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Файл:Физическая химия — основа металлургических процессов. Учебное пособие
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m
ɠ/mɬ
= ɛɜ/ɚɛ
Ʉɨɝɞɚ ɤɨɦɩɨɧɟɧɬɵ ɢɦɟɸɬ
ɛɥɢɡɤɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɩɥɚɜɥɟɧɢɹ
ɬɨɝɞɚ ɞɢɚɝɪɚɦɦɚ ɫɨɫɬɨɹɧɢɹ ɯɚ
ɪɚɤɬɟɪɢɡɭɸɬɫɹ ɧɚɥɢɱɢɟɦ
min
ɜ) ɞɢɚɝɪɚɦɦɵ ɫɨɫɬɨɹ-
T
A
C
B
ɧɢɹ ɫ ɷɜɬɟɤɬɢɤɨɣ ɢɡ ɞɜɭɯ
ɬɜɟɪɞɵɯ ɪɚɫɬɜɨɪɨɜ: I –
ɠɢɞɤɚɹ ɮɚɡɚ; II – ɠɢɞɤɢɣ
ɪɚɫɩɥɚɜ ɢ ɬɜɟɪɞɚɹ ɮɚɡɚ
III – ɠɢɞɤɢɣ ɪɚɫɩɥɚɜ ɢ
A B
A
mBn
ɬɜɟɪɞɚɹ ɮɚɡɚ
ɨɞɧɨɪɨɞɧɵɣ ɬɜɟɪɞɵɣ ɪɚɫ-
ɬɜɨɪ
D
; V – ɨɞɧɨɪɨɞɧɵɣ ɬɜɟɪɞɵɣ ɪɚɫɬɜɨɪ E; VI – ɦɟɯɚɧɢɱɟɫɤɚɹ ɫɦɟɫɶ
D
- ɢ E-ɬɜɟɪɞɵɯɮɚɡ
T
9,
D
,
,,
,9
E
,,,
9
E
ɝ) ɞɢɚɝɪɚɦɦɵ ɫɨɫɬɨɹɧɢɹ
ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɩɪɨɱɧɵɯ ɯɢɦɢɱɟɫɤɢɯ ɫɨɟɞɢɧɟɧɢɣ, ɭɫɬɨɣɱɢɜɵɯ ɜɩɥɨɬɶ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ
ɩɥɚɜɥɟɧɢɹ.
A B
maxɢ
E
; IV –
D
;
ɞ) ɞɢɚɝɪɚɦɦɵ ɫɨɫɬɨɹɧɢɹ ɫ
T
B
B
T
B
B
ɨɛɪɚɡɨɜɚɧɢɟɦ ɧɟɩɪɨɱɧɵɯ ɯɢɦɢɱɟɫɤɢɯ ɫɨɟɞɢɧɟɧɢɣ, ɪɚɫɩɨɥɚɝɚɸ-
L N
ɳɢɯɫɹ ɧɢɠɟ ɬɨɱɤɢ ɩɥɚɜɥɟɧɢɹ
Ⱥ
ɬɪɚɫɩɥɚɜɫɨɫɬɚɜɊlA
mBn
ɬ
A
Ɉɛɪɚɡɨɜɚɧɧɨɟ ɫɨɟɞɢɧɟɧɢɟ ɢ ɤɨɦɩɨɧɟɧɬɵ ɧɟɨɝɪɚɧɢɱɟɧɧɨ ɜɡɚɢɦɨɪɚɫɬɜɨɪɢɦɵ.
