ɢ ɞɪɭ
ɝɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɫɢɥɵ ɩɨɥɹ ɪɚɜɧɨɭɫɤɨɪɟɧɧɨ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ
.
ɩɨɥɸ
ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɱɚɫɬɢɰɚ ɜɵɣɞɟɬ ɡɚ ɩɪɟɞɟɥɵ ɩɨɥɹ
ɢɧɟɪɰɢɢ ɪɚɜɧɨɦɟɪɧɨ ɢ ɩɪɹɦɨɥɢɧɟɣɧɨ
ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɬɪɢɰɚɬɟɥɶɧɚɹ ɱɚɫɬɢɰɚ ɩɟɪɟɦɟɳɚɟɬɫɹ ɩɨ ɩɚɪɚɛɨɥɟ. Ʉɨɝɞɚ
,
ɬɨ ɞɚɥɶɲɟ ɨɧɚ ɞɜɢɠɟɬɫɹ ɩɨ
.
Ɉɫɧɨɜɵɜɚɹɫɶ ɧɚ ɞɨɫɬɢɠɟɧɢɹɯ ɤɥɚɫɫɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɩɪɨɯɨɠɞɟɧɢɹ ɷɥɟɤɬɪɢ
ɱɟɫɤɨɝɨ ɬɨɤɚ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ, ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɨɫɧɨɜɨɩɨɥɚɝɚɸɳɢɟ
ɜɵɜɨɞɵ
:
-
-
-
-
1.
ȼ ɷɥɟɤɬɪɨɥɢɬɚɯ, ɬɚɤ ɠɟ ɤɚɤ ɢ ɜ ɞɪɭɝɢɯ ɫɪɟɞɚɯ, ɷɧɟɪɝɢɹ ɩɟɪɟɞɚɟɬɫɹ ɡɚɪɹ
ɠɟɧɧɵɦ ɱɚɫɬɢɰɚɦ ɢ ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɬɟɩɥɨɜɭɸ ɷɧɟɪɝɢɸ. ɇɟ ɦɨɠɟɬ ɛɵɬɶ ɷɥɟɤ
ɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɛɟɡ ɧɟɤɨɬɨɪɨɝɨ ɩɪɟɜɪɚɳɟɧɢɹ ɷɧɟɪɝɢɢ
2.
ɉɨɬɨɤ ɷɧɟɪɝɢɢ ɜ ɰɟɩɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɥɨɠɧɨɟ ɹɜɥɟɧɢɟ. ɗɥɟɤɬɪɢɱɟ
.
ɫɤɨɟ ɩɨɥɟ ɫɥɭɠɢɬ ɩɨɫɪɟɞɧɢɤɨɦ, ɨɫɭɳɟɫɬɜɥɹɸɳɢɦ ɩɟɪɟɞɚɱɭ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪ
-
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ɝɢɢ ɡɚɪɹɠɟɧɧɵɦ ɱɚɫɬɢɰɚɦ ɜɨ ɜɧɟɲɧɟɣ ɰɟɩɢ, ɚ ɜɧɭɬɪɢ ɢɫɬɨɱɧɢɤɚ ɡɚɪɹɠɟɧɧɵɟ
ɱɚɫɬɢɰɵ ɞɜɢɠɭɬɫɹ ɩɪɨɬɢɜ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɫɢɥɵ
ɫɨɡɞɚɜɚɟɦɨɣ ɡɚɪɹɞɚɦɢ ɧɚ ɡɚɠɢ
-
,
ɦɚɯ. ɗɧɟɪɝɢɹ, ɩɟɪɟɞɚɜɚɟɦɚɹ ɷɥɟɦɟɧɬɚɪɧɨɦɭ ɡɚɪɹɞɭ ɨɞɧɚ ɢ ɬɚ ɠɟ. ȼɬɚɤɨɣɰɟɩɢ
,
ɩɨɱɬɢ ɜɫɹ ɷɧɟɪɝɢɹ
,
ɩɨɥɹ
ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɬɟɩɥɨɜɭɸ. ȿɫɥɢ ɷɥɟɦɟɧɬɚɪɧɵɟ ɡɚɪɹɞɵ ɧɟ ɩɟɪɟɧɨɫɹɬɫɹ, ɬɨ
ɢɫɬɨɱɧɢɤ ɷɧɟɪɝɢɸ ɧɟ ɪɚɫɯɨɞɭɟɬ
ȼ ɷɥɟɤɬɪɨɥɢɬɚɯ ɨɛɳɢɣ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɜɨɡɧɢɤɚɟɬ ɤɚɤ ɪɟɡɭɥɶɬɚɬ ɞɜɢ
3.
