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Файл:Термодинамические циклы теплоэнергетических установок. Учебное пособие
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ɉɪɢ ɩɪɢɧɹɬɵɯ ɩɚɪɚɦɟɬɪɚɯ ɰɢɤɥɚ ȽɌɍ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ ɪ =
U
= const ɬɟɦɩɟɪɚɬɭɪɵ ɜ ɬɨɱɤɚɯ 2, 3 ɢ 4 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ:
Ɍɟɪɦɢɱɟɫɤɢɣ ɄɉȾ ɰɢɤɥɚ:
kTT
S
12
1
k
;
K
t
k
1
k
;
US
TT
13
T
1
T
4
1
.
11
U
.
TT
14
Ⱥɧɚɥɢɡ ɩɨɫɥɟɞɧɟɣ ɮɨɪɦɭɥɵ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɬɟɪɦɢɱɟɫɤɢɣ ɄɉȾ ɰɢɤɥɚ
ɩɪɢ ɩɨɥɧɨɣ ɪɟɝɟɧɟɪɚɰɢɢ ɡɚɜɢɫɢɬ ɨɬ ɧɚɱɚɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɜ ɤɨɧɰɟ ɚɞɢɚɛɚɬɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ. Ɉɛɵɱɧɨ ɞɜɢɝɚɬɟɥɢ ɪɚɛɨɬɚɸɬ ɧɟ
ɩɪɢ ɩɨɥɧɨɣ ɪɟɝɟɧɟɪɚɰɢɢ, ɩɨɷɬɨɦɭ Ɍ
> Ɍ2. ɉɪɢ ɷɬɨɦ ɬɟɪɦɢɱɟɫɤɢɣ ɄɉȾ
6
ɰɢɤɥɚ ɞɨɥɠɟɧ ɭɱɢɬɵɜɚɬɶ ɫɬɟɩɟɧɶ ɪɟɝɟɧɟɪɚɰɢɢ, ɨɩɪɟɞɟɥɹɟɦɭɸ ɤɚɤ ɨɬɧɨɲɟɧɢɟ ɤɨɥɢɱɟɫɬɜɚ ɬɟɩɥɨɬɵ, ɩɟɪɟɞɚɧɧɨɝɨ ɜɨɡɞɭɯɭ, ɤ ɬɨɦɭ ɤɨɥɢɱɟɫɬɜɭ ɬɟɩɥɨɬɵ, ɤɨɬɨɪɨɟ ɦɨɝɥɨ ɛɵ ɛɵɬɶ ɩɟɪɟɞɚɧɨ ɩɪɢ ɨɯɥɚɠɞɟɧɢɢ ɝɚɡɨɜ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ ɜɨɡɞɭɯɚ.
ɋɬɟɩɟɧɶ ɪɟɝɟɧɟɪɚɰɢɢ:
V
25
.
ɌɌɌɌ
64
ȼɟɥɢɱɢɧɚ ɫɬɟɩɟɧɢ ɪɟɝɟɧɟɪɚɰɢɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɱɟɫɬɜɨɦ ɢ ɜɟɥɢɱɢɧɨɣ
ɪɚɛɨɱɢɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ (ɪɟɝɟɧɟɪɚɬɨɪɚ).
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɪɟɝɟɧɟɪɚɰɢɹ ɬɟɩɥɨɬɵ ɧɚɯɨɞɢɬ ɩɪɚɤɬɢɱɟɫɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɨɫɧɨɜɧɨɦ ɜ ɫɬɚɰɢɨɧɚɪɧɵɯ ɭɫɬɚɧɨɜɤɚɯ ɢ ɪɟɠɟ ɜ ɬɪɚɧɫɩɨɪɬɧɵɯ
ɭɫɬɚɧɨɜɤɚɯ ɢɡ-ɡɚ ɛɨɥɶɲɨɣ ɦɚɫɫɵ ɢ ɝɚɛɚɪɢɬɨɜ ɪɟɝɟɧɟɪɚɬɨɪɚ.
2.6. ɉɨɪɲɧɟɜɵɟ ɞɜɢɝɚɬɟɥɢ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ
Ⱦɜɢɝɚɬɟɥɢ, ɜ ɤɨɬɨɪɵɯ ɩɪɨɰɟɫɫ ɫɝɨɪɚɧɢɹ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɪɚɛɨɱɟɦ
ɩɪɨɫɬɪɚɧɫɬɜɟ ɦɚɲɢɧɵ, ɧɚɡɵɜɚɸɬ ɞɜɢɝɚɬɟɥɟɦ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ (Ⱦȼɋ).
ȼ Ⱦȼɋ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɫɥɟɞɭɸɳɢɟ ɰɢɤɥɵ:
ɚ) ɰɢɤɥ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ (
X
= const);
ɛ) ɰɢɤɥ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ (ɪ = const);
ɜ) ɰɢɤɥ ɫɨ ɫɦɟɲɚɧɧɵɦ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ, ɤɚɤ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ, ɬɚɤ ɢ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ.
ȼɨ ɜɫɟɯ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɰɢɤɥɚɯ ɨɬɜɨɞ ɬɟɩɥɨɬɵ ɜ ɰɢɤɥɟ ɩɪɨɢɡɜɨɞɢɬɫɹ
ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ ɜ ɫɢɥɭ ɬɨɝɨ, ɱɬɨ ɪɚɫɲɢɪɟɧɢɟ ɝɚɡɚ ɩɪɨɢɫɯɨɞɢɬ ɧɟ
ɩɨɥɧɨɫɬɶɸ ɢ ɫɬɟɩɟɧɶ ɜɨɡɦɨɠɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ ɜ ɞɜɢɝɚɬɟɥɟ ɨɩɪɟɞɟɥɹɟɬɫɹ
ɩɨɥɨɠɟɧɢɟɦ ɩɨɪɲɧɹ ɜ ɧɢɠɧɟɣ ɦɟɪɬɜɨɣ ɬɨɱɤɟ.