A
A
A
ɋɥɟɜɚ ɨɬ ɜɟɪɬɢɤɚɥɶɧɨɣ ɲɬɪɢɯɨɜɨɣ ɥɢɧɢɢ ɞɟɮɢɰɢɬ ȼ, ɚ ɫɩɪɚɜɚ Ⱥ –
ɫɨɟɞɢɧɟɧɢɹ ɞɚɥɶɬɨɧɨɢɞɵ (ɫ ɨɝɪɚɧɢɱɟɧɧɵɦ ɪɚɫɬɜɨɪɟɧɢɟɦ).
c
b
d
e
a
A
ɟ) ɞɢɚɝɪɚɦɦɵ ɫɨɫɬɨɹɧɢɹ c ɤɨɦɩɨɧɟɧɬɚɦɢ, ɤɨɬɨɪɵɟ ɩɨɥɧɨɫɬɶɸ
ɫɦɟɲɢɜɚɸɬɫɹ ɜ ɠɢɞɤɨɦ ɫɨɫɬɨɹɧɢɢ: I – ɨɞɧɨɪɨɞɧɵɣ ɠɢɞɤɢɣ ɪɚɫɬɜɨɪ;
T
II – ɞɜɚ ɫɨɩɪɹɠɟɧɧɵɯ ɧɚɫɵ-
ɳɟɧɧɵɯ ɠɢɞɤɢɯ ɪɚɫɬɜɨɪɚ, ɨɛ-
P
E
ɪɚɡɭɸɳɢɟ ɧɟɫɦɟɲɢɜɚɸɳɢɟɫɹ
ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɫɥɨɢ.
Tk±ɤɪɢɬɢ
ɱɟɫɤɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɪɚɫɬɜɨɪɟ
A B
A
mBn
ɧɢɹ
ɋɤɨɪɨɫɬɶɯɢɦɢɱɟɫɤɨɣɪɟɚɤɰɢɢɁɚɤɨɧɞɟɣɫɬɜɭɸɳɢɯɦɚɫɫ
ɋɨɜɨɤɭɩɧɨɫɬɶ ɫɬɚɞɢɣ ɢɡ ɤɨɬɨɪɵɯ ɫɨɫɬɨɢɬ ɯɢɦɢɱɟɫɤɚɹ ɪɟɚɤɰɢɹ
ɧɚɡɵɜɚɟɬɫɹ ɦɟɯɚɧɢɡɦɨɦ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ Ɇɧɨɝɨɫɬɚɞɢɣɧɨɫɬɶ
ɨɛɵɱɧɨ ɫɜɹɡɚɧɚ ɫ ɧɢɡɤɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ɨɞɧɨɜɪɟɦɟɧɧɨɝɨ ɫɨɭɞɚɪɟɧɢɹ
ɧɟɫɤɨɥɶɤɢɯ ɱɚɫɬɢɰ ɉɪɨɬɟɤɚɧɢɟ ɞɚɧɧɨɝɨ ɩɪɨɰɟɫɫɚ ɫɜɹɡɚɧɨ ɫɨ ɜɪɟɦɟ
ɧɟɦ ȼ ɷɬɨɦ ɢɨɫɧɨɜɧɨɟ ɨɬɥɢɱɢɟ ɤɢɧɟɬɢɤɢ ɨɬ ɬɟɪɦɨɞɢɧɚɦɢɤɢ Ƚɨɦɨ
ɝɟɧɧɵɟɢɝɟɬɟɪɨɝɟɧɧɵɟɪɟɚɤɰɢɢ ± ɫɨɨɬɜɟɬɫɬɜɟɧɧɨɷɬɢɯɢɦɢɱɟɫɤɢɟɪɟ
ɚɤɰɢɢɩɪɨɬɟɤɚɸɳɢɟɜɨɞɧɨɣɮɚɡɟɢɧɚɝɪɚɧɢɰɟɪɚɡɞɟɥɚɮɚɡ>@
ȿɫɥɢɪɚɫɫɦɚɬɪɢɜɚɬɶɡɚɦɤɧɭɬɭɸɫɢɫɬɟɦɭɬɨɜɧɟɣɫɤɨɪɨɫɬɶɯɢɦɢ
ɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɨɩɢɫɵɜɚɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
dn
n ɱɢɫɥɨɦɨɥɟɣɪɚɫ
dt
