8=A:0O 3>@>4A:0O >;8<?8040
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2003 3>4
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">G:0 42865BAO ?> >:@C6=>AB8 @048CA0 R A
?>AB>O==>9 ?> <>4C;N A:>@>ABLN V . ">G:0
=0G8=05B 42830BLAO 87 ?@>872>;L=>3> ?>;>65=8O A
r
?>AB>O==>9 ?> <>4C;N A:>@>ABLN U U < V ,
( )
?@8G5< 25:B>@ A:>@>AB8 B>G:8 , 2A5 2@5<O
=0?@02;5= =0 B>G:C . > :0:>9 B@05:B>@88 1C45B
42830BLAO B>G:0 ?> ?@>H5AB288 4>AB0B>G=>3>
4;8B5;L=>3> ?@><56CB:0 2@5<5=8? 0: 1C45B 2K3;O45BL MB0 B@05:B>@8O 2
A8AB5<5 >BAG5B0, A2O70==>9 A B>G:>9 ? '5<C 1C45B @02=> @0AAB>O=85 <564C
B>G:0<8? '5<C 1C45B @02=0 A:>@>ABL B>G:8 >B=>A8B5;L=> B>G:8 ?
2. «><=0B0
>445@60=85 =>@<0;L=>9 B5<?5@0BC@K 2>74CE0 2 68;KE ?><5I5=8OE O2;O5BAO
>G5=L 206=>9 ?@>1;5<>9 :0: 4;O 68;LF>2, B0: 8 4;O @01>B=8:>2 68;8I=>-
:><<C=0;L=>3> E>7O9AB20. ;O 87CG5=8O MB>9 ?@>1;5<K ?@>2545= A;54CNI89
<>45;L=K9 M:A?5@8<5=B. =CB@8 70:@KB>3> A>AC40 A 2>74CE>< @07<5AB8;8
=03@520B5;L, :>B>@K9 ?>445@68205BAO ?@8 ?>AB>O==>9 B5<?5@0BC@5 t0 .
"5<?5@0BC@0 =0@C6=>3> 2>74CE0 @02=0 t1. @>2545=K 87<5@5=8O 7028A8<>AB8
B5<?5@0BC@K 2>74CE0 2=CB@8 A>AC40 t >B =0@C6=>9 B5<?5@0BC@K t1, ?@8 42CE
@07;8G=KE 7=0G5=8OE B5<?5@0BC@K =03@520B5;O t0 . 57C;LB0BK MB8E 87<5@5=89
?@54AB02;5=K =0 3@0D8:0E.
0) !45;09B5 @07C<=K5 ?@54?>;>65=8O > ?@>F5AA0E B5?;>?5@540G8,
>1JOA=ONI85 ?>;CG5==K5 7028A8<>AB8;
1) ?>AB@>9B5 3@0D8: 7028A8<>AB8 B5<?5@0BC@K 2>74CE0 2=CB@8 A>AC40 t >B
=0@C6=>9 B5<?5@0BC@K t1, ?@8 B5<?5@0BC@5 =03@520B5;O t0 = 70°C ;
2) ?>AB@>9B5 3@0D8: 7028A8<>AB8 B5<?5@0BC@K 2>74CE0 2=CB@8 A>AC40 t >B
=0@C6=>9 B5<?5@0BC@K t1, ?@8 B5<?5@0BC@5 =03@520B5;O t0 = 70°C , 4;O B0:>3>
65 A>AC40, => B>;I8=0 AB5=>: :>B>@>3> C25;8G5=0 2 420 @070.
3. «8=7K
?B8G5A:0O A8AB5<0 A>AB>8B 87 42CE B>=:8E ;8=7, 3;02=K5 >?B8G5A:85 >A8
:>B>@KE A>2?040NB. 048CA ?5@2>9 ;8=7K r1 = 10A< , @048CA 2B>@>9 r2 = 30A< ,
, ,
D>:CA=>5 @0AAB>O=85 ?5@2>9 f1 = 10A< , 0 2B>@>9 f2 = 15A< . 8=7K
@0A?>;>65=K =0 @0AAB>O=88 BC = a = 50A< 4@C3 >B 4@C30. 0 >?B8G5A:>9 >A8
,
A8AB5<K =0 @0AAB>O=88 AB = l = 10A< >B ?5@2>9 ;8=7K @0A?>;>65=
87>B@>?=K9 B>G5G=K9 8AB>G=8: A25B0 , A 4@C3>9 AB>@>=K =0 @0AAB>O=88
CD = b = 10A< >B 2B>@>9 ;8=7K @0A?>;>65= M:@0=. #:068B5, :0:85 G0AB8
M:@0=0 1C4CB >A25I5=K. 0: 87<5=OBAO >A25I5==K5 >1;0AB8 M:@0=0, 5A;8
2B>@>N ;8=7C A<5AB8BL =0 @0AAB>O=85 x = 10A< ?5@?5=48:C;O@=> >?B8G5A:>9
,
>A8?
