ȼɵɪɚɠɟɧɢɟ (2.30) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɡɚɤɨɧ Ʉɸɪɢ–ȼɟɣɫɫɚ
(ɫɪ. ɫ (2.17)).
ɋɪɚɜɧɟɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɩɨ ɬɟɦɩɟɪɚɬɭɪɧɵɦ ɡɚɜɢɫɢɦɨɫɬɹɦ ɩɚɪɚɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɪɚɡɥɢɱɧɵɯ ɜɟɳɟɫɬɜ ɫ (2.26) ɢ (2.30) ɩɨɡɜɨɥɹɟɬ ɜɵɹɜɢɬɶ ɫɥɟɞɭɸɳɢɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ:
x Ɇɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɩɚɪɚɦɚɝɧɢɬɧɵɯ ɝɚɡɨɜ ɢ ɪɟɞɤɨɡɟɦɟɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ, ɭ ɤɨɬɨɪɵɯ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɧɭɬɪɟɧɧɢɦɢ (ɧɟɞɨɫɬɪɨɟɧɧɵɦɢ) ɫɥɨɹɦɢ ɷɥɟɤɬɪɨɧɧɵɯ ɨɛɨɥɨɱɟɤ, ɫɥɚɛɨ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɦɟɠɞɭ ɫɨɛɨɣ, ɞɨɜɨɥɶɧɨ ɬɨɱɧɨ ɨɩɢɫɵɜɚɟɬɫɹ ɡɚɤɨɧɨɦ Ʉɸɪɢ.
x Ⱦɥɹ ɩɚɪɚɦɚɝɧɢɬɧɵɯ ɦɟɬɚɥɥɨɜ ɩɟɪɟɯɨɞɧɨɝɨ ɪɹɞɚ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɦɚɝɧɢɬɧɵɦɢ ɦɨɦɟɧɬɚɦɢ ɩɨ ȼɟɣɫɫɭ, ɱɬɨ ɜɧɟɤɨɬɨɪɵɯɫɥɭɱɚɹɯɩɨɡɜɨɥɹɟɬɩɨɥɶɡɨɜɚɬɶɫɹɜɵɪɚɠɟɧɢɟɦ(2.30).
x Ⱦɥɹ ɧɟɤɨɬɨɪɵɯ ɳɟɥɨɱɧɵɯ ɦɟɬɚɥɥɨɜ ɦɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɨɱɟɧɶ ɫɥɚɛɨ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ, ɱɬɨ ɩɪɨɬɢɜɨɪɟɱɢɬ ɡɚɤɨɧɚɦ Ʉɸɪɢ ɢ Ʉɸɪɢ–ȼɟɣɫɫɚ.
ȼ 1923 ɝ. ə. Ƚ. Ⱦɨɪɮɦɚɧ ɩɪɟɞɩɨɥɨɠɢɥ, ɱɬɨ ɩɪɢɱɢɧɨɣ ɩɚɪɚɦɚɝɧɟɬɢɡɦɚ ɳɟɥɨɱɧɵɯ ɦɟɬɚɥɥɨɜ ɹɜɥɹɸɬɫɹ ɷɥɟɤɬɪɨɧɵ ɩɪɨɜɨɞɢɦɨɫɬɢ (ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ, ɨɛɪɚɡɨɜɚɧɧɵɣ ɫɜɨɛɨɞɧɵɦɢ ɧɨɫɢɬɟɥɹɦɢ ɡɚɪɹɞɚ). Ⱦɟɥɨ ɜ ɬɨɦ, ɱɬɨ ɬɟɨɪɢɹ ɩɚɪɚɦɚɝɧɟɬɢɡɦɚ Ʌɚɧɠɟɜɟɧɚ ɢ «ɩɨɩɪɚɜɤɢ» ȼɟɣɫɫɚ ɛɵɥɢ ɨɫɧɨɜɚɧɵ ɧɚ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɤɥɚɫɫɢɱɟɫɤɨɣ ɫɬɚɬɢɫɬɢɤɢ Ȼɨɥɶɰɦɚɧɚ, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ ɩɨɞɱɢɧɹɟɬɫɹ ɤɜɚɧɬɨɜɨɣ ɫɬɚɬɢɫɬɢɤɟ Ɏɟɪɦɢ–Ⱦɢɪɚɤɚ. ɉɨ ɷɬɨɣ ɫɬɚɬɢɫɬɢɤɟ ɫ ɭɱɟɬɨɦ ɩɪɢɧɰɢɩɚ ɡɚɩɪɟɬɚ ɉɚɭɥɢ ɩɪɢ 0 Ʉ ɷɥɟɤɬɪɨɧɵ ɩɥɨɬɧɨ ɡɚɩɨɥɧɹɸɬ ɭɪɨɜɧɢ ɫ ɧɚɢɦɟɧɶɲɢɦɢ ɜɨɡɦɨɠɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɷɧɟɪɝɢɢ. Ɉɛɨɡɧɚɱɢɦ ɤɨɧɰɟɧɬɪɚɰɢɸ ɜɫɟɯ ɷɥɟɤɬɪɨɧɨɜ N. ɉɥɨɬɧɨɫɬɶ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɫɨɫɬɨɹɧɢɣ ɷɥɟɤɬɪɨɧɨɜɜɦɟɬɚɥɥɟɤɚɤɮɭɧɤɰɢɹɷɧɟɪɝɢɢɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
g(ȿ) ~ E1/2. |
(2.31) |
ɉɪɢ 0 Ʉ ɜɫɟ ɫɨɫɬɨɹɧɢɹ ɫ ɷɧɟɪɝɢɟɣ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ ȿF ɡɚɩɨɥ- |
|
ɧɟɧɵ ɢ ɬɨɝɞɚ |
|
ȿ ~ N2/3. |
(2.32) |
F |
|
ɉɨɫɤɨɥɶɤɭ ɦɚɝɧɢɬɧɨɟ ɫɩɢɧɨɜɨɟ ɤɜɚɧɬɨɜɨɟ ɱɢɫɥɨ ɢɦɟɟɬ ɬɨɥɶɤɨ ɞɜɚ ɡɧɚɱɟɧɢɹ (±1/2), ɛɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɨɞɧɚ ɩɨɥɨɜɢɧɚ ɷɥɟɤɬɪɨɧɨɜ (N/2) ɢɦɟɟɬ «ɩɨɥɨɠɢɬɟɥɶɧɨɟ» ɧɚɩɪɚɜɥɟɧɢɟ ɫɩɢɧɨɜɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ
41
(+), ɚ ɞɪɭɝɚɹ – «ɨɬɪɢɰɚɬɟɥɶɧɨɟ» (–), ɱɬɨ ɫ ɭɱɟɬɨɦ (2.31) ɜ ɨɬɫɭɬɫɬɜɢɟ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 2.6, ɚ. ɉɪɢ ɷɬɨɦɫɭɦɦɚɪɧɵɣɦɚɝɧɢɬɧɵɣɦɨɦɟɧɬɪɚɜɟɧɧɭɥɸ.