ɫɦɚɬɪɢɜɚɟɦɨɝɨɜɟɳɟɫɬɜɚ ɋɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɡɚɜɢɫɢɬ ɨɬ ɩɪɢɪɨɞɵ ɩɪɨ
ɰɟɫɫɚɭɫɥɨɜɢɣɟɝɨɩɪɨɬɟɤɚɧɢɹɤɨɥɢɱɟɫɬɜɚɢɫɯɨɞɧɵɯɜɟɳɟɫɬɜ
ɋɤɨɪɨɫɬɶ ɝɨɦɨɮɚɡɧɨɝɨ ɯɢɦɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ ɩɨ ɧɟɤɨɬɨɪɨɦɭ
ɤɨɦɩɨɧɟɧɬɭɨɩɪɟɞɟɥɹɟɬɫɹɢɡɦɟɧɟɧɢɟɦɤɨɥɢɱɟɫɬɜɚɷɬɨɝɨɤɨɦɩɨɧɟɧɬɚɜ
ɟɞɢɧɢɰɭɜɪɟɦɟɧɢɜɟɞɢɧɢɰɟɨɛɴɟɦɚ
dn
v
ɉɪɢ
V = constV
dn dc
dt v dt
Vdt
ȿɫɥɢɜɯɨɞɟɪɟɚɤɰɢɢ ɫɨɛɥɸɞɚɟɬɫɹ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɟɭɪɚɜɧɟɧɢɟ
ɬɨɝɞɚ
mn
aA bB
¦ ¦
ii j j
ij
ɢ ɦɟɠɞɭ ɢɡɦɟɧɟɧɢɹɦɢ ɱɢɫɥɚ ɦɨɥɟɣ ɢ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɣ ɜɵɩɨɥɧɹɟɬɫɹ
ɭɫɥɨɜɢɟ
ww w
AA B
>@ >@ >@
at a t Bt
ww w
i
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ ɫɜɹɡɚɧɵ ɦɟɠɞɭ ɫɨɛɨɣ ɫɥɟɞɭɸ
p
p
ɳɟɣɡɚɜɢɫɢɦɨɫɬɶɸ
ªº
w
A
w
>@
v
i
ww
at b t
ij
B
j
¬¼
ȼɨɬɤɪɵɬɨɣɫɢɫɬɟɦɟɢɡɦɟɧɟɧɢɟɤɨɥɢɱɟɫɬɜɚɜɟɳɟɫɬɜɚɩɪɨɢɫɯɨɞɢɬ
ɜɪɟɡɭɥɶɬɚɬɟɯɢɦɢɱɟɫɤɢɯɩɪɟɜɪɚɳɟɧɢɣǻ
n
ɢɦɚɫɫɨɩɟɪɟɞɚɱɢǻnmɢɩɨ
p
ɷɬɨɦɭɫɤɨɪɨɫɬɶɸɯɢɦɢɱɟɫɤɨɣɪɟɚɤɰɢɢɜɨɬɤɪɵɬɨɣɫɢɫɬɟɦɟɧɚɡɵɜɚɟɬɫɹ
ɢɡɦɟɧɟɧɢɟɤɨɥɢɱɟɫɬɜɚ ɜɟɳɟɫɬɜɚɜɟɞɢɧɢɰɭɜɪɟɦɟɧɢɜɟɞɢɧɢɰɟɨɛɴɟɦɚ
ɬɨɥɶɤɨɯɢɦɢɱɟɫɤɢɯɩɪɟɜɪɚɳɟɧɢɣ
vn n
' '
VVdt
dn
m
ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɫɤɨɪɨɫɬɶɢɡɦɟɧɟɧɢɹ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɩɪɨɞɭɤɬɚ
