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2
. (1)
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gt
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T == H" 89,5c (2)
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2
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2
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(
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2
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( )
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2
,
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g�
()
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()
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2 2
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2
(4)
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g t0 + �
( )
)
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2
. (5)
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r r
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()
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?@8 ;N1>< ?>;>65=88 AB5@6=O. "0:8< >1@07><,
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mgl siną > k(2l siną - 2a )l cosą (3)
4>;6=> 2K?>;=OBLAO ?@8 ;N1>< 7=0G5=88 C3;0 ą 2 480?07>=5 >B 0 4> Ą 2 .
"0: :0: 2 MB>< 480?07>=5 siną > 0 , B> =5@025=AB2> (3) <>6=> ?5@5?<A0BL 2
2845
siną - � cosą
2kl ()
m > �" , (4)
g siną
a
345 >1>7=0G5=> � = . 0945< <0:A8<C< DC=:F88
l
siną )
( - � cosą
f (ą ) = = cosą - �ctgą . (5)
siną
KG8A;OO ?@>872>4=CN
�
f 2 (ą ) =- siną +
sin2 ą
8 ?@8@02=820O 55 : =C;N, ?>;CG05< 7=0G5=85 C3;0 ą* , ?@8 :>B>@>< DC=:F8O
(5) ?@8=8<05B <0:A8<0;L=>5 7=0G5=85
3
siną* = � . (6)
0945< :>A8=CA MB>3> C3;0
cosą* = 1 - sin2 ą* = 1 - �2 3
8 ?>4AB028< 2 =5@025=AB2> (4)
siną* - � cosą* 2kl �#1 � ś#
()
2kl
m > �" =-ź# cosą* =
ś#
�#
g siną* g siną* #
3 2
2kl
= 1 - �2 3
()
g
B0:, >:>=G0B5;L=K9 >B25B 7040G8 8<55B 284: AB5@6=8 >?@>:8=CBAO ?@8
3 2
2 3
�# ś#
2kl a
�# ś#
m > ś#1 -ź# .
ś# ź#
�# #
g l
�# #
><<5=B0@88 : 7040G5.
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@8AC=:5 ?>:070= ?@545;L=K9 A;CG09, A>>B25BAB2CNI89 =0945==><C @5H5=8N
7040G8. @0D8: ?>AB@>5= ?@8 � = 05 . B@8F0B5;L=K5 7=0G5=8O <><5=B0 A8;K
,
C?@C3>AB8 2 >1;0AB8 <0;KE C3;>2 A>>B25BAB2CNB A60B8N @578=:8.
2. >:065< B0:65 3@0D8: 8AA;54>20==>9 DC=:F88 f (ą ), ?>:07K20NI89, GB>
=0945==>5 7=0G5=85ą* 459AB28B5;L=> A>>B25BAB2C5B B>G:5 <0:A8<C<0.
3. >7<>6=> B0:65 @5H5=85 40==>9 7040G8 =0 >A=>20=88 0=0;870 7028A8<>AB8
?>B5=F80;L=>9 M=5@388 A8AB5<K >B C3;0 >B:;>=5=8O ?@8 @07;8G=KE 7=0G5=8OE
<0AA 3@C7>2
k 2
U = 2mgl cosą + 2l siną - 2a =
()
2
.
mg 2
ś#
= 2kl2 �# cosą - ( - �
siną ) ź#
ś#
�# #
kl
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8AG57=>25=88 MB>3> <8=8<C<0 A8AB5<0 B0:>3> ?>;>65=8O @02=>25A8O =5
8<55B.
8AC=>: ?>:07K205B 87<5=5=85 7028A8<>AB8 ?>B5=F80;L=>9 M=5@388 >B C3;0 ą
?@8 2>7@0AB0=88 C25;8G5=88 <0AAK 3@C7>2 (2 ?>@O4:5 2>7@0AB0=8O =><5@>2
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A>>B25BAB2CNI59 =0945==><C 3@0=8G=><C 7=0G5=8N <0AAK), <8=8<C<
>BACBAB2C5B.
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2.3 D>@<;5=85 1
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040G0 3
53:> 70<5B8BL, GB> C"t = �Q , �Q -
:>;8G5AB2> B5?;>BK, ?>;CG5==>5 307>< ?@8
87<5=5=88 B5<?5@0BC@K =0 25;8G8=C "t .
!;54>20B5;L=> ?;>I04L, ?>4 3@0D8:><
7028A8<>AB8 C(t ) G8A;5==> @02=0
:>;8G5AB2C ?>;CG5==>9 B5?;>BK. 0 CG0AB:0E
1 2 8 2 3 C > 0 8 "t > 0 , ?>MB><C
=0 MB8E CG0AB:0E 307 ?>;CG05B B5?;>BC >B
=03@520B5;O �Q > 0 . !;54>20B5;L=>,
()
:>;8G5AB2> ?>;CG5==>9 307>< B5?;>BK @02=>
C0 + 2C0 9
Q1 = 2 �" t2 - t1 = 3C0 t2 - t1 = R t2 - t1 . (1)
( ) ( ) ( )
2 2
>4AB0=>2:0 G8A;5==KE 7=0G5=89 ?@82>48B : @57C;LB0BC
9 9
Q1 = R t2 - t1 = �" 831�" 50 H" 1,9 :6 . (2)
,
( )
2 2
0 CG0AB:5 3 1 C > 0 , => "t < 0 , ?>MB><C =0 MB>< CG0AB:5 307 >B405B
B5?;>BC E>;>48;L=8:C �Q < 0 . >;8G5AB2> >B40==>9 B5?;>BK @02=>
()
3
Q2 = C0 t3 - t1 = R t3 - t1 . (3)
( ) ( )
2
> 7025@H5=88 2A53> ?@>F5AA0 1 2 3 1B5<?5@0BC@0 3070 ?@8=8<05B
?5@2>=0G0;L=>5 7=0G5=85, ?>MB><C 87<5=5=85 2=CB@5==59 M=5@388 @02=> =C;N,
A;54>20B5;L=>, @07=>ABL ?>;CG5==>9 8 >B40==>9 B5?;>BK @02=0 @01>B5
A>25@H5==>9 307><
3
A = Q1 - Q2 = C0 t2 - t1 = R t2 - t1 H" 062 :6 . (4)
,
( ) ( )
2
> >?@545;5=8N  40==>3> ?@>F5AA0 @025=
A 1
� = = . (5)
Q1 3
0:A8<0;L=0O B5<?5@0BC@0 3070 2 B>G:5 3, 0 <8=8<0;L=0O 2 B>G:5 1, ?>MB><C ?>
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B5<?5@0BC@ @025= (B5<?5@0BC@K 4>;6=K 1KBL ?5@52545=K 2 01A>;NB=CN H:0;C)
T3 - T1 t3 - t1 100
�max = = = H" 024 . (6)
,
T3 t3 + 273 150 + 273
B0:,  F8:;0 0@=>, ?@8 B5E 65 ?@545;L=KE B5<?5@0BC@0E, >:070;AO
<5=LH5, G5< 2 @0AA<0B@8205<>< ?@>F5AA5. 07@5H5=8O ?0@04>:A0 2 B><, GB>
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87>E>@8G5A:8< ?@>F5AA><.
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