ɚ |
ɛ |
ɜ |
Ɋɢɫ. 2.6. ɂɥɥɸɫɬɪɚɰɢɹ ɩɚɪɚɦɚɝɧɟɬɢɡɦɚ ɷɥɟɤɬɪɨɧɧɨɝɨ ɝɚɡɚ
ɉɪɢ ɩɪɢɥɨɠɟɧɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɭ ɜɫɟɯ ɷɥɟɤɬɪɨɧɨɜ ɫɨ ɫɩɢɧɨɜɵɦ ɦɚɝɧɢɬɧɵɦ ɦɨɦɟɧɬɨɦ, ɧɚɩɪɚɜɥɟɧɧɵɦ ɩɨ ɩɨɥɸ (+), ɷɧɟɪɝɢɹ ɩɨɧɢɡɢɬɫɹ ɧɚ ɜɟɥɢɱɢɧɭ ȝ0ȝBɇ, ɚ ɭ ɷɥɟɤɬɪɨɧɨɜ ɫ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ (–) ɷɧɟɪɝɢɹ ɩɨɜɵɫɢɬɫɹ ɧɚ ɬɚɤɭɸ ɠɟ ɜɟɥɢɱɢɧɭ (ɪɢɫ. 2.6, ɛ). Ɍɚɤ ɤɚɤ ɭɪɨɜɟɧɶ Ɏɟɪɦɢ ɞɥɹ ɜɫɟɯ ɷɥɟɤɬɪɨɧɨɜ ɞɨɥɠɟɧ ɛɵɬɶ ɨɞɢɧ ɢ ɬɨɬ ɠɟ, ɤɚɤɨɟ-ɬɨ ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɩɪɚɜɨɣ ɱɚɫɬɢ (ɫ ɭɜɟɥɢɱɟɧɧɨɣ ɷɧɟɪɝɢɟɣ) ɩɟɪɟɣɞɟɬ ɜ ɥɟɜɭɸ ɱɚɫɬɶ (ɪɢɫ. 2.6, ɜ) ɫ ɩɟɪɟɜɨɪɨɬɨɦ ɫɩɢɧɨɜɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɧɨɜ ɫ ɦɚɝɧɢɬɧɵɦ ɦɨɦɟɧɬɨɦ, ɧɚɩɪɚɜɥɟɧɧɵɦ ɩɨ ɩɨɥɸ, ɫɬɚɧɟɬ ɛɨɥɶɲɟ ɧɚ ǻn:
ǻn = g(EF) ȝ0ȝBɇ. |
|
(2.33) |
|||
ɋ ɭɱɟɬɨɦ ɷɬɨɝɨ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɧɚɦɚɝɧɢɱɟɧ- |
|||||
ɧɨɫɬɢ: |
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Ɇ = ȝ ǻn = g(E )ȝ P2 |
ɇ. |
(2.34) |
|||
B |
F |
0 |
B |
|
|
ɋ ɭɱɟɬɨɦ ɜɵɪɚɠɟɧɢɣ ɞɥɹ g(ȿ) ɢ EF ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɧɚɦɚɝɧɢ- |
|||||
ɱɟɧɧɨɫɬɢ ɩɪɢɦɟɬ ɜɢɞ |
|
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Ɇ = |
3P P2 NH |
. |
|
(2.35) |
|
0 B |
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|
|||
|
2EF |
|
|
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Ɍɨɝɞɚ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɚɪɚɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɷɥɟɤɬɪɨɧɧɨɝɨ ɝɚɡɚ ɛɭɞɟɬ ɜɵɝɥɹɞɟɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
42
Ȥ = |
3P P2 |
N |
. |
(2.36) |
0 B |
|
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|
2EF |
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|
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ɉɨɫɤɨɥɶɤɭ ɬɟɩɥɨɜɚɹ ɷɧɟɪɝɢɹ kT ɫɬɚɧɨɜɢɬɫɹ ɫɨɢɡɦɟɪɢɦɨɣ ɫ EF
ɥɢɲɶ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ ɩɨɪɹɞɤɚ 105 Ʉ, ɬɨ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɝɚɡɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ, ɚ ɟɟ ɡɧɚɱɟɧɢɟ ɛɭɞɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ ɡɧɚɱɟɧɢɹɩɚɪɚɦɚɝɧɢɬɧɨɣɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢɚɬɨɦɨɜɢ ɢɨɧɨɜ.
ɗɥɟɤɬɪɨɧɧɵɣ ɝɚɡ ɨɛɥɚɞɚɟɬ ɢ ɞɢɚɦɚɝɧɟɬɢɡɦɨɦ, ɱɬɨ ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɜ ɜɢɞɭ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɫɭɦɦɚɪɧɨɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɢ ɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ.