51
2.6.1. ɐɢɤɥ ɞɜɢɝɚɬɟɥɹ ɫ ɢɡɨɯɨɪɧɵɦ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ
ɐɢɤɥ ɫ ɢɡɨɯɨɪɧɵɦ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ – ɰɢɤɥ Ɉɬɬɨ – ɷɬɨ ɰɢɤɥ ɛɟɧɡɢɧɨɜɵɯ ɞɜɢɝɚɬɟɥɟɣ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ ɫ ɜɧɟɲɧɢɦ ɫɦɟɫɟɨɛɪɚɡɨɜɚɧɢɟɦ ɜ
ɤɚɪɛɸɪɚɬɨɪɟ ɢ ɩɪɢ ɩɪɢɧɭɞɢɬɟɥɶɧɨɦ ɢɫɤɪɨɜɨɦ ɡɚɠɢɝɚɧɢɢ ɝɨɪɸɱɟɣ ɫɦɟɫɢ.
ɂɯ ɧɚɡɵɜɚɸɬ ɤɚɪɛɸɪɚɬɨɪɧɵɦɢ ɞɜɢɝɚɬɟɥɹɦɢ ɢ ɩɪɢɦɟɧɹɸɬ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɧɚ ɚɜɬɨɬɪɚɧɫɩɨɪɬɟ (ɨɫɨɛɟɧɧɨ ɥɟɝɤɨɜɨɦ) ɢ ɜ ɤɚɱɟɫɬɜɟ ɩɪɢɜɨɞɚ ɧɚ ɝɟɧɟɪɚɬɨɪɚɯ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ.
Ɋɚɫɫɦɨɬɪɢɦ ɪɚɛɨɱɢɣ ɩɪɨɰɟɫɫ
ɩɨɪɲɧɟɜɨɝɨ Ⱦȼɋ (ɪɢɫ. 2.17).
ɉɪɢ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ ɢɡ ɤɪɚɣɧɟɝɨ ɜɟɪɯɧɟɝɨ ɩɨɥɨɠɟɧɢɹ (ɜɟɪɯɧɹɹ
ɦɟɪɬɜɚɹ ɬɨɱɤɚ – ȼɆɌ) ɜ ɤɪɚɣɧɟɟ ɧɢɠɧɟɟ (ɧɢɠɧɹɹ ɦɟɪɬɜɚɹ ɬɨɱɤɚ – ɇɆɌ)
ɢ ɨɬɤɪɵɬɨɦ ɜɫɚɫɵɜɚɸɳɟɦ 8 ɢ ɡɚɤɪɵɬɨɦ 7 ɜɵɯɥɨɩɧɨɦ ɤɥɚɩɚɧɟ ɩɪɨɢɫɯɨɞɢɬ
ɧɚɩɨɥɧɟɧɢɟ ɰɢɥɢɧɞɪɚ ɩɨɪɰɢɟɣ ɝɨɪɹɱɟɣ ɫɦɟɫɢ (ɪɢɫ. 2.17, ɚ).
ɉɪɢ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ ɜɜɟɪɯ ɩɪɨɢɫɯɨɞɢɬ ɫɠɚɬɢɟ ɝɨɪɸɱɟɣ ɫɦɟɫɢ
(ɪɢɫ. 2.17, ɛ). Ʉɥɚɩɚɧɵ 7
ɢ 8 ɡɚɤɪɵɬɵ.
ȼɆɌ
1
ɇɆɌ
6
7
8
2
3
4
5
ɚ ɛ ɜ ɝ
Ɋɢɫ. 2.17. Ɋɚɛɨɱɢɟ ɩɪɨɰɟɫɫɵ ɩɨɪɲɧɟɜɨɝɨ ɞɜɢɝɚɬɟɥɹ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ:
1 – ɰɢɥɢɧɞɪ; 2 – ɩɨɪɲɟɧɶ; 3 – ɲɚɬɭɧ; 4 – ɤɪɢɜɨɲɢɩ; 5 – ɜɫɚɫɵɜɚɸɳɢɣ ɩɚɬɪɭɛɨɤ;
6 – ɧɚɝɧɟɬɚɬɟɥɶɧɵɣ ɩɚɬɪɭɛɨɤ; 7 – ɧɚɝɧɟɬɚɬɟɥɶɧɵɣ ɤɥɚɩɚɧ; 8 – ɜɫɚɫɵɜɚɸɳɢɣ ɤɥɚɩɚɧ
ȼ ȼɆɌ ɝɨɪɸɱɚɹ ɫɦɟɫɶ ɫɝɨɪɚɟɬ ɜ ɰɢɥɢɧɞɪɟ ɞɜɢɝɚɬɟɥɹ ɫ ɩɨɜɵɲɟɧɢɟɦ
ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ. ɉɪɨɞɭɤɬɵ ɫɝɨɪɚɧɢɹ, ɜɨɡɞɟɣɫɬɜɭɹ ɧɚ ɩɨɪɲɟɧɶ,
ɩɟɪɟɦɟɳɚɸɬ ɟɝɨ ɢɡ ȼɆɌ ɜ ɇɆɌ (ɪɢɫ. 2.17, ɜ). Ʉɥɚɩɚɧɵ 7 ɢ 8 ɡɚɤɪɵɬɵ.
ɉɪɢ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ ɜɜɟɪɯ ɢ ɨɬɤɪɵɬɨɦ ɤɥɚɩɚɧɟ 7 ɩɪɨɢɫɯɨɞɢɬ ɜɵɬɚɥɤɢɜɚɧɢɟ ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ (ɪɢɫ. 2.17, ɝ).
ɇɚ ɪ-V-ɞɢɚɝɪɚɦɦɟ (ɪɢɫ. 2.18, ɚ): 5–1 – ɩɪɨɰɟɫɫ ɜɫɚɫɵɜɚɧɢɹ ɜ ɰɢɥɢɧɞɪ
ɝɨɪɸɱɟɣ ɫɦɟɫɢ; 1–2 – ɫɠɚɬɢɟ ɫɦɟɫɢ; 2–3 – ɩɪɨɰɟɫɫ ɝɨɪɟɧɢɹ ɫɦɟɫɢ, ɜɨɫɩɥɚɦɟɧɟɧɢɟ ɤɨɬɨɪɨɣ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɨɬ ɫɩɟɰɢɚɥɶɧɨɝɨ ɡɚɩɚɥɶɧɢɤɚ – ɫɜɟɱɢ;
3–4 ɩɪɨɰɟɫɫ ɪɚɫɲɢɪɟɧɢɹ ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ; 4–1–5 – ɩɪɨɰɟɫɫ ɜɵɯɥɨɩɚ
ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ ɜ ɚɬɦɨɫɮɟɪɭ.