ɨɩɪɟɞɟɥɹɟɬɫɹɧɚɥɨɠɟɧɢɟɦɞɜɭɯ ɩɪɨɰɟɫɫɨɜɟɝɨɨɛɪɚɡɨɜɚɧɢɟɦ ɢɪɚɫɯɨ
ɞɨɜɚɧɢɟɦɪɚɡɪɭɲɟɧɢɟɦ
dc
vv
dt
ɉɪɢ ɡɚɞɚɧɧɵɯ ɜɧɟɲɧɢɯ ɭɫɥɨɜɢɹɯ ɫɤɨɪɨɫɬɶ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ
ɹɜɥɹɟɬɫɹɮɭɧɤɰɢɟɣɤɨɧɰɟɧɬɪɚɰɢɢɢɨɩɢɫɵɜɚɟɬɫɹɫɟɟɩɨɦɨɳɶɸ
vKA A A
n
±ɩɨɪɹɞɨɤɪɟɚɤɰɢɢɩɨɜɟɳɟɫɬɜɭ>Ai@
ɝɞɟ
i
>@>@
nn
n
i
>@
i
ɋɭɦɦɭɩɨɪɹɞɤɨɜɪɟɚɤɰɢɢɩɨɜɫɟɦɪɟɚɝɢɪɭɸɳɢɦɜɟɳɟɫɬɜɚɦɧɚɡɵ
ɜɚɸɬɩɨɪɹɞɤɨɦɪɟɚɤɰɢɢ
ɇɚɩɪɢɦɟɪɞɥɹɨɞɧɨɫɬɚɞɢɣɧɨɣɪɟɚɤɰɢɢɷɬɨɜɵɪɚɠɟɧɢɟɢɦɟɟɬɫɥɟ
ɞɭɸɳɢɣɜɢɞ
aA bB
6
ii ii
6
i
i
e
E
E
a
i
vKɉ A
i
>@
i
ȼɞɚɧɧɨɦɫɥɭɱɚɟɨɧɨɧɟɹɜɥɹɟɬɫɹɨɛɳɟɣɮɨɪɦɭɥɨɣɤɢɧɟɬɢɱɟɫɤɨɝɨ
ɭɪɚɜɧɟɧɢɹɞɥɹɥɸɛɨɣɪɟɚɤɰɢɢȼɛɨɥɶɲɨɦɱɢɫɥɟɫɥɭɱɚɟɜɡɚɜɢɫɢɦɨɫɬɶ
ɫɤɨɪɨɫɬɢɧɚɤɨɩɥɟɧɢɹɩɪɨɞɭɤɬɚɫɥɨɠɧɨɣɪɟɚɤɰɢɢɨɬɤɨɧɰɟɧɬɪɚɰɢɢɪɟ
ɚɝɢɪɭɸɳɢɯɜɟɳɟɫɬɜɜɨɨɛɳɟɨɩɢɫɵɜɚɟɬɫɹɫɬɟɩɟɧɧɨɣɮɭɧɤɰɢɟɣ
ɍɪɚɜɧɟɧɢɟȺɪɪɟɧɢɭɫɚɗɧɟɪɝɢɹɚɤɬɢɜɚɰɢɢ
ɂɫɯɨɞɹɢɡɭɪɚɜɧɟɧɢɹ ȼɚɧɬȽɨɮɮɚdlnɄ/dT = q/RT2ɤɨɬɨɪɨɟɭɫɬɚ
ɧɚɜɥɢɜɚɟɬ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɤɨɧɫɬɚɧɬɨɣ ɪɚɜɧɨɜɟɫɢɹ
ɩɪɢ
P = constɢɥɢV = constɢɬɟɩɥɨɬɨɣɤɨɬɨɪɚɹɩɨɝɥɨɳɟɧɚɩɪɢɷɬɢɯ
Ʉ ɢɡɦɟɪɟɧɧɨɣ
ɭɫɥɨɜɢɹɯȺɪɪɟɧɢɭɫɞɥɹɨɩɪɟɞɟɥɟɧɢɹɤɨɧɫɬɚɧɬɵɫɤɨɪɨɫɬɢɯɢɦɢɱɟɫɤɨɣ
ɪɟɚɤɰɢɢɩɪɟɞɥɨɠɢɥɫɥɟɞɭɸɳɟɟɭɪɚɜɧɟɧɢɟ
ȿ
±ɷɧɟɪɝɢɹɚɤɬɢɜɚɰɢɢ
ɝɞɟ
ɚ
dK
T
w
ɚ
RT
OQ
Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɤɨɧɫɬɚɧɬɵ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ ɩɪɨɜɟɞɟɦ ɫɥɟɞɭɸ
ɳɢɟɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