ɉɚɪɚɦɚɝɧɢɬɧɵɣ ɷɮɮɟɤɬ (ɜɜɢɞɭ ɫɜɨɟɣ ɦɚɥɨɫɬɢ) ɧɚɲɟɥ ɤɪɚɣɧɟ ɨɝɪɚɧɢɱɟɧɧɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɬɟɯɧɢɤɟ. Ɉɞɧɢɦ ɢɡ ɩɪɢɦɟɪɨɜ ɟɝɨ ɩɪɢɦɟɧɟɧɢɹ ɹɜɥɹɟɬɫɹ ɦɟɬɨɞ ɩɨɥɭɱɟɧɢɹ ɫɜɟɪɯɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪ ɩɭɬɟɦ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɪɚɡɦɚɝɧɢɱɢɜɚɧɢɹ ɩɚɪɚɦɚɝɧɢɬɧɵɯ ɫɨɥɟɣ. Ɉɧ ɛɵɥ ɩɪɟɞɥɨɠɟɧ ɜ 1926–1927 ɝɝ. Ⱦɠɢɨɤɨɦ ɢ Ⱦɟɛɚɟɦ (ɧɟɡɚɜɢɫɢɦɨ ɞɪɭɝ ɨɬ ɞɪɭɝɚ). ɂɞɟɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɟɫɥɢ ɩɪɨɰɟɫɫ ɪɚɡɦɚɝɧɢɱɢɜɚɧɢɹ ɩɪɨɢɫɯɨɞɢɬ ɜ ɚɞɢɚɛɚɬɢɱɟɫɤɢɯ ɭɫɥɨɜɢɹɯ, ɬɨ ɪɚɛɨɬɚ, ɡɚɬɪɚɱɢɜɚɟɦɚɹ ɧɚ ɫɨɡɞɚɧɢɟ ɛɟɫɩɨɪɹɞɤɚ ɜ ɦɚɝɧɢɬɧɨɣ ɫɢɫɬɟɦɟ, ɫɨɜɟɪɲɚɟɬɫɹ ɡɚ ɫɱɟɬ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɬɟɥɚ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɩɨɧɢɠɟɧɢɸ ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɵ. Ɍɟɯɧɢɱɟɫɤɚɹ ɪɟɚɥɢɡɚɰɢɹ ɦɟɬɨɞɚ ɫɯɟɦɚɬɢɱɟɫɤɢ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 2.7.
Ɋɢɫ. 2.7. ɋɯɟɦɚ ɦɟɬɨɞɚ ɨɯɥɚɠɞɟɧɢɹ ɚɞɢɚɛɚɬɢɱɟɫɤɢɦ ɪɚɡɦɚɝɧɢɱɢɜɚɧɢɟɦ
43
Ɋɚɛɨɱɟɟ ɜɟɳɟɫɬɜɨ 1, ɜ ɤɚɱɟɫɬɜɟ ɤɨɬɨɪɨɝɨ ɱɚɳɟ ɜɫɟɝɨ ɭɩɨɬɪɟɛɥɹɸɬ ɫɨɥɢ ɬɢɩɚ ɤɜɚɫɰɨɜ, ɫɨɞɟɪɠɚɳɢɟ ɢɨɧɵ ɩɟɪɟɯɨɞɧɵɯ ɷɥɟɦɟɧɬɨɜ (ɧɚɩɪɢɦɟɪ, NH4Fe(SO4)2·12H2O), ɩɨɦɟɳɚɟɬɫɹ ɜɧɭɬɪɶ ɨɛɴɟɦɚ 2. Ɉɛɴɟɦ ɫ ɪɚɛɨɱɢɦ ɜɟɳɟɫɬɜɨɦ ɩɨɦɟɳɚɟɬɫɹ ɜ ɞɶɸɚɪ ɫ ɠɢɞɤɢɦ ɝɟɥɢɟɦ, ɬɟɩɥɨɢɡɨɥɢɪɨɜɚɧɧɵɣ ɞɶɸɚɪɨɦ ɫ ɠɢɞɤɢɦ ɚɡɨɬɨɦ (ɫɦ. ɪɢɫ. 2.7). ȼɫɟ ɭɫɬɪɨɣɫɬɜɨ ɪɚɫɩɨɥɚɝɚɸɬ ɦɟɠɞɭ ɩɨɥɸɫɚɦɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɚ. ɋɧɚɱɚɥɚ ɜ ɪɚɛɨɱɢɣ ɨɛɴɟɦ ɜɩɭɫɤɚɸɬ ɝɚɡɨɨɛɪɚɡɧɵɣ ɝɟɥɢɣ ɩɪɢ ɞɚɜɥɟɧɢɢ 5…10 ɉɚ. Ɉɧ ɫɨɡɞɚɟɬ ɬɟɩɥɨɜɨɣ ɤɨɧɬɚɤɬ ɦɟɠɞɭ ɪɚɛɨɱɢɦ ɜɟɳɟɫɬɜɨɦ ɢ ɜɚɧɧɨɣ ɫ ɠɢɞɤɢɦ ɝɟɥɢɟɦ. ɉɚɪɵ ɠɢɞɤɨɝɨ ɝɟɥɢɹ ɨɬɤɚɱɢɜɚɸɬ ɬɚɤ, ɱɬɨɛɵ ɨɧ ɤɢɩɟɥ ɩɪɢ ɞɚɜɥɟɧɢɢ ɨɤɨɥɨ 100 ɉɚ, ɩɨɫɥɟ ɱɟɝɨ ɜɤɥɸɱɚɸɬ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɇ ~ 106 Ⱥ/ɦ ɢ ɜɵɠɢɞɚɸɬ, ɩɨɤɚ ɪɚɛɨɱɟɟ ɜɟɳɟɫɬɜɨ ɩɪɢɦɟɬ ɬɟɦɩɟɪɚɬɭɪɭ ɠɢɞɤɨɝɨ ɝɟɥɢɹ. Ɂɚɬɟɦ ɨɛɴɟɦ 2 ɨɬɤɚɱɢɜɚɸɬ ɞɨ ɜɵɫɨɤɨɝɨ ɜɚɤɭɭɦɚ, ɬɟɦ ɫɚɦɵɦ ɬɟɩɥɨɢɡɨɥɢɪɭɹ ɪɚɛɨɱɢɣ ɨɛɴɟɦ. ɉɨɫɥɟ ɜɵɤɥɸɱɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɪɚɛɨɱɟɟ ɜɟɳɟɫɬɜɨ ɨɯɥɚɠɞɚɟɬɫɹ. ɉɪɨɰɟɞɭɪɭ ɦɨɠɧɨ ɩɨɜɬɨɪɢɬɶ ɧɟɫɤɨɥɶɤɨ ɪɚɡ. Ɍɟɯɧɢɱɟɫɤɚɹ ɪɟɚɥɢɡɚɰɢɹ ɦɟɬɨɞɚ ɩɨɫɬɨɹɧɧɨ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɥɚɫɶ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɭɞɚɥɨɫɶ ɩɨɥɭɱɢɬɶ ɬɟɦɩɟɪɚɬɭɪɭ ɜ ɪɚɛɨɱɟɦ ɨɛɴɟɦɟ Ɍ § 0,004 Ʉ.
