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ɂɡ ɞɢɚɝɪɚɦɦɵ ɫɥɟɞɭɟɬ, ɱɬɨ ɩɪɢ P = const 'ɞ =
ɪ
ɪ
R
Ɋɚɫɱɟɬɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ '
ɞɥɹ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɵɯ ɪɚɫɬɜɨɪɨɜ ɧɟɞɢɫɫɨɰɢɢɪɭɸɳɢɯɫɹ ɜɟɳɟɫɬɜ:
ɞɥɹ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɵɯ ɪɚɫɬɜɨɪɨɜ ɞɢɫɫɨɰɢɢɪɭɸɳɢɯɫɹ ɜɟɳɟɫɬɜ:
'
ɞ:
2
ɤɢɩ
T
' , (185)
ɞ
R
ɞ
ɪɥɹ ɤ
ɪɥɹ
r
ɩ
2
ɤɢɩ
c
T
ɪɥɹ ɤ
ɪɥɹ
r
ɩ
ɤɢɩ
T
c
c
ɤ
, (186)
bc
1
ɤ
ɤɢɩ
–
T
ɪɚ
.
ɥɹ
ɝɞɟ R = 8,31, Ⱦɠ/(ɦɨɥɶÂɄ);
– ɤɨɧɰɟɧɬɪɚɰɢɹ ɪɚɫɬɜɨɪɟɧɧɨɝɨ ɜɟɳɟɫɬɜɚ ɜ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɨɦ ɪɚɫɬɜɨɪɟ,
c
ɤ
ɦɨɥɶ/ɦɨɥɶ;
ɪɥɹ
r– ɬɟɩɥɨɬɚ ɢɫɩɚɪɟɧɢɹ ɪɚɫɬɜɨɪɢɬɟɥɹ, Ⱦɠ/ɦɨɥɶ;
ɩ
ɤɢɩ
T
– ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ ɪɚɫɬɜɨɪɢɬɟɥɹ, Ʉ;
ɪɥɹ
b – ɤɨɧɫɬɚɧɬɚ, ɨɩɪɟɞɟɥɹɟɦɚɹ ɨɩɵɬɧɵɦ ɩɭɬɟɦ.
Ɉɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ.
ɋɯɟɦɚ ɜɵɩɚɪɧɨɣ ɭɫɬɚɧɨɜɤɢ ɟɫɬɟɫɬɜɟɧɧɨɣ ɰɢɪɤɭɥɹɰɢɢɫ ɜɵɧɟɫɟɧɧɨɣ ɝɪɟɸɳɟɣ ɤɚɦɟɪɨɣ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 50.
Ɋɢɫ. 50. ɋɯɟɦɚ ɜɵɩɚɪɧɨɣ ɭɫɬɚɧɨɜɤɢ ɟɫɬɟɫɬɜɟɧɧɨɣ ɰɢɪɤɭɥɹɰɢɢ
ɫ ɜɵɧɟɫɟɧɧɨɣ ɝɪɟɸɳɟɣ ɤɚɦɟɪɨɣ:
1 – ɝɪɟɸɳɚɹ ɤɚɦɟɪɚ, 2 – ɜɵɩɚɪɧɨɣ ɚɩɩɚɪɚɬ, 3 – ɛɪɵɡɝɨɭɥɚɜɥɢɜɚɬɟɥɶ,
4 – ɰɢɪɤɭɥɹɰɢɨɧɧɚɹ ɬɪɭɛɚ
61
Ɋɚɛɨɬɚ ɭɫɬɚɧɨɜɤɢ
ɂɫɯɨɞɧɵɣ ɪɚɫɬɜɨɪ ɩɨɞɚɟɬɫɹ ɩɨ ɬɪɭɛɚɦ ɤɢɩɹɬɢɥɶɧɢɤɚ 1, ɝɞɟ ɧɚɝɪɟɜɚɟɬɫɹ ɞɨ
ɬɟɦɩɟɪɚɬɭɪɵ ɤɢɩɟɧɢɹ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɩɚɪɨɠɢɞɤɨɫɬɧɨɣ ɫɦɟɫɢ, ɤɨɬɨɪɚɹ ɞɚɥɟɟ
ɩɨɫɬɭɩɚɟɬ ɜ ɜɵɩɚɪɧɨɣ ɚɩɩɚɪɚɬ (ɫɟɩɚɪɚɬɨɪ) 2.