52
ȼɫɚɫɵɜɚɧɢɟ 5–1 ɢ ɜɵɬɚɥɤɢɜɚɧɢɟ 1–5 ɧɟ ɹɜɥɹɸɬɫɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢ-
XXH
O
X
ɦɢ ɩɪɨɰɟɫɫɚɦɢ, ɬɚɤ ɤɚɤ ɩɚɪɚɦɟɬɪɵ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ ɩɪɢ ɷɬɨɦ ɧɟ ɦɟɧɹɸɬɫɹ.
ɉɥɨɳɚɞɶ ɩɨɞ ɥɢɧɢɟɣ 5–1 ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɪɚɛɨɬɭ ɜɫɚɫɵɜɚɧɢɹ L
ɚ ɩɥɨɳɚɞɶ ɩɨɞ ɥɢɧɢɟɣ 1–5 – ɪɚɛɨɬɭ ɜɵɬɚɥɤɢɜɚɧɢɹ L
ɜɫɚɫɵɜɚɧɢɹ ɢ ɜɵɬɚɥɤɢɜɚɧɢɹ ɧɚɩɪɚɜɥɟɧɵ ɜ ɪɚɡɧɵɟ ɫɬɨɪɨɧɵ, ɬɨ:
Lȼɋ + L
ȼɕɌ
= 0.
. Ɍɚɤ ɤɚɤ ɩɪɨɰɟɫɫɵ
ȼɕɌ
ȼɋ
Ɉɛɪɚɬɢɦɵɣ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɣ ɰɢɤɥ ɧɚ 1 ɤɝ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɧɚ ɪɬɢɹ (ɩɪɨɰɟɫɫ 1-2), ɩɨɞɜɨɞɚ ɤ ɝɚɡɭ ɬɟɩɥɨɬɵ ɩɪɢ
X
-ɞɢɚɝɪɚɦɦɟ (ɪɢɫ. 2.18, ɛ), ɫɨɫɬɨɢɬ ɢɡ ɚɞɢɚɛɚɬɧɨɝɨ ɫɠɚ-
X
= const (ɩɪɨɰɟɫɫ 2–3),
ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɪɚɫɲɢɪɟɧɢɹ (ɩɪɨɰɟɫɫ 3–4) ɢ ɨɬɞɚɱɢ ɝɚɡɨɦ ɬɟɩɥɨɬɵ
ɩɪɢ
X
= const (ɩɪɨɰɟɫɫ 4–1).
p
3
p
q
1
2
4
5
V
c
V
h
1
V
2
3
4
q
2
1
,
ɚ ɛ
X
Ɋɢɫ. 2.18. ɐɢɤɥ Ⱦȼɋ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ
= const ɜ ɞɢɚɝɪɚɦɦɚɯ
ɐɢɤɥ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ
X
= const ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɚɞɚɧɢɟɦ
ɧɚɱɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɬɨɱɤɟ 1 ɢ ɩɚɪɚɦɟɬɪɨɜ ɰɢɤɥɚ:
ɫɠɚɬɢɹ
,/
21
./23pp
ɫɬɟɩɟɧɢ ɩɨɜɵɲɟɧɢɹ ɞɚɜɥɟɧɢɹ
ɉɚɪɚɦɟɬɪɵ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ ɜ ɭɡɥɨɜɵɯ ɬɨɱɤɚɯ ɰɢɤɥɚ ɨɩɪɟɞɟɥɹɸɬɫɹ
ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɨɬɞɟɥɶɧɵɯ ɩɪɨɰɟɫɫɨɜ, ɧɚɯɨɞɹɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ, ɤɨɬɨɪɵɟ
ɛɵɥɢ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɩ. 1.2:
53
ɬɨɱɤɚ 2
X
O
ɬɨɱɤɚ 3
ɬɨɱɤɚ 4
p
2
p
1
Ɍ
2
Ɍ
1
p
3
p
2
Ɍ
3
Ɍ
2
§
·
X
p
p
3
4
¨
¸
¨
¸
X
4
3
©
¹
§
X
Ɍ
4
¨
¨
Ɍ
X
3
©
k
§
·
X
1
¨
¨
X
2
©
·
§
X
1
¸
¨
¸
¨
X
2
¹
©
,
O
p
3
,
p
2
§
X
¨
¨
©
1
k
·
3
¸
¸
4
¹
k
¸
¸
¹
k
;
H
1
1
k
;
H
kk
·
1
2
¸
¸
1
¹
H
,
k
HX
1
1
k
,
T
4
k
;
ppH
12
1
kɌɌ
ɪpp
123
ɌɌɌ
123
p
4
H
;
H
12
k
;
OHO
1
k
;
OHO
p
3
k
H
T
3
k
1
;
O
p
1
.
O
T
1
Ɍɟɪɦɢɱɟɫɤɢɣ ɄɉȾ ɷɬɨɝɨ ɰɢɤɥɚ ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧ ɫ ɩɨɦɨɳɶɸ
ɭɪɚɜɧɟɧɢɹ:
l
q
ɐ
2
.1
K
t
q
q
11
Ʉɨɥɢɱɟɫɬɜɨ ɩɨɞɜɨɞɢɦɨɣ ɢ ɨɬɜɨɞɢɦɨɣ ɬɟɩɥɨɬɵ ɧɚ 1 ɤɝ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ, ɭɱɚɫɬɜɭɸɳɟɝɨ ɜ ɰɢɤɥɟ, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ, ɢɫɩɨɥɶɡɭɹ ɩɟɪɜɵɣ ɡɚɤɨɧ
ɬɟɪɦɨɞɢɧɚɦɢɤɢ:
.dd
pTcdq
X
Ⱦɥɹ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɩɪɢ X = const (dX = 0):
X
ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɰɢɤɥɚ, ɢɞɭɳɟɝɨ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ, ɩɪɢ X = const:
54
,12TTcq
1
k
TcTTcq
1231
XX
TcTTcq
1142
XX
,1
OH
.1
ɉɨɞɜɨɞɢɦɚɹ ɬɟɩɥɨɬɚ q1 ɧɚ T-s-ɞɢɚɝɪɚɦɦɟ (ɪɢɫ. 2.19) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨ-
O
H
X
X
ɛɨɣ ɩɥɨɳɚɞɶ 2–3–3'–1', ɚ ɨɬɜɨɞɢɦɚɹ ɬɟɩɥɨɬɚ q
Ɍɟɪɦɢɱɟɫɤɢɣ ɄɉȾ ɰɢɤɥɚ ɪɚɜɟɧ:
Tc
1
X
1
K
t
ɢɥɢ
X
K
t
k
Tc
1
X
11
X
– ɩɥɨɳɚɞɶ 1–4–3'–1'.