2.4.Ɏɟɪɪɨɦɚɝɧɟɬɢɡɦ
Ʉɮɟɪɪɨɦɚɝɧɟɬɢɤɚɦ ɨɬɧɨɫɹɬɫɹ ɠɟɥɟɡɨ, ɧɢɤɟɥɶ ɢ ɤɨɛɚɥɶɬ, ɚ ɬɚɤɠɟ ɢɯ ɫɨɟɞɢɧɟɧɢɹ ɢ ɫɩɥɚɜɵ. ɉɪɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɮɟɪɪɨɦɚɝɧɢɬɧɵ ɧɟɤɨɬɨɪɵɟ ɪɟɞɤɨɡɟɦɟɥɶɧɵɟ ɷɥɟɦɟɧɬɵ. Ɉɫɧɨɜɧɵɦɢ ɫɜɨɣɫɬɜɚɦɢ ɮɟɪɪɨɦɚɝɧɟɬɢɤɨɜ ɹɜɥɹɸɬɫɹ:
x ɫɩɨɫɨɛɧɨɫɬɶ ɧɚɦɚɝɧɢɱɢɜɚɬɶɫɹ ɞɨ ɧɚɫɵɳɟɧɢɹ ɜ ɫɥɚɛɵɯ ɦɚɝɧɢɬɧɵɯ ɩɨɥɹɯ;
x ɧɟɥɢɧɟɣɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɨɬ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ;
x ɛɨɥɶɲɚɹ (ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ 1) ɦɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ (ɩɪɨɧɢɰɚɟɦɨɫɬɶ);
x ɫɢɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɢ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ;
x ɬɨɱɤɚ Ʉɸɪɢ – ɬɟɦɩɟɪɚɬɭɪɚ, ɜɵɲɟ ɤɨɬɨɪɨɣ ɜɟɳɟɫɬɜɨ ɬɟɪɹɟɬ ɮɟɪɪɨɦɚɝɧɢɬɧɵɟ ɫɜɨɣɫɬɜɚ.
44
Ɏɨɪɦɚɥɶɧɚɹ ɬɟɨɪɢɹ ɮɟɪɪɨɦɚɝɧɟɬɢɡɦɚ
Ɉɛɴɹɫɧɟɧɢɟ ɹɜɥɟɧɢɹ ɮɟɪɪɨɦɚɝɧɟɬɢɡɦɚ ɧɚɱɚɥɨɫɶ ɫ ɢɫɫɥɟɞɨɜɚɧɢɣ Ɋɨɡɢɧɝɚ (1892) ɢ ȼɟɣɫɫɚ (1907), ɪɚɡɪɚɛɨɬɚɜɲɢɯ ɮɨɪɦɚɥɶɧɭɸ ɬɟɨɪɢɸ, ɨɫɧɨɜɚɧɧɭɸ ɧɚ ɩɪɟɞɫɬɚɜɥɟɧɢɹɯ ɤɥɚɫɫɢɱɟɫɤɨɣ ɮɢɡɢɤɢ. Ɉɧɢ ɩɪɟɞɩɨɥɨɠɢɥɢ, ɱɬɨ ɜ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚɯ ɫɭɳɟɫɬɜɭɟɬ ɫɢɥɶɧɨɟ ɜɧɭɬɪɟɧɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɧɚɡɜɚɧɧɨɟ ɦɨɥɟɤɭɥɹɪɧɵɦ ɩɨɥɟɦ, ɤɨɬɨɪɨɟ ɢ ɩɪɢɜɨɞɢɬ ɤ ɫɩɨɧɬɚɧɧɨɦɭ (ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɦɭ) ɧɚɦɚɝɧɢɱɢɜɚɧɢɸ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚ ɞɨ ɧɚɫɵɳɟɧɢɹ ɞɚɠɟ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɩɟɪɜɚɹ ɝɢɩɨɬɟɡɚ ȼɟɣɫɫɚ). Ɉɞɧɚɤɨ ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɜ ɨɬɫɭɬɫɬɜɢɟ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɮɟɪɪɨɦɚɝɧɢɬɧɨɟ ɬɟɥɨ ɢɦɟɟɬ ɧɭɥɟɜɨɣ ɪɟɡɭɥɶɬɢɪɭɸɳɢɣ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ. Ⱦɥɹ ɨɛɴɹɫɧɟɧɢɹ ɧɚɛɥɸɞɚɟɦɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ȼɟɣɫɫ ɩɪɟɞɩɨɥɨɠɢɥ, ɱɬɨ ɩɪɢ ɇ = 0 ɜɟɳɟɫɬɜɨ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨ ɪɚɡɛɢɜɚɟɬɫɹ ɧɚ ɦɧɨɠɟɫɬɜɨ ɦɚɤɪɨɨɛɥɚɫɬɟɣ (ɞɨɦɟɧɨɜ), ɤɚɠɞɚɹ ɢɡ ɤɨɬɨɪɵɯ ɧɚɦɚɝɧɢɱɟɧɚ ɞɨ ɧɚɫɵɳɟɧɢɹ, ɚ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɨɬɞɟɥɶɧɵɯ ɞɨɦɟɧɨɜ ɪɚɜɧɨɜɟɪɨɹɬɧɨ ɨɪɢɟɧɬɢɪɨɜɚɧɵ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɷɬɨɝɨ ɫɭɦɦɚɪɧɵɣ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɬɟɥɚ ɪɚɜɟɧ ɧɭɥɸ (ɜɬɨɪɚɹ ɝɢɩɨɬɟɡɚ ȼɟɣɫɫɚ). Ȼɨɥɟɟ ɩɨɞɪɨɛɧɨ ɜɨɩɪɨɫɵ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɞɨɦɟɧɨɜ ɢ ɢɯ ɜɥɢɹɧɢɹ ɧɚ ɩɪɨɰɟɫɫɵ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɛɭɞɭɬ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɫɥɟɞɭɸɳɢɯ ɝɥɚɜɚɯ. Ɂɞɟɫɶ ɠɟ ɨɫɬɚɧɨɜɢɦɫɹ ɧɚ ɹɜɥɟɧɢɢ ɫɩɨɧɬɚɧɧɨɝɨ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚ ɜɧɭɬɪɢ ɞɨɦɟɧɚ ɩɨɞ ɜɥɢɹɧɢɟɦ ɦɨɥɟɤɭɥɹɪɧɨɝɨ ɩɨɥɹ (ɩɟɪɜɚɹ ɝɢɩɨɬɟɡɚ ȼɟɣɫɫɚ).