ȼ ɫɟɩɚɪɚɬɨɪɟ 2 ɩɚɪɨɠɢɞɤɨɫɬɧɚɹ ɫɦɟɫɶ ɪɚɡɞɟɥɹɟɬɫɹ ɧɚ ɩɚɪ ɪɚɫɬɜɨɪɢɬɟɥɹ ɢ
ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɵɣ ɪɚɫɬɜɨɪ.
ɉɚɪɵ ɪɚɫɬɜɨɪɢɬɟɥɹ ɩɪɨɯɨɞɹɬ ɱɟɪɟɡ ɛɪɵɡɝɨɭɥɚɜɥɢɜɚɬɟɥɶ 3 ɢ ɜɵɜɨɞɹɬɫɹ ɢɡ
ɩɪɨɰɟɫɫɚ ɢɡ ɜɟɪɯɚ ɫɟɩɚɪɚɬɨɪɚ
ɜ ɜɢɞɟ ɩɚɪɨɜɨɝɨ ɩɨɬɨɤɚ Gɩ.
ȼɵɞɟɥɟɧɧɚɹ ɛɪɵɡɝɨɭɥɚɜɥɢɜɚɬɟɥɟɦ ɠɢɞɤɚɹ ɮɚɡɚ ɢɡ ɩɚɪɨɜ ɪɚɫɬɜɨɪɢɬɟɥɹ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɤɢɩɹɬɢɥɶɧɢɤ 1 ɩɨ ɰɢɪɤɭɥɹɰɢɨɧɧɨɣ ɬɪɭɛɟ 4.
ɋɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɵɣ ɪɚɫɬɜɨɪ ɜ ɜɢɞɟ ɩɨɬɨɤɚ G
ɜɵɜɨɞɢɬɫɹ ɢɡ ɧɢɡɚ ɫɟɩɚɪɚ-
ɤ
ɬɨɪɚ.
ɉɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ – ɤɨɧɰɟɧɬɪɚɰɢɹ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɨɝɨ
ɪɚɫɬɜɨɪɚ ɫ
.
ɤ
ɐɟɥɶ ɭɩɪɚɜɥɟɧɢɹ – ɨɛɟɫɩɟɱɟɧɢɟ ɫ
= ɫ
ɤ
(ɧɚ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɨɦ ɞɥɹ
ɤɡɞ
ɞɚɧɧɨɣ ɭɫɬɚɧɨɜɤɢ ɡɧɚɱɟɧɢɢ).
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɪɚɫɬɜɨɪɟɧɧɨɦɭ ɜɟɳɟɫɬɜɭ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dc
U
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ
Sh GcGc
ɤɚɩɩɤ ɪɧ ɤɤ
dc
ɤ
0
:
dt
ɂɡ ɜɵɪɚɠɟɧɢɣ (187) ɢ (188) ɫɥɟɞɭɟɬ:
ɤ
. (187)
dt
Gc Gc . (188)
ɪɧ ɤɤ
(,)cfGG . (189)
ɤɪɤ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ: Gɪ.
