ИЗМЕНЕНИЕ ЭНТРОПИИ ПРИ СОВЕРШЕНИИ

536.24.01
Ⱥɥɟɤɫɚɧɞɪ Ⱥɥɟɤɫɚɧɞɪɨɜɢɱ Ʉɭɥɢɤɨɜ,
,
ltuttsu@mail.ru
ɂɪɢɧɚ ɇɢɤɨɥɚɟɜɧɚ Ⱦɸɤɨɜɚ,
ltuttsu@mail.ru
ɂɪɟɧɚ ȼɢɤɬɨɪɨɜɧɚ ɂɜɚɧɨɜɚ,
,
ltuttsu@mail.ru
-
ɂɁɆȿɇȿɇɂȿ ɗɇɌɊɈɉɂɂ
ɉɊɂ ɋɈȼȿɊɒȿɇɂɂ ɆȿɏȺɇɂɑȿɋɄɈɃ ɊȺȻɈɌɕ
ȼ ɇȿɊȺȼɇɈȼȿɋɇɈɆ ɌȿɊɆɈȾɂɇȺɆɂɑȿɋɄɈɆ ɉɊɈɐȿɋɋȿ
ȼɨɡɪɚɫɬɚɧɢɟ ɷɧɬɪɨɩɢɢ, ɧɟɪɚɜɧɨɜɟɫɧɵɟ ɩɪɨɰɟɫɫɵ, ɫɨɜɟɪɲɟɧɢɟ ɪɚɛɨɬɵ,
ɢɡɨɥɢɪɨɜɚɧɧɚɹ ɫɢɫɬɟɦɚ, ɢɞɟɚɥɶɧɵɣ ɝɚɡ.
Increase entropy, nonequilibrium processes, fulfilment of the work, the isolated system, ideal gas.
.
,
,
[1].
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,
.
Ɇɟɬɨɞɢɤɚ ɢɫɫɥɟɞɨɜɚɧɢɣ.
,
,
),
[2]:
υ
du = dq – p dυ
u–
–
124
dq = du + p dυ,
,
,
;υ–
( -
/ ;q–
(1)
,
,
3
/ .
/ ;
,
,
-
:
du = cυ dT,
(2)
p υ = RT,
(3)
cυ –
,
,
, ;R–
(2) (3) (1)
,
/( · );
/( · ).
–
:
dq cυ dT Rdυ
.


T
T
υ
(4)
(4)
:
dq
T
 cυ ln T  R ln υ  C,
–
(5)
.
,
(5)
,
:
dq
T
s(T, υ) –
/( · ); so –
/( · ).
,
-
υ, . .
–
.
 s(T , υ)  cυ ln T  R ln υ  so ,
(6)
,
,
, so = C,
(6)
,
dq / T = ds.
,
so
,υ ,
= 273
,
=1
(7)
–
[3–5]
:
.(
,
-
).
s( , υ )
s o  s (T , υ )  cυ ln T  R ln υ .
(6)
:
(8)
125
(8)
-
,
s
,υ ,
,
(6)
.
(8)
-
,
, υ, :
s(T , υ)  cυ ln T  R ln υ  s(T , υ ) 
 s(T , υ )  cυ ln
 R ln
 R ln υ 
υ
.
υ
(9)
,υ ,
.
(9)
,
υ ln T
s( , υ )
Δs
:
s  s (T ,υ)  s (T ,υ )  cυ ln
(3)
 R ln
υ
.
υ
(10),
s  s (T , )  s (T ,
(10)
:
)  c ln
 R ln
p
,
p
–
,
(10)
(11)
(11)
/ · .
,
-
.
s( , υ ),
(9)
s( ,
),
.
:
(7)
0
[6].
-
,
:
T
T
dq
 T   ds  s(T ,
0
0
)  s (0, p )  s (T ,
).
(12)
,
,
126
,
(12).
,
,
(12)
s (T ,
[7]:
dT

)
T
0
hi
,
i  1 Ti
n

(13)
–
0
(13)
; Δhi –
,
/ ; Ti –
.
,
ii-
,
; n –
-
, υ ,
Δhi.
0
1,
-
,
,
. 1.
2.
3,
4,
5.
–6
-
:
– 7.
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-
.
,
,υ
,
.
,
,υ ,
.
, . .
–
= Δ ≠ 0,
Δ –
(
)
,
.
.
.
127
. 1.
1–
4–
;2–
;5–
7–
;3–
;6–
;
;
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[8].
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Δ
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128
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υ-
,
(
. 2,
υ ( 3/ ).
),
-
υ-
. 2.
,υ
1,
:
,
,
.
.
Δ
.
,
υ.
[8],
,
α–
-
,
,
-
1,
.
,
υ .
,
,
.
,
129
,
1.
, . .
.
,
(
1
. 2)
2.
2
s (T2 , υ2 )  s (T1, υ1 )  cυ ln
2
 R ln
1
T2  υ1 

T1  υ2 
υ2
.
υ1
(14)
k 1
,
(15)
, k = cp / c;
k–
-
(10):
υ
–
,
/( · ).
(15)
(14),
:
-
s (T2 , υ2 )  s (T1 , υ1 )  0.
1(
,
.
υ
. 2)
,
,
,
3(
,
. 2)
3,
–
3
4,
,
.
.
υ3,
3.
4.
υ3 = υ4:
3
(14)
s (T3 , υ3 )  s (T4 , υ4 )  cυ ln
,
3
T3
.
T4
4,
,
s (T3 , υ3 )  s (T4 , υ4 ).
(16)
,
,
4
(16)
1
:
s (T3 , υ3 )  s (T1 , υ1 ).
130
(15)
(17)
3
,
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α, . .
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Δ ,
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(
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(
. 2).
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Δ ,
[8],
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υ-
β–
(
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1,
-
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131
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1.
-
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Δ ,
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Ɋɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɣ.
,
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-
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132
.
ȼɵɜɨɞɵ.
,
,
,
,
.
Ȼɢɛɥɢɨɝɪɚɮɢɱɟɫɤɢɣ ɫɩɢɫɨɤ
1.
, .
, .
.
2.
, Э.
3.
, . .
[
]:
/
4.
, . .
[
]/ . .
.
5.
, . .
[
]/ . .
.
6. Э
, . .
.:
, 1948. 420 .
7.
, .
. .
.
:
8.
, . .
[
[
, 2002. 461 .
[
] :
- , 1969. 139 .
]:
.
./ .
-
.
:
./ . .
.
.:
. .
.
. 1.
.:
-
. 2.
.:
-
. /
.:
.
, 1965. 750 .
, 1962. 1160 .
[
, 1962. 915 .
]:
.
[
] /
, 2010. 80 .
]/ . .
, . .
, . .
. 2013. № 6.1 (42). . 131–166.
. //
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133
***
The analysis of change
in the isolated thermodynamic system is lead at
presence of nonequilibrium processes of transfer of energy between its components in
the form of mechanical work.
The case when properties of components of system correspond to properties of
ideal gases is considered. Nonequilibrium processes it was caused by final speed of
movement of the surfaces dividing gases inside of system.
On the basis of the first law of thermodynamics and properties of ideal gas, without attraction of any additional data, it is proved, that total entropy the isolated system,
equal to the sum entropy its components, as a result of fulfilment of mechanical work
in nonequilibrium processes increases.
134