ɉɭɫɬɶ ɮɟɪɪɨɦɚɝɧɟɬɢɤ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ «ɝɚɡ ɷɥɟɤɬɪɨɧɧɵɯ ɫɩɢɧɨɜ», ɩɨɞ ɤɨɬɨɪɵɦ ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɫɨɜɨɤɭɩɧɨɫɬɶ ɧɟɫɤɨɦɩɟɧɫɢɪɨɜɚɧɧɵɯ ɫɩɢɧɨɜɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ N ɨɞɢɧɚɤɨɜɵɯ ɚɬɨɦɨɜ ɜ ɭɡɥɚɯ ɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣ ɪɟɲɟɬɤɢ ɜɟɳɟɫɬɜɚ (ɦɨɞɟɥɶ ɂɡɢɧɝɚ). ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɚɬɨɦɨɜ ɦɨɝɭɬ ɢɦɟɬɶ ɬɨɥɶɤɨ ɞɜɟ ɨɪɢɟɧɬɚɰɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɵɛɪɚɧɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ, ɧɚɩɪɢɦɟɪ «ɜɩɪɚɜɨ» ɢɥɢ «ɜɥɟɜɨ». Ɉɛɨɡɧɚɱɢɦ ɤɨɥɢɱɟɫɬɜɨ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɫ «ɩɪɚɜɨɣ» ɨɪɢɟɧɬɚɰɢɟɣ r, ɚ ɤɨɥɢɱɟɫɬɜɨ ɦɨɦɟɧɬɨɜ ɫ «ɥɟɜɨɣ» ɨɪɢɟɧɬɚɰɢɟɣ l. Ɍɨɝɞɚ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɜɵɪɚɠɟɧɢɟɦ
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y = |
r l |
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(2.37) |
ɢɥɢ |
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N |
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r = |
(1 + y), |
l = |
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(1 – y). |
(2.38) |
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45
ɉɨɫɤɨɥɶɤɭ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɥɹ ɢ ɬɟɦɩɟɪɚɬɭɪɵ y = f(H, T), ɟɟ ɜɟɥɢɱɢɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɢɧɢɦɭɦɨɦ ɫɜɨɛɨɞɧɨɣ ɷɧɟɪɝɢɢ:
F = U – ST, |
(2.39) |
ɝɞɟ U – ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɬɟɥɚ; S – ɷɧɬɪɨɩɢɹ ɬɟɥɚ.
ɗɧɬɪɨɩɢɹ ɬɟɥɚ ɫɜɹɡɚɧɚ ɫɨ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ɫɨ-
ɫɬɨɹɧɢɹ W ɪɚɜɟɧɫɬɜɨɦ |
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S = k ln W, |
(2.40) |
ɝɞɟ k – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ. |
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ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɧɚɫ ɢɧɬɟɪɟɫɭɟɬ ɱɚɫɬɶ ɷɧɬɪɨɩɢɢ, ɫɜɹɡɚɧɧɚɹ ɫ ɨɪɢɟɧɬɚɰɢɟɣ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ, ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɬɚɬɢɫɬɢɱɟɫɤɚɹ ɜɟɪɨɹɬɧɨɫɬɶ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɫ ɡɚɞɚɧɧɨɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶɸ y. Ɍɨɝɞɚ W ɛɭɞɟɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɱɢɫɥɭ ɜɨɡɦɨɠɧɵɯ ɫɩɨɫɨ-
ɛɨɜ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɫ ɡɚɞɚɧɧɨɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶɸ y: |
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ɉɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ (2.41) ɜ (2.40) ɩɨɥɭɱɢɦ: |
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S = k(ln N! – ln r! – ln l!). |
(2.42) |
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ȼɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɮɨɪɦɭɥɨɣ ɋɬɢɪɥɢɧɝɚ: ln n! = n(ln n – 1), ɩɪɟɨɛɪɚɡɭɟɦ (2.42) ɤ ɜɢɞɭ
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S = k(N ln N – r ln r – l ln l). |
(2.43) |
ɍɱɢɬɵɜɚɹ (2.37) ɢ (2.38), ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɷɧɬɪɨɩɢɢ: |
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S = |
N k [(1 + y)ln(1 + y) + (1 – y) ln(1 – y)]. |
(2.44) |
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Ɇɢɧɢɦɭɦ ɫɜɨɛɨɞɧɨɣ ɷɧɟɪɝɢɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ |
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( F/ y) = 0. |
(2.45) |
ȼ ɨɬɫɭɬɫɬɜɢɟ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɨɡɦɨɠɧɵ ɞɜɚ ɫɥɭɱɚɹ: 1. ȼɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ U ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ y, ɢ
ɬɨɝɞɚ ɩɪɢ ɭɫɥɨɜɢɢ ɜɵɩɨɥɧɟɧɢɹ (2.45) ɩɨɥɭɱɢɦ: |
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ln(1 + y) – ln(1 – y) = 0. |
(2.46) |
ȼɵɩɨɥɧɟɧɢɟ ɪɚɜɟɧɫɬɜɚ (2.46) ɜɨɡɦɨɠɧɨ, ɥɢɲɶ ɟɫɥɢ y = 0, ɬ. ɟ. ɜ ɫɥɭɱɚɟ ɨɬɫɭɬɫɬɜɢɹ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɩɪɢ ɇ = 0, ɱɬɨ ɩɪɨɬɢɜɨɪɟɱɢɬ ɝɢɩɨɬɟɡɟ ȼɟɣɫɫɚ.
46
2. ȼɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɢɥɢ ɟɟ ɱɚɫɬɶ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ U = f (ɭ).