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɜɵɩɚɪɧɨɣ ɭɫɬɚɧɨɜɤɢ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ:
0
d
T
UU T
()
Vc Vc Gc
ɩɩɪɩ ɤɤɪɤ ɬɪɬɬ
Gc G c Gc Wr Q
r
TTT
ɪ ɪɪ ɪ ɤɬ ɪɤɬ ɤɬ ɤ ɪɤ ɤ ɩ ɤɨɧɰ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
Gc Gc Wr Q
ɤɬ ɪɤɬ ɤɬ ɤ ɪɤ ɤ ɩ ɤɨɧɰ
T
d
ɚɩɩ
0
:
dt
Gc Gc
TT
ɬɪɬɬ ɪɪɪɪ
TT
ɚɩɩ
dt
B
62
. (190)
. (191)
ȼ ɜɵɪɚɠɟɧɢɹɯ (190) ɢ (191) ɩɪɢɧɹɬɨ:
TTT
f
f
WG G G – ɤɨɥɢɱɟɫɬɜɨ ɢɫɩɚɪɹɟɦɨɝɨ ɪɚɫɬɜɨɪɢɬɟɥɹ;
ɪɤɩ
(,), (,)cfccfc
TT
– ɭɞɟɥɶɧɵɟ ɬɟɩɥɨɟɦɤɨɫɬɢ ɢɫɯɨɞɧɨɝɨ ɢ ɤɨɧ-
ɪɪ ɪ ɧ ɪɤ ɤ ɤ
TT
;
ɤɩɚɩɩ
ɪɥɹ
,
ɩɧɩ
ɰɟɧɬɪɢɪɨɜɚɧɧɨɝɨ ɪɚɫɬɜɨɪɨɜ, ɤɨɬɨɪɵɟ ɧɟ ɩɨɞɱɢɧɹɸɬɫɹ ɡɚɤɨɧɭ ɚɞɞɢɬɢɜɧɨɫɬɢ;
GqQ '
,
ɤɤɨɧɰ
ɝɞɟ 'q – ɬɟɩɥɨɜɨɣ ɷɮɮɟɤɬ ɪɚɫɬɜɨɪɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɧɚ ɨɫɧɨɜɚɧɢɢ ɡɚɤɨɧɚ Ƚɟɫɫɚ:
() (),
ɢ qɤ – ɢɧɬɟɝɪɚɥɶɧɵɟ ɬɟɩɥɨɬɵ ɪɚɫɬɜɨɪɟɧɢɹ ɜ ɧɚɱɚɥɟ ɢ ɤɨɧɰɟ ɩɪɨɰɟɫɫɚ.
ɝɞɟ q
ɧ
qqc qc'
ɤɤ ɧɧ
Ⱦɠ
,
ɤɝ
ɇɚ ɨɫɧɨɜɚɧɢɢ (190) ɢ (191):
T
(,,)
GGG
. (192)
ɚɩɩ ɬ ɪ ɤ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɵɟ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ:
ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɩɪɨɰɟɫɫɚ – ɪɚɫɯɨɞ ɬɟɩɥɨɧɨɫɢɬɟɥɹ Gɬ;
ɞɥɹ ɤɨɫɜɟɧɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɩɨɤɚɡɚɬɟɥɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ
()
T
ɚɩɩ ɤ
c
– ɪɚɫɯɨɞ ɢɫɯɨɞɧɨɝɨ ɪɚɫɬɜɨɪɚ Gɪ.
ȼ ɬɢɩɨɜɨɦ ɪɟɲɟɧɢɢ ɚɜɬɨɦɚɬɢɡɚɰɢɢ:
ɞɥɹ ɤɨɫɜɟɧɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɩɨɤɚɡɚɬɟɥɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ
ɜɵɩɚɪɢɜɚɧɢɹ ɢɫɩɨɥɶɡɭɸɬ ɧɟ ɬɟɦɩɟɪɚɬɭɪɭ ɜ ɚɩɩɚɪɚɬɟ, ɚ ɬɟɦɩɟɪɚɬɭɪɧɭɸ ɞɟɩɪɟɫɫɢɸ:
ɤɢɩ
ɤɢɩ
TT
ɥɹɪ
ɪɚɪɞ
)(
cf '
.
ɤ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ (ɞɥɹ ɪɚɫɬɜɨɪɚ)
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
U
ɤɚɩɩ ɪ ɤ ɩ
ɤ
SGGG
. (193)
dt
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
ɇɚ ɨɫɧɨɜɚɧɢɢ (193) ɢ (194):
GGG . (194)
ɪɤɩ
(,, )hfGGG . (195)
ɤɪɤɩ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ – Gɤ.