2
1
,
1
1
k
OH
1
.
(2.4)
T
3
= const
2
4
= const
1
1' 3'
s
Ɋɢɫ. 2.19. ɐɢɤɥ Ⱦȼɋ ɫ ɩɨɞɜɨɞɨɦ
X
ɬɟɩɥɨɬɵ ɩɪɢ
= const ɜ Ɍs-ɞɢɚɝɪɚɦɦɟ
Ɋɚɛɨɬɚ ɰɢɤɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨɦ ɩɨɞɜɨɞɢɦɨɣ ɬɟɩɥɨɬɵ ɢ ɡɧɚɱɟɧɢɟɦ ɬɟɪɦɢɱɟɫɤɨɝɨ ɄɉȾ:
1
k
Tcql
XX
11
tɐ
§
1
11
OHK
¨
©
·
.
¸
1
k
H
¹
Ⱥɧɚɥɢɡ ɭɪɚɜɧɟɧɢɹ (2.4) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɬɟɪɦɢɱɟɫɤɢɣ ɄɉȾ ɰɢɤɥɚ
ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ
ɇɚ ɪɢɫ. 2.20 ɩɪɟɞɫɬɚɜɥɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ
X
= const ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ H.
K
= f (H) ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɪɚɛɨ-
t
X
ɱɢɯ ɜɟɳɟɫɬɜ (ɪɚɡɥɢɱɧɵɯ k). ɋ ɭɜɟɥɢɱɟɧɢɟɦ ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ ɜɵɲɟ 1012
ɬɟɦɩ ɜɨɡɪɚɫɬɚɧɢɹ
K
ɭɦɟɧɶɲɚɟɬɫɹ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɬɟɩɟɧɶ ɫɠɚɬɢɹ ɛɨɥɟɟ
t
X
ɱɟɦ 1012 ɩɪɢɦɟɧɹɬɶ ɧɟɰɟɥɟɫɨɨɛɪɚɡɧɨ, ɬɚɤ ɤɚɤ ɡɧɚɱɢɬɟɥɶɧɨ ɜɨɡɪɚɫɬɚɟɬ
ɦɚɤɫɢɦɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ ɜ ɰɢɤɥɟ.
55
H
K
t
X
0,6
0,5
0,4
0,3
0,2
0,1
0
1 2 3 4 5 6 7 8 9
Ɋɢɫ. 2.20. Ɂɚɜɢɫɢɦɨɫɬɶ ɬɟɪɦɢɱɟɫɤɨɝɨ
ɄɉȾ ɰɢɤɥɚ ɨɬ ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ
k =1,4
k =1,3
k =1,2
ȼ ɞɜɢɝɚɬɟɥɹɯ, ɪɚɛɨɬɚɸɳɢɯ ɩɨ ɰɢɤɥɭ X = const, ɜ ɰɢɥɢɧɞɪ ɞɜɢɝɚɬɟɥɹ
ɩɨɫɬɭɩɚɟɬ ɫɜɟɠɚɹ ɪɚɛɨɱɚɹ ɫɦɟɫɶ – ɫɦɟɫɶ ɜɨɡɞɭɯɚ ɫ ɬɨɩɥɢɜɨɦ. Ɍɨɩɥɢɜɨɜɨɡɞɭɲɧɚɹ ɫɦɟɫɶ ɫɠɢɦɚɟɬɫɹ ɢ ɨɤɨɥɨ ȼɆɌ ɡɚɠɢɝɚɟɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɢɫɤɪɨɣ. ɉɪɢ ɛɨɥɶɲɢɯ ɫɬɟɩɟɧɹɯ ɫɠɚɬɢɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɡɧɚɱɢɬɟɥɶɧɨɝɨ ɩɨɜɵɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɜ ɤɨɧɰɟ ɩɪɨɰɟɫɫɚ ɫɠɚɬɢɹ ɦɨɠɟɬ ɧɚɫɬɭɩɢɬɶ ɫɚɦɨɜɨɫɩɥɚɦɟɧɟɧɢɟ ɫɦɟɫɢ. Ʉɪɨɦɟ ɬɨɝɨ, ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ,
ɢ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ ɤɨɧɰɚ ɫɠɚɬɢɹ ɩɨɹɜɥɹɟɬɫɹ ɞɟɬɨɧɚɰɢɹ
ɫɜɟɠɟɣ ɪɚɛɨɱɟɣ ɫɦɟɫɢ, ɤɨɬɨɪɚɹ ɩɪɢɜɨɞɢɬ ɤ ɜɡɪɵɜɧɨɦɭ ɯɚɪɚɤɬɟɪɭ ɫɝɨɪɚɧɢɹ.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɞɟɬɨɧɚɰɢɢ ɩɪɨɰɟɫɫ ɫɝɨɪɚɧɢɹ ɧɚɪɭɲɚɟɬɫɹ, ɦɨɳɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɚɞɚɟɬ, ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ ɪɚɫɬɟɬ. ɉɨɹɜɥɟɧɢɟ ɞɟɬɨɧɚɰɢɢ ɹɜɥɹɟɬɫɹ ɩɪɢɱɢɧɨɣ ɬɨɝɨ, ɱɬɨ ɩɪɚɤɬɢɱɟɫɤɢ ɜ ɞɜɢɝɚɬɟɥɹɯ, ɪɚɛɨɬɚɸɳɢɯ ɩɨ ɰɢɤɥɭ
X
= const,
ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ ɢɦɟɸɬ ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɟɧɧɵɟ ɩɪɟɞɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ.