ȼɢɞ ɷɬɨɣ ɮɭɧɤɰɢɢ ɧɟɢɡɜɟɫɬɟɧ, ɧɨ ɦɨɠɧɨ ɩɪɟɞɩɨɥɨɠɢɬɶ, ɱɬɨ ɨɧɚ ɞɨɥɠɧɚ ɜɤɥɸɱɚɬɶ ɜ ɫɟɛɹ ɷɧɟɪɝɢɸ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɦɚɝɧɢɬɧɵɦɢ ɦɨɦɟɧɬɚɦɢ, ɩɪɢɯɨɞɹɳɭɸɫɹ ɧɚ ɨɞɧɭ ɱɚɫɬɢɰɭ ɩɪɢ y = ±1 (ɨɛɨɡɧɚɱɢɦ ɟɟ Ⱥ1 > 0). ȿɫɥɢ ɨɛɨɡɧɚɱɢɬɶ ɨɛɳɟɟ ɤɨɥɢɱɟɫɬ-
ɜɨ ɱɚɫɬɢɰ ɫɢɦɜɨɥɨɦ N ɢ ɭɱɟɫɬɶ ɬɨɬ ɮɚɤɬ, ɱɬɨ U ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɡɧɚ-
ɤɚ ɭ, ɬɨ ɫɩɪɚɜɟɞɥɢɜɨ ɜɵɪɚɠɟɧɢɟ |
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U(y) = –A |
1 |
Ny2. |
(2.47) |
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ɉɨɞɫɬɚɜɢɜ (2.47) ɢ (2.44) ɜ (2.39), ɚ ɡɚɬɟɦ ɩɨɞɫɬɚɜɢɜ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ F ɜ (2.45), ɩɨɥɭɱɢɦ:
4A1 |
ɭ = ln |
1 |
y |
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(2.48) |
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kT |
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y |
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ɍɪɚɜɧɟɧɢɟ (2.48) ɪɟɲɚɟɬɫɹ ɝɪɚɮɢɱɟɫɤɢ, ɞɥɹ ɷɬɨɝɨ ɧɚɞɨ ɜɜɟɫɬɢ ɜɫɩɨɦɨɝɚɬɟɥɶɧɭɸ ɩɟɪɟɦɟɧɧɭɸ q ɢ ɪɚɫɫɦɨɬɪɟɬɶ ɞɜɟ ɮɭɧɤɰɢɢ:
q = |
4A1 |
y; |
q = ln |
1 |
y |
. |
(2.49) |
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ɉɟɪɜɚɹ ɮɭɧɤɰɢɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɹɦɭɸ ɫ ɧɚɤɥɨɧɨɦ, ɨɩɪɟɞɟɥɹɟɦɵɦ ɬɟɦɩɟɪɚɬɭɪɨɣ, ɚ ɜɬɨɪɚɹ – ɤɪɢɜɭɸ, ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɩɪɢɛɥɢɠɚɸɳɭɸɫɹ ɤ ɭ = ±1 ɩɪɢ q ± . Ƚɪɚɮɢɱɟɫɤɨɟ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (2.49) ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 2.8, ɝɞɟ
ɤɪɢɜɵɟ II, III, IV ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɪɚɡɧɵɦ ɬɟɦɩɟɪɚɬɭɪɚɦ.
Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (2.49) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɬɨɱɤɚɦ ɩɟɪɟɫɟɱɟɧɢɹ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɮɭɧɤɰɢɣ.
ɉɪɢ ɧɢɡɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɩɪɹɦɚɹ IV ɩɟɪɟɫɟɤɚɟɬ ɤɪɢɜɭɸ ɜ ɬɪɟɯ ɬɨɱɤɚɯ: ɭ = 0 ɢ ɭ = ±ɭ1. ɉɪɢ ɩɨ-
ɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɤɪɚɣɧɢɟ
Ɋɢɫ. 2.8. Ɂɚɜɢɫɢɦɨɫɬɢ y = f (q)
ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɫɛɥɢɠɚɸɬɫɹ, ɢ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ Ĭ (ɬɨɱɤɚ Ʉɸɪɢ, ɩɪɢ ɤɨɬɨɪɨɣ ɩɪɹɦɚɹ ɩɪɟɜɪɚɳɚɟɬɫɹ
ɜ ɤɚɫɚɬɟɥɶɧɭɸ ɤ ɤɪɢɜɨɣ ɜ ɬɨɱɤɟ ɭ = 0) ɨɧɢ ɫɥɢɜɚɸɬɫɹ ɫɨ ɫɪɟɞɧɟɣ ɬɨɱɤɨɣ (ɭ = 0). ɉɪɢ ɬɟɦɩɟɪɚɬɭɪɟ ɜɵɲɟ Ĭ ɢɦɟɟɬɫɹ ɬɨɥɶɤɨ ɨɞɧɚ ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ: ɩɪɢ ɭ = 0.
47
Ɂɧɚɱɟɧɢɟ ɝɪɚɧɢɱɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ Ĭ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɭɫɥɨ-
ɜɢɹ ɫɨɜɩɚɞɟɧɢɹ ɭɝɥɨɜ ɧɚɤɥɨɧɚ ɮɭɧɤɰɢɣ (2.49) ɜ ɬɨɱɤɟ ɭ = 0: |
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Ĭ = 2Ⱥ1/k. |
(2.50) |
ɉɪɢ ɜɫɟɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɜɵɲɟ Ĭ ɭ = 0, ɬ. ɟ. ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɚɹ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɨɬɫɭɬɫɬɜɭɟɬ.
Ɉɩɪɟɞɟɥɢɦ, ɤɚɤɢɟ ɢɡ ɬɨɱɟɤ ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɵɯ ɨɬɜɟɱɚɸɬ ɭɫɥɨɜɢɸ ɦɢɧɢɦɭɦɚ ( 2F/ ɭ2) > 0. Ɋɚɫɫɦɨɬɪɢɦ ɫɧɚɱɚɥɚ ɬɨɱɤɭ ɭ = 0. ɂɡ
(2.48) ɢ (2.50) ɫɥɟɞɭɟɬ, ɱɬɨ
( 2F/ ɭ2)ɭ = 0 = Nk(T – Ĭ).
Ɉɬɫɸɞɚ ɜɢɞɧɨ, ɱɬɨ ɩɪɢ T < Ĭ ɷɬɚ ɜɟɥɢɱɢɧɚ ɨɬɪɢɰɚɬɟɥɶɧɚ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɬɨɱɤɚ ɭ = 0 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦɚɤɫɢɦɭɦɭ ɫɜɨɛɨɞɧɨɣ ɷɧɟɪɝɢɢ, ɚ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɩɪɢ ɭ = ±ɭ1 ɨɬɜɟɱɚɸɬ ɦɢɧɢɦɭɦɭ, ɬɚɤ ɤɚɤ ɞɜɚ
ɦɚɤɫɢɦɭɦɚ ɧɚɯɨɞɢɬɶɫɹ ɪɹɞɨɦ ɧɟ ɦɨɝɭɬ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɟɥɨ, ɜ ɤɨɬɨɪɨɦ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ (ɢɥɢ ɟɟ ɱɚɫɬɶ) ɡɚɜɢɫɢɬ ɨɬ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ, ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɚɯ ɧɢɠɟ Ĭ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɫɨɫɬɨɹɧɢɢ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɩɪɢ ɇ = 0. Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɭɦɚ (ɭ = 1) ɩɪɢ Ɍ = 0. ɉɪɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɭ ɫɧɚɱɚɥɚ ɦɟɞɥɟɧɧɨ, ɚ ɡɚɬɟɦ ɛɵɫɬɪɨ ɫɩɚɞɚɟɬ ɢ ɩɪɢ Ɍ Ĭ ɭ = 0.