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɩɚɪɨɜɨɣ ɮɚɡɟ (ɞɥɹ ɪɚɫɬɜɨɪɚ)
63
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
ɚɩɩ
VMdP
– ɦɨɥɶɧɚɹ ɦɚɫɫɚ ɩɚɪɨɜɨɣ ɮɚɡɵ (ɪɚɫɬɜɨɪɢɬɟɥɹ), ɤɝ/ɦɨɥɶ;
ɝɞɟ Ɇ
ɩ
– ɞɚɜɥɟɧɢɟ ɜ ɫɟɩɚɪɚɬɨɪɟ, ɉɚ;
Ɋ
ɩ
T
=
T
=
T
ɩ
– ɨɛɴɟɦ ɩɚɪɨɜɨɣ ɮɚɡɵ ɜ ɫɟɩɚɪɚɬɨɪɟ, ɦ3.
V
ɩ
– ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɫɟɩɚɪɚɬɨɪɟ, Ʉ;
ɤ
ɚɩɩ
ɩɩɩ
R
T
ɩ
, (196)
dt
GGG
ɪɤɩ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
ɇɚ ɨɫɧɨɜɚɧɢɢ (198) ɢ (199):
ɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ G
.
ɩ
GGG . (197)
ɪɤɩ
(,,)P fGGG ɢ ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜ-
ɩɪɤɩ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ (ɞɥɹ ɬɟɩɥɨɧɨɫɢɬɟɥɹ)
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
U
ɤɬ ɚɩɩ ɬ ɤɬ
ɤɬ
SGG
. (198)
dt
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
ɇɚ ɨɫɧɨɜɚɧɢɢ (198) ɢ (199):
GG . (199)
ɬɤɬ
(, )hfGG . (200)
ɤɬ ɬ ɤɬ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ – Gɤɬ.
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɩɚɪɨɜɨɣ ɮɚɡɟ (ɞɥɹ ɬɟɩɥɨɧɨɫɢɬɟɥɹ)
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
– ɦɨɥɶɧɚɹ ɦɚɫɫɚ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, ɤɝ/ɦɨɥɶ;
ɝɞɟ Ɇ
ɩ
ɦɬɪ
– ɞɚɜɥɟɧɢɟ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɜ ɦɟɠɬɪɭɛɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɤɢɩɹɬɢɥɶɧɢɤɚ, ɉɚ;
Ɋ
ɬ
T
– ɬɟɦɩɟɪɚɬɭɪɚ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, Ʉ;
ɬ
ɦɬɪ
– ɨɛɴɟɦ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɜ ɦɟɠɬɪɭɛɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɤɢɩɹ-
V
ɬ
ɬɢɥɶɧɢɤɚ, ɦ
3
.
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
ɇɚ ɨɫɧɨɜɚɧɢɢ (201) ɢ (202):
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ G
ɦɬɪ ɦɬɪ
VMdP
ɬɬɬ
R
T
ɬ
ɦɬɪ
ɬɬɤɬ
, (201)
dt
GG . (202)
ɬɤɬ
(, )PfGG . (203)
64
GG
ɬɤɬ
.
ɬ
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ. 51.
Ɋɢɫ. 51. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ:
ȼɨɡɦɨɠɧɵɟ ɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ȼɨɡɦɨɠɧɵɟ ɧɟɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ɬɟɩɥɨɟɦɤɨɫɬɢ ɩɨɬɨɤɨɜ ɫ
ɢ ɬɟɩɥɨɬɚ ɢɫɩɚɪɟɧɢɹ ɪɚɫɬɜɨɪɢɬɟɥɹ rɩ.
ɪi
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɟɦɵɟ ɩɟɪɟɦɟɧɧɵɟ:
,,,GGGG.
ɬɪɩɤ
,,ɫ
TT
ɧɬɪ
,, ,ɫ hP
T
ɤɤɚɩɩɩ
.
,,,,ɫɫɫɫr – ɭɞɟɥɶɧɵɟ
ɪɬ ɪɪ ɪɤ ɪɩ ɩ
.