E
dK dT
OQ
OQ
Kconst
KAe
ɚ
RT
RT
ɚERT
ɚ
ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɨɫɧɨɜɧɚɹ ɢɞɟɹ Ⱥɪɪɟɧɢɭɫɚ ɫɨɫɬɨɹɥɚ ɜ ɬɨɦ ɱɬɨ
ɦɨɥɟɤɭɥɵ ɩɪɟɬɟɪɩɟɜɚɸɳɢɟ ɯɢɦɢɱɟɫɤɢɟ ɩɪɟɜɪɚɳɟɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɢ
ɛɨɝɚɱɟ ɨɛɵɱɧɵɯ ɦɨɥɟɤɭɥ ɢɡ ɤɨɬɨɪɵɯ ɫɨɫɬɨɢɬ ɫɬɚɛɢɥɶɧɚɹ ɫɢɫɬɟɦɚ
ɉɨɷɬɨɦɭɞɚɠɟɩɪɨɫɬɟɣɲɚɹɪɟɚɤɰɢɹɞɨɥɠɧɚɩɪɨɬɟɤɚɬɶɱɟɪɟɡɧɟɫɤɨɥɶɤɨ
ɫɬɚɞɢɣ ɧɨɪɦɚɥɶɧɵɟ ɦɨɥɟɤɭɥɵ ɪɟɚɝɟɧɬɨɜ
K
K
K
K
K
o ɦɨɥɟɤɭɥɵɩɪɨɞɭɤɬɨɜ
ɚɤɬɢɜɧɵɟ ɦɨɥɟɤɭɥɵ
l
Ⱦɥɹ ɩɪɢɦɟɪɚ ɪɚɫɫɦɨɬɪɢɦ ɨɩɪɟɞɟɥɟɧɢɟɷɧɟɪɝɢɢ ɚɤɬɢɜɚɰɢɢ ɯɢɦɢ
ɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɢɞɭɳɟɣɫ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɨɣ ɫɤɨɪɨ
ɫɬɶɸ ɢ ɤɨɬɨɪɚɹ ɧɟ ɩɪɨɬɢɜɨɪɟɱɢɬ ɡɚɤɨɧɭ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ȼɨɥɶɰɦɚɧɚ
ɉɪɢ ɷɬɨɦ ɱɢɫɥɨ ɦɨɥɟɤɭɥ
ɷɧɟɪɝɢɟɣ
İ
ɪɚɜɧɨ
ɚ
ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɚɤɬɢɜɧɨɦ ɫɨɫɬɨɹɧɢɢ ɫ
T
H
a
Pe
¦
a
a
NN
a
¦
Pe
i
i
KT
H
i
ɉɭɫɬɶɞɥɹɤɚɠɞɨɣɦɨɥɟɤɭɥɵɧɚɯɨɞɹɳɟɣɫɹɜɫɨɫɬɨɹɧɢɢaɢɦɟɟɬɫɹ
ɜɟɪɨɹɬɧɨɫɬɶ
Ʉ
ɩɪɨɪɟɚɝɢɪɨɜɚɬɶ ɜɬɟɱɟɧɢɟɨɞɧɨɣɫɟɤɭɧɞɵɬɨɝɞɚ ɱɢɫɥɨ
ɚ
ɦɨɥɟɤɭɥɪɟɚɝɢɪɭɸɳɢɯɜɫɟɤɭɧɞɭɛɭɞɟɬɫɥɟɞɭɸɳɟɟ
T
H
PK e
¦
aa
dN
ɩɪɢɷɬɨɦɤɨɧɫɬɚɧɬɚɩɟɪɜɨɝɨɩɨɪɹɞɤɚɯɢɦɢɱɟɫɤɨɣɪɟɚɤɰɢɢɪɚɜɧɚ
a
dt
a
N
K
Pe
¦
i
dN
Ndt
a
KT
H
i
i
ɬɨɝɞɚ
aa
Pe
i
a
H
KT
i
PK e
¦
a
Ʉ
¦
i
KT
H