ɍɪɚɜɧɟɧɢɟ (2.48) ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ |
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y = th |
4 y. |
(2.51) |
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T |
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ɇɚ ɪɢɫ. 2.9 ɩɨɤɚɡɚɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɞɥɹ ɠɟɥɟɡɚ (Ɍɫ = 1026 Ʉ), ɧɢɤɟɥɹ (Ɍɫ = 638 Ʉ) ɢ ɤɨɛɚɥɶɬɚ (Ɍɫ = = 1273 Ʉ). ȼɢɞɧɨ, ɱɬɨ ɪɚɫɱɟɬɧɵɟ ɞɚɧɧɵɟ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ ɫɨɜɩɚɞɚɸɬɫɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ.
Ɋɚɫɫɦɨɬɪɢɦ ɩɨɜɟɞɟɧɢɟ ɦɨɞɟɥɢ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ȼɟɣɫɫɚ ɩɪɢ ɧɚɥɢɱɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɇ 0). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɫɜɨɛɨɞɧɨɣ ɷɧɟɪɝɢɢ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
Ɏ = F(y T) – MH = 1 |
NkT[(1 + y) ln(1 + y) + |
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1 |
2 |
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y2 – N ȝ ɭɇ. |
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+ (1 – y) ln(1 – y)] – NA |
(2.52) |
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ɦ |
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ɂɡ (2.52) ɜɢɞɧɨ, ɱɬɨ ɩɪɢ Ɍ = 0 Ɏ ɦɢɧɢɦɚɥɶɧɚ ɩɪɢ ɭɫɥɨɜɢɢ ɭ = 1, ɱɬɨ ɨɬɜɟɱɚɟɬ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ Ɇ = Ɇ0 = ȝ0 ȝɦN.
48
Ɋɢɫ. 2.9. ɋɪɚɜɧɟɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɡɚɜɢɫɢɦɨɫɬɟɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɧɚɫɵɳɟɧɢɹ ɫ ɪɚɫɫɱɢɬɚɧɧɨɣ ɩɨ (2.51):
Ms – ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɧɚɫɵɳɟɧɢɹ ɩɪɢ ɬɟɤɭɳɟɣ ɬɟɦɩɟɪɚɬɭɪɟ, Ɇ0 – ɩɪɢ 0 Ʉ
ɉɪɢ Ɍ > 0 ɭɫɥɨɜɢɟ ɷɤɫɬɪɟɦɭɦɚ Ɏ/ ɭ = 0 ɞɚɟɬ ɜɵɪɚɠɟɧɢɟ
ln (1 ɭ) |
= |
4Ⱥ1 y + |
2P0Pɦɇ |
, |
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(1 ɭ) |
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kT |
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kT |
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ɢɥɢ |
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ɭ = th P0Pɦ |
§ |
2Ⱥ1ɭ |
ɇ |
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= th P0Pɦ (H + H). |
(2.53) |
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¸ |
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kT |
¨P P |
ɦ |
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1 |
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© 0 |
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ɉɟɪɜɵɣ ɱɥɟɧ ɜ (2.53) ɦɨɠɧɨ ɮɨɪɦɚɥɶɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɧɟɤɨɬɨɪɨɟ ɜɧɭɬɪɟɧɧɟɟ ɦɨɥɟɤɭɥɹɪɧɨɟ ɩɨɥɟ:
2Ⱥ1ɭ P0Pɦ = ɇ1. |
(2.54) |
ɂɡ (2.50) ɢ (2.54) ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨɪɹɞɨɤ ɷɧɟɪɝɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɦɚɝɧɢɬɧɵɦɢ ɦɨɦɟɧɬɚɦɢ Ⱥ1 ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɦɨɥɟ-
ɤɭɥɹɪɧɨɝɨ ɩɨɥɹ ɇ1. ȿɫɥɢ ɩɨɥɨɠɢɬɶ Ĭ § 103 Ʉ ɢ ȝɦ = ȝȼ, ɬɨ ɩɪɢ ɭ = 1 ɩɨɥɭɱɢɦ Ⱥ1 § 10–20 Ⱦɠ, ɇ1 § 109 Ⱥ/ɦ.