ɇɚ ɨɫɧɨɜɚɧɢɢ ɪɢɫ. 51 ɜɵɩɚɪɧɚɹ ɭɫɬɚɧɨɜɤɚ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɵɦ ɦɧɨɝɨɫɜɹɡɧɵɦ ɨɛɴɟɤɬɨɦ ɩɨ ɜɨɡɦɨɠɧɵɦ ɭɩɪɚɜɥɹɸɳɢɦ ɜɨɡɞɟɣɫɬɜɢɹɦ
Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ. 52.
,,GGG.
ɪɤɩ
Ɋɢɫ. 52. Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ
65
Ɍɢɩɨɜɨɟ ɪɟɲɟɧɢɟ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ
Ɋɟɝɭɥɢɪɨɜɚɧɢɟ:
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɬɟɦɩɟɪɚɬɭɪɧɨɣ ɞɟɩɪɟɫɫɢɢ ǻ
ɬɜɨɪɚ G
ɫɬɢ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ ɫ
ɬɟɥɹ G
ɪɚɫɬɜɨɪɚ G
– ɤɚɤ ɩɚɪɚɦɟɬɪɚ, ɤɨɫɜɟɧɧɨ ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɝɨ ɩɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨ-
ɪ
;
ɤ
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɞɚɜɥɟɧɢɹ ɜ ɫɟɩɚɪɚɬɨɪɟ
– ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɩɚɪɨɜɨɣ ɮɚɡɟ;
ɩ
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɭɪɨɜɧɹ ɜ ɫɟɩɚɪɚɬɨɪɟ h
– ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ.
ɤ
ɋɬɚɛɢɥɢɡɚɰɢɹ ɪɚɫɯɨɞɚ ɬɟɩɥɨɧɨɫɢɬɟɥɹ G
– ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚ-
ɬ
ɩɨ ɩɨɞɚɱɟ ɢɫɯɨɞɧɨɝɨ ɪɚɫ-
ɞ
ɚɩɩ
Ɋ ɩɨ ɨɬɛɨɪɭ ɩɚɪɨɜ ɪɚɫɬɜɨɪɢ-
ɩ
ɩɨ ɨɬɛɨɪɭ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɨɝɨ
ɤ
ɥɚɧɫɚ ɭɫɬɚɧɨɜɤɢ.
Ʉɨɧɬɪɨɥɶ:
ɪɚɫɯɨɞɵ – G
ɬɟɦɩɟɪɚɬɭɪɵ –
ɞɚɜɥɟɧɢɟ –
ɭɪɨɜɟɧɶ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɨɝɨ ɪɚɫɬɜɨɪɚ ɜ ɚɩɩɚɪɚɬɟ – h
, Gɪ, Gɤ, Gɩ;
ɬ
,,, ,
TTTT T
ɬɪɤɚɩɩ
ɚɩɩ
Ɋ , Ɋɬ;
ɩ
' ;
.
ɤ
ɋɢɝɧɚɥɢɡɚɰɢɹ.
ɋɭɳɟɫɬɜɟɧɧɵɟ ɨɬɤɥɨɧɟɧɢɹ
ɞɤ
ɉɪɟɤɪɚɳɟɧɢɟ ɩɨɞɚɱɢ ɢɫɯɨɞɧɨɝɨ ɪɚɫɬɜɨɪɚ G
ɨɬ ɡɚɞɚɧɢɹ.
()fc'
, ɩɪɢ ɷɬɨɦ ɮɨɪɦɢɪɭɟɬɫɹ ɫɢɝɧɚɥ
ɪ
«ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ».
ɋɢɫɬɟɦɚ ɡɚɳɢɬɵ.
ɉɨ ɫɢɝɧɚɥɭ «ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ» – ɨɬɤɪɵɜɚɟɬɫɹ ɦɚɝɢɫɬɪɚɥɶ G
, ɨɬɤɥɸɱɚɟɬɫɹ
ɩ
ɩɨɞɚɱɚ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɢ ɨɬɛɨɪ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɨɝɨ ɪɚɫɬɜɨɪɚ.