ɠɟɧɢɹ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɷɥɟɦɟɧɬɚɪɧɵɯ ɡɚɪɹɞɨɜ, ɩɪɨɬɟɤɚɸɳɢɯ ɡɚ ɫɟɤɭɧɞɭ (ɜɵɡɵ
ɤɨɬɨɪɭɸ ɞɜɢɠɭɳɢɟɫɹ ɡɚɪɹɞɵ ɩɨɥɭɱɢɥɢ ɨɬ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ
.
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-
ɜɚɸɳɢɯ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɢɯ ɞɜɢɠɟɧɢɹ
59
),
ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɷɥɟ
-
ɦɟɧɬɚɪɧɵɯ ɡɚɪɹɞɨɜ, ɩɪɨɬɟɤɚɸɳɢɯ ɡɚ ɫɟɤɭɧɞɭ (ɜɵɡɵɜɚɸɳɢɯ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ
,
ɜ ɧɚɩɪɚɜɥɟɧɢɢ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɦ ɢɯ ɞɜɢɠɟɧɢɸ
ɜɧɟɲɧɟɣ ɰɟɩɢ ɨɬ ɚɧɨɞɚ ɤ ɤɚɬɨɞɭ
.
ȼɷɥɟɤɬɪɨɥɢɬɟɬɨɤɢɞɟɬ, ɧɚɨɛɨɪɨɬ, ɨɬ ɤɚɬɨɞɚ ɤ
).
ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɬɟɱɟɬ ɜɨ
ɚɧɨɞɭ
,
ɧɟɫɦɨɬɪɹ ɧɚ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɨɬɬɚɥɤɢɜɚɧɢɟ ɷɬɢɯ ɱɚɫɬɢɰ ɨɬ ɡɚɠɢɦɨɜ ɢɫɬɨɱ
ɧɢɤɚ. ȼ ɷɬɨɦ ɩɪɨɰɟɫɫɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɯɢɦɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ (ɡɚɤɨɧ Ƚɟɫɫɚ) ɞɥɹ ɧɚ
ɫɢɥɶɫɬɜɟɧɧɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɤ ɡɚɠɢɦɚɦ ɢɫɬɨɱɧɢɤɚ
.
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-
Ɋɢɫ. 11. Ɉɬɪɢɰɚɬɟɥɶɧɚɹ ɱɚɫɬɢɰɚ ɜ ɩɨɩɟɪɟɱɧɨɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ
4.
Ʉɥɚɫɫɢɱɟɫɤɚɹ ɬɟɨɪɢɹ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɫɜɹɡɚɬɶ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬ
ɪɵ ɫ ɬɟɩɥɨɜɵɦɢ, ɩɨɫɤɨɥɶɤɭ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɥɸɛɨɝɨ ɞɜɢɠɟɧɢɹ ɥɸɛɨɝɨ
ɩɪɟɞɦɟɬɚ ɦɨɠɧɨ ɢɡɦɟɪɢɬɶ ɜ ɤɚɥɨɪɢɹɯ ɬɨɱɧɨ ɬɚɤ ɠɟ
1
( ,101,44
=mV
172
−
⋅
Ⱦɠ
ɚɬɚɤɠɟ
ȼ
=
19
−
101,61
⋅
Ⱦɠ
,
ɤɚɤ ɢ ɜ ɞɠɨɭɥɹɯ
ɧɚ ɷɥɟɦɟɧɬɚɪɧɵɣ ɡɚɪɹɞ
2
18
Ⱥ
=
⋅
5.
Ɉɞɧɚɤɨ, ɧɟɫɦɨɬɪɹ ɧɚ ɡɧɚɱɢɬɟɥɶɧɵɟ ɞɨɫɬɢɠɟɧɢɹ ɭɱɟɧɵɯ ɜ ɪɚɡɜɢɬɢɢ ɬɟɨ
Ⱦɠ
106,251
ɷɥɟɦɟɧɬɚɪɧɵɯ ɡɚɪɹɞɨɜ ɜ ɫɟɤɭɧɞɭ
).
ɪɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ, ɞɨ ɫɟɝɨɞɧɹɲɧɟɝɨ ɞɧɹ ɧɟɬ ɟɞɢɧɨɣ ɦɟ
60
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,
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