əɜɥɟɧɢɟ ɞɟɬɨɧɚɰɢɢ ɜ ɡɧɚɱɢɬɟɥɶɧɨɣ ɫɬɟɩɟɧɢ ɡɚɜɢɫɢɬ ɨɬ ɦɚɪɤɢ ɩɪɢɦɟɧɹɟɦɨɝɨ ɬɨɩɥɢɜɚ, ɨɬ ɟɝɨ ɚɧɬɢɞɟɬɨɧɚɰɢɨɧɧɵɯ ɤɚɱɟɫɬɜ. ɉɨɷɬɨɦɭ ɦɚɪɤɚ ɩɪɢɦɟɧɹɟɦɨɝɨ ɬɨɩɥɢɜɚ ɨɩɪɟɞɟɥɹɟɬ ɜɵɛɨɪ ɩɪɟɞɟɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ.
2.6.2. ɐɢɤɥ ɞɜɢɝɚɬɟɥɹ ɫ ɢɡɨɛɚɪɧɵɦ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ
Ⱦɜɢɝɚɬɟɥɢ, ɪɚɛɨɬɚɸɳɢɟ ɩɨ ɰɢɤɥɭ X = const, ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɛɨɬɚɸɬ
ɩɪɢ ɦɚɥɵɯ ɡɧɚɱɟɧɢɹɯ ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ
ɤɢɟ ɡɧɚɱɟɧɢɹ ɬɟɪɦɢɱɟɫɤɨɝɨ ɄɉȾ
H
, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢɦɟɸɬ ɧɟɜɵɫɨ-
K
. ɍɜɟɥɢɱɟɧɢɟ
t
K
ɜ ɞɜɢɝɚɬɟɥɹɯ ɦɨɠɧɨ
t
ɞɨɫɬɢɱɶ, ɟɫɥɢ ɫɨɡɞɚɬɶ ɬɚɤɨɣ ɩɪɨɰɟɫɫ, ɩɪɢ ɤɨɬɨɪɨɦ ɛɵ ɩɪɨɢɡɜɨɞɢɥɨɫɶ ɪɚɡɞɟɥɶɧɨɟ ɫɠɚɬɢɟ ɜɨɡɞɭɯɚ ɢ ɬɨɩɥɢɜɚ. ɗɬɨ ɩɨɡɜɨɥɢɥɨ ɛɵ ɞɜɢɝɚɬɟɥɸ ɪɚɛɨɬɚɬɶ
H
ɫ ɜɵɫɨɤɢɦɢ ɫɬɟɩɟɧɹɦɢ ɫɠɚɬɢɹ
= 1418.
Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɧɰɢɩɢɚɥɶɧɭɸ ɫɯɟɦɭ ɢ ɰɢɤɥ ɞɜɢɝɚɬɟɥɹ ɜɧɭɬɪɟɧɧɟɝɨ
ɫɝɨɪɚɧɢɹ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ ɪ = const (ɪɢɫ. 2.21).
ȼ ɞɜɢɝɚɬɟɥɟ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ (ɪɢɫ. 2.21, ɚ) ɢɫɩɨɥɶɡɭɟɬɫɹ ɫɥɚɛɨɥɟɬɭɱɟɟ ɦɨɬɨɪɧɨɟ ɬɨɩɥɢɜɨ (ɤɟɪɨɫɢɧ, ɫɨɥɹɪɨɜɨɟ ɦɚɫɥɨ, ɞɢɡɟɥɶɧɨɟ ɬɨɩɥɢɜɨ).
56
ɐɢɥɢɧɞɪ 1 ɞɜɢɝɚɬɟɥɹ ɨɩɢɪɚɟɬɫɹ ɧɚ ɫɬɚɧɢɧɭ 3, ɫɤɪɟɩɥɟɧɧɭɸ ɫ ɮɭɧɞɚɦɟɧɬ-
ɪ
ɧɨɣ ɩɥɢɬɨɣ 4. ȼ ɤɪɵɲɤɟ 6 ɰɢɥɢɧɞɪɚ ɧɚɯɨɞɹɬɫɹ ɮɨɪɫɭɧɤɢ 5 ɞɥɹ ɩɨɞɚɱɢ
ɪɚɫɩɵɥɟɧɧɨɝɨ ɬɨɩɥɢɜɚ. ɐɢɥɢɧɞɪ ɢ ɤɪɵɲɤɚ ɨɯɥɚɠɞɚɸɬɫɹ ɜɨɞɨɣ.
ɒɚɬɭɧɧɨ-ɤɪɢɜɨɲɢɩɧɵɣ ɦɟɯɚɧɢɡɦ ɩɪɟɨɛɪɚɡɭɟɬ ɜɨɡɜɪɚɬɧɨ-ɩɨɫɬɭɩɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɩɨɪɲɧɹ 8 ɜɨ ɜɪɚɳɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɜɚɥɚ 9. ȼ ɰɢɥɢɧɞɪɟ ɢɦɟɸɬɫɹ ɩɪɨɞɭɜɨɱɧɵɟ 7 ɢ
ɜɵɩɭɫɤɧɵɟ 2 ɨɤɧɚ, ɨɬɤɪɵɜɚɸɳɢɟɫɹ ɩɪɢ
ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ.