1.3. ɍɩɪɚɜɥɟɧɢɟ ɦɚɫɫɨɨɛɦɟɧɧɵɦɢ ɩɪɨɰɟɫɫɚɦɢ
ȼɢɞ ɞɢɚɝɪɚɦɦɵ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɫɢɫɬɟɦɵ ɫ 3 ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ (ɪɢɫ. 53)
* = f (c2) ɩɪɢ ș = const ɢ P = const.
c
1
Ɋɢɫ. 53. ȼɢɞ ɞɢɚɝɪɚɦɦɵ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɫɢɫɬɟɦɵ ɫ 3 ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ:
– ɤɨɧɰɟɧɬɪɚɰɢɹ ɤɨɦɩɨɧɟɧɬɚ ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ, cy, c2 – ɤɨɧɰɟɧɬɪɚɰɢɹ ɤɨɦɩɨɧɟɧɬɚ ɜ ɠɢɞɤɨɣ
c
1
. ɉɪɢ cɯ = c2 ɪɚɜɧɨɜɟɫɧɨɟ ɡɧɚɱɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ ɛɭɞɟɬ cy* = c1*
ɮɚɡɟ, c
ɯ
66
ȼɢɞ ɞɢɚɝɪɚɦɦɵ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɫɢɫɬɟɦɵ ɫ 2 ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ (ɪɢɫ. 54)
c
* = f (c2) ɩɪɢ Ɋ = const.
1
Ɋɢɫ. 54. ȼɢɞ ɞɢɚɝɪɚɦɦɵ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɫɢɫɬɟɦɵ ɫ 2 ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ
Ʉɚɠɞɚɹ ɬɨɱɤɚ ɤɪɢɜɨɣ ɪɢɫ. 54 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɚɜɧɨɜɟɫɧɨɦɭ ɫɨɫɬɨɹɧɢɸ ɩɪɢ
ɪɚɡɥɢɱɧɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ.
Ɉɬɧɨɲɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɣ ɮɚɡ ɩɪɢ ɪɚɜɧɨɜɟɫɢɢ ɧɚɡɵɜɚɸɬ ɤɨɷɮɮɢɰɢɟɧɬɨɦ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ:
*
c
1
Ƚɪɚɮɢɱɟɫɤɢ m ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ:
m
. (204)
c
2
tgmD , ɬ. ɟ. ɤɚɤ ɬɚɧɝɟɧɫ ɭɝɥɚ ɧɚɤɥɨɧɚ
ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɥɢɧɢɢ ɪɚɜɧɨɜɟɫɢɹ, ɟɫɥɢ ɨɧɚ ɧɟɥɢɧɟɣɧɚ, ɢɥɢ ɤɚɤ ɬɚɧɝɟɧɫ ɭɝɥɚ
ɧɚɤɥɨɧɚ ɫɚɦɨɣ ɥɢɧɢɢ ɪɚɜɧɨɜɟɫɢɹ, ɟɫɥɢ ɨɧɚ ɥɢɧɟɣɧɚ.
ɍɪɚɜɧɟɧɢɟ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɩɪɨɰɟɫɫɚ ɦɚɫɫɨɩɟɪɟɞɚɱɢ ɩɪɢ ɩɪɨɬɢɜɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ
ɋɯɟɦɚ ɞɜɢɠɟɧɢɹ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯɫɹ ɜɟɳɟɫɬɜ ɩɪɨɬɢɜɨɬɨɤɨɦ (ɪɢɫ. 55).