ɉɪɟɞɩɨɥɨɠɢɦɱɬɨɄ1ɡɚɜɢɫɢɬɨɬɬɟɦɩɟɪɚɬɭɪɵɌɬɨɝɞɚ
K
aa
Pe
¦
s
¦
a
H
i
PK e
a
¦
PK e
KT
¦
a
dK
dT
dK
dT
a
KT
KT
i
H
aa a
a
H
i
Pe
i
i
PK e Pe
¦¦
ai
KT
H
KT
ai
aa i
¦
PK e
¦
a
¦
i
KT
H
KT
i
Pe
i
i
KT
H
a
aa i
Pe
i
i
H
KT
a
H
TKT
HH
H
KT
H
KT
HH
i
¦
i
Pe
Pe
ii
i
H
KT
i
i
KT
H
Pe
i
a
H
KT
H
i
¦
PK e
¦
aa a
OQdK
KT
dT
a
¦
i
ȼ ɜɵɲɟ ɩɪɟɞɫɬɚɜɥɟɧɧɨɦ ɭɪɚɜɧɟɧɢɢ ɩɟɪɜɵɣ ɱɥɟɧ ɫɩɪɚɜɚ ɷɬɨ
İ
ɫɪɟɞɧɹɹɷɧɟɪɝɢɹɚɤɬɢɜɧɵɯ
H
ɦɨɥɟɤɭɥɬɨɝɞɚ
ɦɨɥɟɤɭɥɚɜɬɨɪɨɣɫɪɟɞɧɹɹɷɧɟɪɝɢɹɜɫɟɯ
H
KT
dT
OQdK
HH
ɢɥɢ
(İ* –
H
OQ
dK
dT
)N = E
EKT
A
A
ɉɨɷɬɨɦɭɦɨɠɧɨɡɚɤɥɸɱɢɬɶɱɬɨɫɪɟɞɧɹɹɷɧɟɪɝɢɹɦɨɥɟɤɭɥɵɹɜɥɹ
ɟɬɫɹɮɭɧɤɰɢɟɣɬɟɦɩɟɪɚɬɭɪɵ
ɉɪɟɞɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɣɦɧɨɠɢɬɟɥɶ
Ɋɚɫɫɦɨɬɪɢɦ ɱɢɫɥɨ ɞɜɨɣɧɵɯ ɫɨɭɞɚɪɟɧɢɣ ɦɨɥɟɤɭɥ ɪɚɡɧɵɯ ɪɚɡɦɟ
ɪɨɜɄɢɧɟɬɢɱɟɫɤɭɸɷɧɟɪɝɢɸɞɜɭɯɦɨɥɟɤɭɥɦɚɫɫɚɦɢ
m
ɢm2ɦɨɠɧɨɜɵ
1
ɪɚɡɢɬɶɱɟɪɟɡɤɨɦɩɨɧɟɧɬɵɫɤɨɪɨɫɬɢɢɥɢɚɛɫɨɥɸɬɧɨɣɫɤɨɪɨɫɬɢ
muvw muvw
H
H
ɬɫ ɬɫ
ȼɜɟɞɟɦɧɨɜɵɟɩɟɪɟɦɟɧɧɵɟ
um u m
u
ȿɫɥɢɩɨɥɨɠɢɬɶɱɬɨ
mm
Į = u2 – u
c
v
2
= u
1
vm v m
mm
ȕ = v
2
2
+ v2 + w
– v
Ȗ = w
1
2
v
wm w m
W
– w
2
1
2
= Į2 + ȕ2 + Ȗ
mm
2
ɬɨɝɞɚɤɢɧɟ
ɬɢɱɟɫɤɭɸɷɧɟɪɝɢɸɦɨɠɧɨɩɪɟɞɫɬɚɜɢɬɶɜɜɢɞɟ
mmc v
H
mm
mm
ȼɜɟɞɹɩɨɥɧɭɸɢɩɪɢɜɟɞɟɧɧɭɸɦɚɫɫɵɬɨɝɞɚɨɧɚɢɦɟɟɬɫɥɟɞɭɸɳɢɣ
ɜɢɞ
mc v
HP
Ɍɨɟɫɬɶɤɢɧɟɬɢɱɟɫɤɚɹɷɧɟɪɝɢɹɦɨɥɟɤɭɥɵɪɚɡɥɚɝɚɟɬɫɹɧɚɞɜɟɱɚɫɬɢ±
ɩɟɪɜɚɹɫɜɹɡɚɧɚɫɞɜɢɠɟɧɢɟɦɰɟɧɬɪɚ ɬɹɠɟɫɬɢɚɜɬɨɪɚɹ ±ɫɨɬɧɨɫɢɬɟɥɶ