1
2
3
4
5
6
7
p
2 3
ȼɨɡɞɭɯ
ɜɵɫɨɤɨɝɨ
ɞɚɜɥɟɧɢɹ
4
8
5
9
1
V
ɚ ɛ
Ɋɢɫ. 2.21. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ (ɚ) ɢ ɰɢɤɥ Ⱦȼɋ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ
ɩɪɢ ɪ = const ɜ ɪV-ɞɢɚɝɪɚɦɦɟ (ɛ): 1 – ɰɢɥɢɧɞɪ; 2 – ɜɵɩɭɫɤɧɵɟ ɨɤɧɚ;
3 – ɫɬɚɧɢɧɚ; 4 – ɮɭɧɞɚɦɟɧɬɧɚɹ ɩɥɢɬɚ; 5 – ɮɨɪɫɭɧɤɚ; 6 – ɤɪɵɲɤɚ ɰɢɥɢɧɞɪɚ;
7 – ɩɪɨɞɭɜɨɱɧɵɟ ɨɤɧɚ; 8 – ɩɨ
ɲɟɧɶ; 9 – ɜɚɥ
ɉɨɪɲɟɧɶ 8 ɧɚɯɨɞɢɬɫɹ ɜ ɇɆɌ ɢ ɰɢɥɢɧɞɪ ɡɚɩɨɥɧɟɧ ɜɨɡɞɭɯɨɦ ɫ ɚɬɦɨɫɮɟɪɧɵɦ ɞɚɜɥɟɧɢɟɦ, ɬ. ɤ. ɩɨɥɨɫɬɶ ɰɢɥɢɧɞɪɚ ɫɨɨɛɳɚɟɬɫɹ ɱɟɪɟɡ ɜɵɩɭɫɤɧɵɟ
ɨɤɧɚ 2 ɫ ɚɬɦɨɫɮɟɪɨɣ (ɬɨɱɤɚ 5 ɧɚ p-
X
-ɞɢɚɝɪɚɦɦɟ (ɪɢɫ. 2.21, ɛ)).
ɉɪɢ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ ɜɜɟɪɯ, ɩɨɤɚ ɨɬɤɪɵɬɵ ɜɵɩɭɫɤɧɵɟ ɨɤɧɚ, ɞɚɜɥɟɧɢɟ ɛɭɞɟɬ ɨɫɬɚɜɚɬɶɫɹ ɩɨɫɬɨɹɧɧɵɦ, ɩɪɨɰɟɫɫ 5–1. Ⱦɚɥɟɟ ɛɭɞɟɬ ɩɪɨɢɫɯɨɞɢɬɶ
ɫɠɚɬɢɟ ɜɨɡɞɭɯɚ – ɩɪɨɰɟɫɫ 12. Ⱦɚɜɥɟɧɢɟ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡɪɚɫɬɚɸɬ.
ȼ ɤɨɧɰɟ ɫɠɚɬɢɹ (ɬɨɱɤɚ 2) ɬɟɦɩɟɪɚɬɭɪɚ ɫɬɚɧɨɜɢɬɫɹ ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɵ ɜɨɫɩɥɚɦɟɧɟɧɢɹ ɫɠɢɝɚɟɦɨɝɨ ɬɨɩɥɢɜɚ.
ɉɪɢ ɧɚɯɨɠɞɟɧɢɢ ɩɨɪɲɧɹ ɜ ȼɆɌ ɜ ɞɜɢɝɚɬɟɥɶ ɩɨɞɚɟɬɫɹ ɦɟɥɤɨ ɪɚɫɩɵɥɟɧɧɨɟ ɬɨɩɥɢɜɨ. Ɍɨɩɥɢɜɨ ɜɨɫɩɥɚɦɟɧɹɟɬɫɹ. ȼ ɞɚɥɶɧɟɣɲɟɦ ɩɨɞɜɨɞ ɬɨɩɥɢɜɚ
ɢ ɟɝɨ ɫɝɨɪɚɧɢɟ ɞɨɡɢɪɭɸɬɫɹ ɬɚɤ, ɱɬɨɛɵ ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ ɞɚɜɥɟɧɢɟ ɧɟ
ɢɡɦɟɧɹɥɨɫɶ, – ɩɪɨɰɟɫɫ 23.
57
ɉɨ ɨɤɨɧɱɚɧɢɢ ɝɨɪɟɧɢɹ ɬɨɩɥɢɜɚ (ɬɨɱɤɚ 3) ɧɚɱɢɧɚɟɬɫɹ ɪɚɫɲɢɪɟɧɢɟ ɩɪɨ-
t
XXH
XXU
X
ɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ – ɩɪɨɰɟɫɫ 34, ɩɨɤɚ ɩɨɪɲɟɧɶ ɧɟ ɨɬɤɪɨɟɬ ɜɵɩɭɫɤɧɵɟ ɨɤɧɚ.
Ɍɨɝɞɚ ɩɪɨɢɫɯɨɞɢɬ ɜɵɯɥɨɩ ɨɬɪɚɛɨɬɚɜɲɢɯ ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ, ɞɚɜɥɟɧɢɟ ɜ
ɰɢɥɢɧɞɪɟ ɩɚɞɚɟɬ ɞɨ ɚɬɦɨɫɮɟɪɧɨɝɨ, ɩɪɨɰɟɫɫ 41.
ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ ɜɧɢɡ ɩɪɨɢɫɯɨɞɢɬ «ɩɪɨɞɭɜɤɚ» ɰɢɥɢɧɞɪɚ ɱɟɪɟɡ ɩɪɨɞɭɜɨɱɧɵɟ ɨɤɧɚ 8 ɫɠɚɬɵɦ ɜɨɡɞɭɯɨɦ (ɩɪɨɰɟɫɫ 15).
ɉɪɢ ɭɩɪɨɳɟɧɢɢ
ɢɡɨɛɚɪɧɵɣ ɩɨɞɜɨɞ ɬɟɩɥɨɬɵ q
ɫɝɨɪɚɧɢɹ; 41 – ɢɡɨɯɨɪɧɵɣ ɨɬɜɨɞ ɬɟɩɥɨɬɵ q
ɉɪɢ ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ
ɩɪɨɰɟɫɫɵ: 12 – ɚɞɢɚɛɚɬɧɨɟ ɫɠɚɬɢɟ ɜɨɡɞɭɯɚ; 23 –
; 34 – ɚɞɢɚɛɚɬɧɨɟ ɪɚɫɲɢɪɟɧɢɢ ɩɪɨɞɭɤɬɨɜ
1
.