ɉɪɨɢɫɯɨɠɞɟɧɢɟ ɷɧɟɪɝɢɢ Ⱥ1 ɢ ɩɪɢɪɨɞɚ ɩɨɥɹ, ɩɪɢɜɨɞɹɳɟɝɨ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɮɟɪɪɨɦɚɝɧɟɬɢɤɨɜ, ɜ ɮɨɪɦɚɥɶɧɨɣɬɟɨɪɢɢ ȼɟɣɫɫɚ ɧɟ ɭɬɨɱɧɹɸɬɫɹ. Ɉɞɧɚɤɨ ȼɟɣɫɫ ɩɪɟɞɩɨɥɚɝɚɥ, ɱɬɨ Ⱥ1 ɢɦɟɟɬ ɦɚɝɧɢɬɧɭɸ ɩɪɢɪɨɞɭ. ȿɫɥɢ ɪɚɫɫɦɚɬɪɢɜɚɬɶ Ⱥ1 ɤɚɤ ɷɧɟɪɝɢɸ
49
Ɍɨɥɶɤɨ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɋɉɛȽɗɌɍ "ɅɗɌɂ" ɢɦ. ȼ.ɂ. ɍɥɶɹɧɨɜɚ (Ʌɟɧɢɧɚ)
ɞɢɩɨɥɶɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɷɥɟɦɟɧɬɚɪɧɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ (ɧɚɩɪɢɦɟɪ, ɪɚɜɧɵɯ ȝȼ), ɬɨ ɩɨɥɭɱɢɦ ɡɧɚɱɟɧɢɟ ~10–23 Ⱦɠ, ɱɬɨ ɞɨɥɠɧɨ
ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ Ĭ § 1 Ʉ. Ʉɪɨɦɟ ɬɨɝɨ, ɢɡɦɟɪɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɮɟɪɪɨɦɚɝɧɟɬɢɤɟ (ɧɚɦɚɝɧɢɱɟɧɧɨɣ ɧɢɤɟɥɟɜɨɣ ɮɨɥɶɝɟ), ɩɪɨɜɟɞɟɧɧɵɟ ɜ 1927 ɝ. ə. Ƚ. Ⱦɨɪɮɦɚɧɨɦ, ɞɚɥɢ ɪɟɡɭɥɶɬɚɬ ɇ1 § 107 Ⱥ/ɦ, ɱɬɨ ɧɚ ɞɜɚ ɩɨ-
ɪɹɞɤɚ ɧɢɠɟ ɧɟɨɛɯɨɞɢɦɨɝɨ ɡɧɚɱɟɧɢɹ. ɗɬɢ ɧɟɫɨɨɬɜɟɬɫɬɜɢɹ ɭɤɚɡɵɜɚɸɬ ɧɚ ɧɟɦɚɝɧɢɬɧɭɸ ɩɪɢɪɨɞɭ ɫɢɥ, ɩɪɢɜɨɞɹɳɢɯ ɤ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɷɥɟɦɟɧɬɚɪɧɵɯ ɡɚɪɹɞɨɜ, ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɦɟɠɚɬɨɦɧɨɦ ɪɚɫɫɬɨɹɧɢɢ, ɫɨɫɬɚɜɥɹɟɬ ~10–19…10–20 Ⱦɠ, ɱɬɨ ɫɨɩɨɫɬɚɜɢɦɨ ɫ ɷɧɟɪɝɢɟɣ, ɧɟɨɛɯɨɞɢɦɨɣ ɞɥɹ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɝɨ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. Ʉɥɚɫɫɢɱɟɫɤɚɹ ɮɢɡɢɤɚ ɧɟ ɦɨɝɥɚ ɨɛɴɹɫɧɢɬɶ, ɤɚɤɢɦ ɨɛɪɚɡɨɦ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɟ ɩɨɥɟ ɦɨɠɟɬ ɜɥɢɹɬɶ ɧɚ ɦɚɝɧɢɬɧɵɟ ɫɜɨɣɫɬɜɚ ɜɟɳɟɫɬɜɚ. Ɍɨɥɶɤɨ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɤɜɚɧɬɨɜɨɣ ɦɟɯɚɧɢɤɢ ɞɚɥɨ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɴɹɫɧɢɬɶ ɩɪɢɪɨɞɭ ɦɨɥɟɤɭɥɹɪɧɨɝɨ ɩɨɥɹ ȼɟɣɫɫɚ.
ɇɟɤɨɬɨɪɵɟ ɫɜɟɞɟɧɢɹ ɢɡ ɤɜɚɧɬɨɜɨɣ ɦɟɯɚɧɢɤɢ
ɂɡɜɟɫɬɧɨ, ɱɬɨ ɷɥɟɤɬɪɨɧ, ɤɚɤ ɢ ɞɪɭɝɢɟ ɚɬɨɦɧɵɟ ɱɚɫɬɢɰɵ, ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɨɦ ɤɨɪɩɭɫɤɭɥɹɪɧɨ-ɜɨɥɧɨɜɨɝɨ ɞɭɚɥɢɡɦɚ, ɬ. ɟ. ɩɪɨɹɜɥɹɟɬ ɜ ɪɚɡɥɢɱɧɵɯ ɩɪɨɰɟɫɫɚɯ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɤɨɪɩɭɫɤɭɥɹɪɧɵɟ ɢɥɢ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɜɨɥɧɨɜɵɟ ɫɜɨɣɫɬɜɚ. ɗɬɨ ɤɚɱɟɫɬɜɟɧɧɨɟ ɨɬɥɢɱɢɟ ɫɜɨɣɫɬɜ ɷɥɟɤɬɪɨɧɚ ɨɬ ɫɜɨɣɫɬɜ ɤɥɚɫɫɢɱɟɫɤɨɝɨ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɨɝɨ ɬɟɥɚ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɟɝɨ ɩɨɜɟɞɟɧɢɟ ɧɟɥɶɡɹ ɨɩɢɫɚɬɶ ɡɚɤɨɧɚɦɢ ɧɶɸɬɨɧɨɜɫɤɨɣ ɦɟɯɚɧɢɤɢ. Ɉɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɨɬɥɢɱɢɣ ɡɚɤɨɧɨɜ ɤɜɚɧɬɨɜɨɣ ɦɟɯɚɧɢɤɢ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ ɨɧɢ ɹɜɥɹɸɬɫɹ ɫɬɚɬɢɫɬɢɱɟɫɤɢɦɢ.
Ⱥɬɨɦɧɚɹ ɫɢɫɬɟɦɚ, ɫɨɫɬɨɹɳɚɹ ɢɡ ɦɧɨɠɟɫɬɜɚ ɷɥɟɤɬɪɨɧɨɜ ɢ ɚɬɨɦɧɵɯ ɹɞɟɪ, ɦɨɠɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɪɚɡɥɢɱɧɵɯ ɦɢɤɪɨɫɨɫɬɨɹɧɢɹɯ. ȼ ɤɥɚɫɫɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɟ ɞɥɹ ɩɨɥɧɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɫɨɫɬɨɹɧɢɹ ɬɚɤɨɣ ɫɢɫɬɟɦɵ ɧɚɞɨ ɡɚɞɚɬɶ, ɧɚɩɪɢɦɟɪ, ɤɨɨɪɞɢɧɚɬɵ q1, q2, q3, …, qn ɜɫɟɯ ɱɚɫɬɢɰ. ȼ ɤɜɚɧɬɨɜɨɣ ɦɟɯɚɧɢɤɟ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɚɞɚɧɢɟɦ ɜɟɪɨɹɬɧɨɫɬɟɣ W(q1, …, qn, t) dq1, …, dqn ɬɨɝɨ, ɱɬɨ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɤɨɨɪɞɢɧɚɬɵ ɫɢɫɬɟɦɵ ɥɟɠɚɬ ɜ ɨɩɪɟɞɟɥɟɧɧɵɯ ɢɧɬɟɪɜɚɥɚɯ dq1, …, dqn. Ɏɭɧɤɰɢɹ W(q, t) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ, ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɤɜɚɞɪɚɬ ɦɨɞɭɥɹ ɤɨɦɩɥɟɤɫɧɨɣ ɮɭɧɤɰɢɢ Ȍ:
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