ɧɵɦ ɞɜɢɠɟɧɢɟɦ ɦɨɥɟɤɭɥɵ Ɉɱɟɜɢɞɧɨ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɦɨɥɟɤɭɥɹɪ
ɧɵɯ ɫɨɭɞɚɪɟɧɢɣ ɧɭɠɧɨ ɭɱɢɬɵɜɚɬɶ ɬɨɥɶɤɨ ɜɬɨɪɭɸ ɢɡ ɧɢɯ Ɂɚɩɢɫɚɜ
ɭɪɚɜɧɟɧɢɟȻɨɥɶɰɦɚɧɚɜɫɮɟɪɢɱɟɫɤɢɯɤɨɨɪɞɢɧɚɬɚɯ
vv
PP
mm
VLQ
³ ³
dw e d d v dv e v dv
v
SS
TT
TT
TTI S
v
P
S
P
ɄɌ
KT
ɟ vdv
³
ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɫɱɢɬɚɬɶɱɬɨ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɨɩɪɟɞɟɥɹɟɬ
ɜɟɪɨɹɬɧɨɫɬɶ ɩɟɪɜɨɣ ɱɚɫɬɢɰɵ ɢɦɟɬɶ ɫɤɨɪɨɫɬɶ
v + dvɜɬɨɜɪɟɦɹɤɚɤ
ɜɬɨɪɚɹɩɨɤɨɢɬɫɹ ȼɞɚɥɶɧɟɣɲɟɦɪɚɫɫɦɨɬɪɢɦɱɢɫɥɨɫɨɭɞɚɪɟɧɢɣɜɨɞɧɭ
ɫɟɤɭɧɞɭ ɦɟɠɞɭ ɛɨɥɶɲɨɣ ɦɨɥɟɤɭɥɨɣ
ɬɪɚɰɢɹɤɨɬɨɪɵɯ
n
ɜɨɞɧɨɦɤɭɛɢɱɟɫɤɨɦ ɫɚɧɬɢɦɟɬɪɟ ɂɡ ɨɛɳɟɝɨɱɢɫɥɚ
2
m1r
ɢ ɦɟɧɶɲɟɣ m
1
ɤɨɧɰɟɧ
2r2
ɩɨɥɨɠɟɧɢɹ ɫɥɟɞɭɟɬ ɱɬɨ ɱɢɫɥɨ ɫɬɨɥɤɧɨɜɟɧɢɣ ɪɚɜɧɨ ɩɪɨɢɡɜɟɞɟɧɢɸ
ɩɥɨɳɚɞɢ ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɫɟɱɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɢɫɬɚɥɤɢɜɚɸɳɢɯɫɹ ɦɨ
ɥɟɤɭɥɢɫɤɨɪɨɫɬɢɫɛɥɢɠɟɧɢɹɰɟɧɬɪɨɜɬɹɠɟɫɬɢɦɨɥɟɤɭɥ
ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɪɚɜɧɚ ɩɥɨɳɚɞɢ
ɤɪɭɝɚɫɪɚɞɢɭɫɨɦ
n2dw
ɪɚɜɧɚ
v
r
+ r
= ı
1
Ʉɨɧɰɟɧɬɪɚɰɢɹɫɨɭɞɚɪɹɸɳɢɯɫɹɦɨɥɟɤɭɥ
2
12
ɋɬɨɥɤɧɭɬɫɹɫɩɨɜɟɪɯɧɨɫɬɶɸ ɬɨɥɶɤɨɬɟɦɨɥɟɤɭɥɵ ɤɨɬɨɪɵɟɢɦɟɸɬ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟɧɚɩɪɚɜɥɟɧɢɟȼɟɪɨɹɬɧɨɫɬɶɬɨɝɨɱɬɨɦɨɥɟɤɭɥɵɛɭɞɭɬ