2
H
= 1418 ɫɠɚɬɵɣ ɜɨɡɞɭɯ, ɩɨɫɬɭɩɢɜɲɢɣ ɜɧɭɬɪɶ
ɰɢɥɢɧɞɪɚ, ɜ ɤɨɧɰɟ ɫɠɚɬɢɹ ɢɦɟɟɬ ɞɚɜɥɟɧɢɟ 34 Ɇɉɚ ɢ ɬɟɦɩɟɪɚɬɭɪɭ, ɪɚɜ-
ɧɭɸ 500800 °ɋ, ɤɨɬɨɪɚɹ ɨɛɟɫɩɟɱɢɜɚɟɬ ɧɚɞɟɠɧɨɟ ɫɚɦɨɜɨɫɩɥɚɦɟɧɟɧɢɟ ɢ
ɫɝɨɪɚɧɢɟ ɬɨɩɥɢɜɚ. ȼɜɨɞ ɬɨɩɥɢɜɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫɠɚɬɵɦ ɜɨɡɞɭɯɨɦ, ɩɨɞɚɜɚɟɦɵɦ ɨɬ ɤɨɦɩɪɟɫɫɨɪɚ ɩɨɞ ɞɚɜɥɟɧɢɟ 56 Ɇɉɚ.
Ⱦɜɢɝɚɬɟɥɢ, ɤɨɬɨɪɵɟ ɪɚɛɨɬɚɸɬ ɩɨ ɪɚɫɫɦɨɬɪɟɧɧɨɦɭ ɰɢɤɥɭ, ɩɪɟɞɥɨɠɟɧ-
ɧɨɦɭ Ⱦɢɡɟɥɟɦ, ɧɚɡɵɜɚɸɬɫɹ ɞɢɡɟɥɹɦɢ.
ɗɬɨɬ ɰɢɤɥ ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɚɞɢɚɛɚɬ
ɫɠɚɬɢɹ ɢ ɪɚɫɲɢɪɟɧɢɹ, ɢɡɨɛɚɪɵ ɩɨɞɜɨɞɚ ɬɟɩɥɨɬɵ ɢ ɢɡɨɯɨɪɵ ɨɬɜɨɞɚ ɬɟɩɥɨɬɵ (ɪɢɫ. 2.22).
q
p
2 3
1
4
q
2
1
Ɋɢɫ. 2.22. ɐɢɤɥ Ⱦȼɋ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ
ɩɪɢ ɪ = cons
ɜ ɪ-X -ɞɢɚɝɪɚɦɦɟ
ɉɪɢ ɡɚɞɚɧɧɨɦ ɧɚɱɚɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢ (ɬɨɱɤɚ 1) ɰɢɤɥ ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟ-
ɞɟɥɹɟɬɫɹ ɞɜɭɦɹ ɩɚɪɚɦɟɬɪɚɦɢ: ɫɬɟɩɟɧɶɸ ɫɠɚɬɢɹ:
/
ɢ ɫɬɟɩɟɧɶɸ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ:
21
./
23
ɉɚɪɚɦɟɬɪɵ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ ɜ ɭɡɥɨɜɵɯ ɬɨɱɤɚɯ ɰɢɤɥɚ, ɨɩɪɟɞɟɥɹɟɦɵɟ
ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɨɬɞɟɥɶɧɵɯ ɩɪɨɰɟɫɫɨɜ, ɧɚɯɨɞɹɬɫɹ ɢɡ ɨɛɳɢɯ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɨɨɬɧɨɲɟɧɢɣ:
58
ɬɨɱɤɚ 2
K
K
ɬɨɱɤɚ 3
ɬɨɱɤɚ 4
k
,
ppH
12
k
,
ppp
H
1
·
§
X
Ɍ
k
,
ppU
14
Ɍ
3
4
3
¸
¨
¨
©
¸
X
4
¹
123
1
§
·
§
X
3
¨
¨
X
1
©
¨
¸
¨
¸
©
¹
1
kɌɌ
X
;
H
12
1
;
kɌɌ
UH
13
1
kkk
·
2
¸
¸
XXX
231
¹
1
k
U
,
1
k
H
k
.
ɌɌU
14
Ɍɟɩɥɨɬɚ q1, ɩɨɞɜɟɞɟɧɧɚɹ ɤ ɝɚɡɭ ɜ ɩɪɨɰɟɫɫɟ 2–3, ɢ ɬɟɩɥɨɬɚ q2, ɨɬɜɟɞɟɧɧɚɹ ɨɬ ɝɚɡɚ ɜ ɩɪɨɰɟɫɫɟ 4–1, ɪɚɜɧɵ:
1
k
TcTTcq
1231
pp
TcTTcq
1142
XX
,1
UH
1
k
.
U
ɉɨɞɫɬɚɜɥɹɹ ɡɧɚɱɟɧɢɹ q1 ɢ q2 ɜ ɮɨɪɦɭɥɭ ɞɥɹ ɬɟɪɦɢɱɟɫɤɨɝɨ ɄɉȾ ɰɢɤɥɚ,
ɩɨɥɭɱɚɟɦ:
ɢɥɢ
Ɋɚɛɨɬɚ ɰɢɤɥɚ:
q
2
K
tp
K
tp
ptpɐ
11
q
1
1
k
1
k
UHK
Tcql
11
U
k
k
1
U
Tc
1
X
1
k
UH
Tc
1
p
k
1
1
UH
ª
11
«
¬
1
.
(2.5)
1
k
U
1
k
k
,
º
1
.
»
1
UH
¼
Ⱥɧɚɥɢɡ ɮɨɪɦɭɥɵ (2.5) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ
ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɢ ɬɟɪɦɢɱɟɫɤɢɣ ɄɉȾ ɰɢɤɥɚ.