G
1 c1
ɫ
1ɧ ɫ1ɤ
ɫ
2ɤ ɫ2ɧ
G
2 c2
Ɋɢɫ. 55. ɋɯɟɦɚ ɞɜɢɠɟɧɢɹ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯɫɹ ɜɟɳɟɫɬɜ ɩɪɨɬɢɜɨɬɨɤɨɦ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɪɨɰɟɫɫɚ ɩɨ ɰɟɥɟɜɨɦɭ ɤɨɦɩɨɧɟɧɬɭ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ
ɜɢɞɟ:
Gc Gc Gc Gc
11ɧ 22ɧ 11ɤ 22ɤ
(205)
ɢɥɢ
()( )
Ⱦɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɫɟɱɟɧɢɹ ɚɩɩɚɪɚɬɚ ɫ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ ɫ
Gc ɫ Gc ɫ . (206)
11ɧ 122ɤ 2ɧ
ɤ
1 ɢ ɫ2 ɦɨɠɧɨ ɡɚ-
ɩɢɫɚɬɶ:
67
Gc Gc Gc Gc
11ɧ 22 22ɤ 11
(207)
ɢɥɢ
ȼɵɪɚɡɢɦ ɢɡ (208) ɡɚɜɢɫɢɦɨɫɬɶ ɫ1 = f (ɫ2):
Gc Gc G c G c . (208)
11 11ɧ 22ɤ 22
GG
ccc c
121ɧ 2ɤ
GG
§·
22
¨¸
©¹
11
. (209)
ȼɵɪɚɠɟɧɢɟ (209) – ɭɪɚɜɧɟɧɢɟ ɪɚɛɨɱɟɣ ɥɢɧɢɢ (ɪɚɛɨɱɢɯ ɤɨɧɰɟɧɬɪɚɰɢɣ) ɦɚɫɫɨɩɟɪɟɞɚɱɢ.
G
ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɩɪɹɦɨɣ ɫ
tg
D
.
2
G
1
Ɋɚɛɨɱɚɹ ɥɢɧɢɹ ɜɫɟɝɨ ɚɩɩɚɪɚɬɚ ɨɝɪɚɧɢɱɟɧɚ ɬɨɱɤɚɦɢ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ ɫ
ɫ
, ɫ2ɧ.
2ɧ
ȼɢɞ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɩɪɢ ɩɪɨɬɢɜɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ (ɪɢɫ. 56).
, ɫ1ɤ,
1ɧ
Ɋɢɫ. 56. ȼɢɞ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɩɪɢ ɩɪɨɬɢɜɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ
ɍɪɚɜɧɟɧɢɟ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɩɪɨɰɟɫɫɚ ɩɪɢ ɩɪɹɦɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ
ɋɯɟɦɚ ɞɜɢɠɟɧɢɹ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯɫɹ ɜɟɳɟɫɬɜ ɩɪɹɦɨɬɨɤɨɦ (ɪɢɫ. 57).
G1 c1
ɫ
1ɧ ɫ1ɤ
ɫ
2ɧ ɫ2ɤ
G
2 c2
Ɋɢɫ. 57. ɋɯɟɦɚ ɞɜɢɠɟɧɢɹ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯɫɹ ɜɟɳɟɫɬɜ ɩɪɹɦɨɬɨɤɨɦ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɪɨɰɟɫɫɚ ɩɨ ɰɟɥɟɜɨɦɭ ɤɨɦɩɨɧɟɧɬɭ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ
ɜɢɞɟ:
cGcGcGcG "
(210)
2ɤ21ɤ12ɧ21ɧ1
ɢɥɢ
()( )Gc ɫ Gc ɫ . (211)
11ɧ 1ɤ 22ɤ 2ɧ
68
Ⱦɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɫɟɱɟɧɢɹ ɚɩɩɚɪɚɬɚ ɫ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ ɫ1 ɢ ɫ2 ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ:
Gc Gc Gc G c (212)
11ɧ 22ɧ 11 2 2
ɢɥɢ
ȼɵɪɚɡɢɦ ɢɡ (213) ɡɚɜɢɫɢɦɨɫɬɶ ɫ
Gc Gc Gc Gc . (213)
11 22 22ɧ 11ɧ
= f (ɫ2):
1
GG
cccc
121ɧ 2ɧ
GG
§·
22
¨¸
©¹
11
. (214)
ȼɵɪɚɠɟɧɢɟ (214) – ɭɪɚɜɧɟɧɢɟ ɪɚɛɨɱɟɣ ɥɢɧɢɢ (ɪɚɛɨɱɢɯ ɤɨɧɰɟɧɬɪɚɰɢɣ ɦɚɫɫɨɩɟɪɟɞɚɱɢ) ɩɪɢ ɩɪɹɦɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ.