ɞɜɢɝɚɬɶɫɹ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɦɟɠɞɭɩɪɨɢɡɜɨɥɶɧɵɦɢ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɨɛɨ
ɡɧɚɱɚɟɬɫɹ ɱɟɪɟɡ
ɧɚɩɪɚɜɥɟɧɢɹ ɱɟɪɟɡ
T
G
T
UÂVLQT
=sinșdș/2
ɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɨɬɧɨɲɟɧɢɟ ɩɥɨ
ɗɬɨ ɜɵɪɚɠɟɧɢɟ ɩɪɟɞ
ș ɫɨɟɞɢɧɟɧɢɟ ɢɯ
ș + dș =
ɳɚɞɢ ɢɡɨɝɧɭɬɨɝɨ ɤɨɥɶɰɚ
ʌ
rsinșrdșɤɩɥɨɳɚɞɢɫɮɟɪɵʌr
2
ɉɨɫɥɟɞɧɢɣ ɫɨɦɧɨɠɢɬɟɥɶ ɜɵ
ɪɚɠɚɟɬɫɤɨɪɨɫɬɶ ɫɛɥɢɠɟɧɢɹɦɨɥɟ
ɤɭɥ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɩɨɜɟɪɯɧɨɫɬɢ ɫɮɟɪɵ ɢ ɪɚɜɟɧ
K
vcosșɝɞɟș± ɭɝɨɥ ɦɟɠɞɭɧɚɩɪɚɜɥɟɧɢɟɦɞɜɢɠɟɧɢɹY ɢ ɥɢɧɢɟɣɫɨɟɞɢ
ɧɹɸɳɟɣ ɰɟɧɬɪɵ ɦɨɥɟɤɭɥ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɱɢɫɥɨ ɫɨɭɞɚɪɟɧɢɣ ɡɚ ɨɞɧɭ
ɫɟɤɭɧɞɭɦɟɠɞɭɨɞɧɨɣɦɨɥɟɤɭɥɨɣɩɟɪɜɨɝɨɬɢɩɚɢ ɜɵɞɟɥɟɧɧɵɦɢ ɦɨɥɟ
ɤɭɥɚɦɢɜɬɨɪɨɝɨɬɢɩɚɪɚɜɧɨ
v
P
S
VLQ
FRV
dz n e v dv v
SV T
PTT
KT
KT
ȿɫɥɢɤɨɧɰɟɧɬɪɚɰɢɹɦɨɥɟɤɭɥɩɟɪɜɨɝɨɬɢɩɚ
ɧɨɜɟɧɢɣɜɟɞɢɧɢɰɟɨɛɴɟɦɚɜ
dz n n e v dv d
SV T TT
n
ɪɚɡɛɨɥɶɲɟɢɫɨɫɬɚɜɥɹɟɬ
1
P
VLQFRV
KT
v
P
KT
d
n
ɬɨɝɞɚɱɢɫɥɨɫɬɨɥɤ
1
ɂɧɬɟɝɪɢɪɭɹɷɬɨɜɵɪɚɠɟɧɢɟɜɩɪɟɞɟɥɚɯ
vɨɬɞɨɢșɨɬɞɨʌ
ɩɨɥɭɱɚɟɦ
S
v
P
f
³³
znn e vdv nn
SV T T V
PS
VLQFRV
KT
KT
ªº
znnrr KT
S
«»
¬¼
zze
v
P
T
mm
KT
P
Ⱦɥɹɪɟɚɤɰɢɢɜɬɨɪɨɝɨɩɨɪɹɞɤɚ
N
K
N
KrrKT e
S±ɤɨɥɢɱɟɫɬɜɨɫɥɚɝɚɟɦɵɯɷɧɟɪɝɢɣ
ɝɞɟ
AB
ªº
S
«»
¬¼
mm S
A
dn
dt n n
AB
ERT
ERT
S
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