ɋɨɩɨɫɬɚɜɥɹɹ ɡɧɚɱɟɧɢɹ ɬɟɪɦɢɱɟɫɤɢɯ ɄɉȾ ɰɢɤɥɨɜ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ
ɩɪɢ
X
= const ɢ ɪ = const, ɦɨɠɧɨ ɭɜɢɞɟɬɶ, ɱɬɨ ɩɪɢ ɨɞɢɧɚɤɨɜɵɯ ɫɬɟɩɟɧɹɯ
>
ɫɠɚɬɢɹ
ɋɪɚɜɧɢɜɚɹ ɰɢɤɥɵ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ ɪ = const ɢ
.
tp
X
t
X
= const ɩɪɢ
ɨɞɢɧɚɤɨɜɵɯ ɦɚɤɫɢɦɚɥɶɧɵɯ ɞɚɜɥɟɧɢɹɯ ɢ ɬɟɦɩɟɪɚɬɭɪɚɯ ɢ ɪɚɡɥɢɱɧɵɯ ɫɬɟɩɟɧɹɯ ɫɠɚɬɢɹ
H
(ɪɢɫ. 2.23) ɢ ɧɟɢɡɦɟɧɧɨɦ ɤɨɥɢɱɟɫɬɜɟ ɨɬɜɨɞɢɦɨɣ ɬɟɩɥɨɬɵ
59
ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɜ Ɍs-ɞɢɚɝɪɚɦɦɟ ɩɥɨɳɚɞɶ ɩɨɞ ɥɢɧɢɟɣ ɩɪɨɰɟɫɫɚ ɯɚɪɚɤ-
K
K
X
X
ɬɟɪɢɡɭɟɬ ɬɟɩɥɨɬɭ ɩɪɨɰɟɫɫɚ, ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ:
q
2
K
tp
11
q
1
q
2
K
t
X
11
q
1
Ⱥɩɥ.
ɋɩɥ.ȼɩɥ.Ⱥɩɥ.
Ⱥɩɥ.
ȼɩɥ.Ⱥɩɥ.
ȼɩɥ.
ɋɩɥ.ȼɩɥ.
.
ȼɩɥ.Ⱥɩɥ.
,
ɋɩɥ.ȼɩɥ.Ⱥɩɥ.
T
Ɋɢɫ. 2.23. ɐɢɤɥ Ⱦȼɋ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ
ɩɪɢ ɪ = const ɜ Ɍs -ɞɢɚɝɪɚɦɦɟ
2'
2
1
p = const
ɋ
ȼ
Ⱥ
= const
= const
3
4
s
Ɍɚɤ ɤɚɤ ɜɵɪɚɠɟɧɢɟ ɬɟɪɦɢɱɟɫɤɨɝɨ ɄɉȾ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɚɜɢɥɶ-
ɧɭɸ ɞɪɨɛɶ, ɬɨ ɩɪɢɛɚɜɥɟɧɢɟ ɤ ɱɢɫɥɢɬɟɥɸ ɢ ɡɧɚɦɟɧɚɬɟɥɸ ɨɞɢɧɚɤɨɜɨɣ ɜɟɥɢɱɢɧɵ (ɩɥɨɳɚɞɶ ɋ) ɞɚɟɬ ɭɜɟɥɢɱɟɧɢɟ ɄɉȾ ɢ
>
tp
.
X
t
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɛɨɱɢɣ ɩɪɨɰɟɫɫ ɜ ɞɜɢɝɚɬɟɥɹɯ ɫ ɫɚɦɨɜɨɫɩɥɚɦɟɧɟɧɢɟɦ
ɨɬ ɫɠɚɬɢɹ ɩɪɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɹɯ ɫɬɟɩɟɧɢ ɫɠɚɬɢɹ ɜɵɝɨɞɧɟɟ, ɱɟɦ ɪɚɛɨɱɢɣ
ɩɪɨɰɟɫɫ ɜ ɞɜɢɝɚɬɟɥɹɯ ɫ ɢɫɤɪɨɜɵɦ ɡɚɠɢɝɚɧɢɟɦ.
ɋɬɟɩɟɧɶ ɫɠɚɬɢɹ H ɞɨɥɠɧɚ ɨɛɟɫɩɟɱɢɬɶ ɫɚɦɨɜɨɫɩɥɚɦɟɧɟɧɢɟ ɬɨɩɥɢɜɚ ɢ
ɫɨɡɞɚɬɶ ɧɟɨɛɯɨɞɢɦɵɟ ɬɟɦɩɟɪɚɬɭɪɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɛɵɫɬɪɨɝɨ ɩɪɨɬɟɤɚɧɢɹ
ɩɪɨɰɟɫɫɚ ɝɨɪɟɧɢɹ. ɗɬɢɦ ɭɫɥɨɜɢɹɦ ɜ ɤɨɦɩɪɟɫɫɨɪɧɵɯ ɞɢɡɟɥɹɯ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɡɧɚɱɟɧɢɹ ɫɬɟɩɟɧɟɣ ɫɠɚɬɢɹ ɨɬ 14 ɞɨ 18.
2.6.3. ɐɢɤɥ ɞɜɢɝɚɬɟɥɹ ɫɨ ɫɦɟɲɚɧɧɵɦ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ
ɉɨɥɨɠɢɬɟɥɶɧɵɟ ɫɜɨɣɫɬɜɚ ɰɢɤɥɨɜ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɨɬɵ ɩɪɢ ɪ = const
ɢ
X
= const ɩɪɢɜɟɥɢ ɤ ɩɨɹɜɥɟɧɢɸ ɛɟɫɤɨɦɩɪɟɫɫɨɪɧɵɯ ɞɜɢɝɚɬɟɥɟɣ, ɜ ɤɨɬɨɪɵɯ ɪɚɫɩɵɥɟɧɢɟ ɬɨɩɥɢɜɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɦɟɯɚɧɢɱɟɫɤɢɦ ɩɭɬɟɦ. Ɍɨɩɥɢɜɨ
ɫɠɢɦɚɟɬɫɹ ɜ ɧɚɫɨɫɟ ɢɥɢ ɧɚɫɨɫɟ-ɮɨɪɫɭɧɤɟ ɞɨ ɞɚɜɥɟɧɢɹ 150 Ɇɉɚ.
ȼɩɪɵɫɤɢɜɚɟɦɨɟ ɬɨɩɥɢɜɨ ɩɨɫɬɭɩɚɟɬ ɜ ɤɚɦɟɪɭ ɫɝɨɪɚɧɢɹ ɢɥɢ ɫɩɟɰɢɚɥɶ-
ɧɵɟ ɩɪɟɞɤɚɦɟɪɵ. ɉɪɨɰɟɫɫ ɫɝɨɪɚɧɢɹ ɢɞɟɬ ɜɧɚɱɚɥɟ ɫ ɩɨɜɵɲɟɧɢɟɦ ɞɚɜɥɟɧɢɹ,
60
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