G
ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɩɪɹɦɨɣ ɫ
tg
D
2
.
G
1
Ɋɚɛɨɱɚɹ ɥɢɧɢɹ ɜɫɟɝɨ ɚɩɩɚɪɚɬɚ ɨɝɪɚɧɢɱɟɧɚ ɬɨɱɤɚɦɢ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ ɫ
, ɫ2ɧ (ɫɦ. ɪɢɫ. 58).
ɫ
2ɧ
, ɫ1ɤ,
1ɧ
Ɋɢɫ. 58. ȼɢɞ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɩɪɢ ɩɪɹɦɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ
Ɋɢɫ. 59. Ⱦɢɚɝɪɚɦɦɚ ɫ
ɩɪɢ ɪɚɫɩɨɥɨɠɟɧɢɢ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɜɵɲɟ ɪɚɜɧɨɜɟɫɧɨɣ
1–ɫ2
69
ɂɡ ɞɢɚɝɪɚɦɦɵ ɪɢɫ. 59 ɫɥɟɞɭɟɬ:
M
**
111 2 2 2
ɢ ccc ccc' ' .
ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɰɟɥɟɜɨɣ ɤɨɦɩɨɧɟɧɬ ɛɭɞɟɬ ɩɟɪɟɯɨɞɢɬɶ ɢɡ ɮɚɡɵ G
Ⱦɢɚɝɪɚɦɦɚ ɫ
ɩɪɢ ɪɚɫɩɨɥɨɠɟɧɢɢ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɧɢɠɟ ɪɚɜɧɨɜɟɫɧɨɣ
1–ɫ2
ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ. 60.
ɜ ɮɚɡɭ G2.
1
Ɋɢɫ. 60. Ⱦɢɚɝɪɚɦɦɚ ɫ
ɩɪɢ ɪɚɫɩɨɥɨɠɟɧɢɢ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɧɢɠɟ ɪɚɜɧɨɜɟɫɧɨɣ
1–ɫ2
ɂɡ ɞɢɚɝɪɚɦɦɵ ɫɥɟɞɭɟɬ:
**
111 2 2 2
ɢ .ccc c c c' '
ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɰɟɥɟɜɨɣ ɤɨɦɩɨɧɟɧɬ ɛɭɞɟɬ ɩɟɪɟɯɨɞɢɬɶ ɢɡ ɮɚɡɵ G
ɋɪɟɞɧɹɹ ɞɜɢɠɭɳɚɹ ɫɢɥɚ ɩɪɨɰɟɫɫɨɜ ɦɚɫɫɨɩɟɪɟɞɚɱɢ:
'
ɧ
'!' d':
ɩɪɢ
'!' !':
ɩɪɢ
Ɉɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɦɚɫɫɨɩɟɪɟɞɚɱɢ
ɢ 2
ɧɤ
ɢ 2
ɤ
ɧ
ɤ
ɤ
''
ɧ
ɫ
' ; (215)
ɪ
2
'
ɧ
ɤ
ɧɤ
''
ɫɪ
'
. (216)
ɧ
'
ln
ɤ
'
KF ɫɪ ', (217)
ɝɞɟ Ɇ – ɦɚɫɫɚ ɩɟɪɟɧɨɫɢɦɨɝɨ ɜɟɳɟɫɬɜɚ, ɤɝ/ɫ;
ɤɝ
Ʉ – ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɫɫɨɩɟɪɟɞɚɱɢ,
ɦɫ
;
2
¨ɫɪ – ɫɪɟɞɧɹɹ ɞɜɢɠɭɳɚɹ ɫɢɥɚ ɩɪɨɰɟɫɫɚ ɦɚɫɫɨɩɟɪɟɞɚɱɢ.
70
ɜ ɮɚɡɭ G1.
2
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