4. «>A:8.
25 >48=0:>2KE 4>A:8 ;560B =0 3>@87>=B0;L=>9 ?>25@E=>AB8, >4=0 =0 4@C3>9.
0AA0 :064>9 4>A:8 @02=0 m , :>MDD8F85=B B@5=8O <564C 4>A:0<8 8 <564C
=86=59 4>A:>9 8 3>@87>=B0;L=>9 ?>25@E=>ABLN @025= µ . >A:8 A2O70=K
=525A><>9 =5@0ABO68<>9 =8BLN, ?5@51@>H5==>9 G5@57 ;53:89 =5?>4286=K9
1;>:, 70:@5?;5==K9 =0 =5?>4286=>9 AB5=:5. 0:CN <8=8<0;L=CN
3>@87>=B0;L=> =0?@02;5==CN A8;C
A;54C5B ?@8;>68BL : =86=59 4>A:5,
GB>1K A428=CBL 55 A <5AB0?
:0:CN <8=8<0;L=CN
3>@87>=B0;L=> =0?@02;5==CN A8;C
A;54C5B ?@8;>68BL : 25@E=59 4>A:5,
GB>1K A428=CBL 55 A <5AB0?
8=A:0O 3>@>4A:0O >;8<?8040
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10 :;0AA.
1. «!8D>=
#7:0O B@C1:0 A ?;>I04LN ?>?5@5G=>3> A5G5=8O s 4;8=>9 l 8
<0AAK m A ?><>ILN :>@>B:>3> 381:>3> H;0=30 A>548=5=0 A
3>@87>=B0;L=> @0A?>;>65==>9 B@C1>9 B0:>3> 65 ?>?5@5G=>3>
A5G5=8O. 0 =86=5< :>=F5 B@C1K 70:@5?;5=0 =0A04:0 (<0AA0
:>B>@>9 m0 ), 87<5=ONI0O =0?@02;5=85 42865=8O 684:>AB8 =0
90° . > B@C15 ?@>?CA:0NB 684:>ABL ?;>B=>AB8 Á ,
4286CICNAO 2=CB@8 B@C1K A> A:>@>ABLN V . 0948B5 C3>;
>B:;>=5=8O B@C1:8 >B 25@B8:0;8 ?@8 42865=88 684:>AB8.
2. «(0@8:8
51>;LH85 <5B0;;8G5A:85 H0@8:8 <>3CB A:>;L78BL 157 B@5=8O
?> 4;8==><C =5?@>2>4OI5<C B>=:><C AB5@6=N. 0AA0 :064>3>
H0@8:0 @02=0 m .
1. 2C< H0@8:0< A>>1I8;8 >48=0:>2K5 ?>;>68B5;L=K5 70@O4K
+ q , =86=89 H0@8: 70:@5?8;8, 0 25@E=89 >B?CAB8;8. 0 :0:><
@0AAB>O=88 z0 @0A?>;>60BAO H0@8:8?
2. 2C< H0@8:0< A>>1I8;8 70@O4K Ä… q >48=0:>2K5 ?> 25;8G8=5,
=> ?@>B82>?>;>6=K5 ?> 7=0:C. 5@E=89, ?>;>68B5;L=>
70@O65==K9 70:@5?8;8, 0 =86=89 >B?CAB8;8. 0 :0:><
@0AAB>O=88 z1 @0A?>;>60BAO H0@8:8?
3. "@8 H0@8:0 (70@O4K 42CE, 25@E=8E @02=K + q , 0 =86=53> - q )
@0A?>;>68;8 =0 @0AAB>O=88 z0 (A<. ?.1) @C3 >B 4@C30.
&5=B@0;L=K9 70:@5?8;8, 0 :@09=85 >B?CAB8;8. 0 :0:8E @0AAB>O=8OE
@0A?>;>60BAO H0@8:8?
3. «-;5:B@>;8B
:N25BC, 8<5NICN D>@<C ?0@0;;5;5?8?540 2KA>B>9
h = 10A< 8 B>;I8=>9 a = 10A< , 24>;L 55 1>:>2KE AB5=>:
,
?><5AB8;8 425 <5B0;;8G5A:85 ?;0AB8=:8 2KA>B>9
h0 = 70A< , ?>4:;NG5==K5 : 8AB>G=8:C ?>AB>O==>3>
,
=0?@O65=8O U = 220B . 0B5< :N25BC ?>;=>ABLN
70?>;=8;8 2>4>9, =0E>4OI59AO ?@8 B5<?5@0BC@5
t0 = 20°C . >AB@>9B5 3@0D8:8 7028A8<>AB59 >B 2@5<5=8
0)B5<?5@0BC@K 2>4K; 1) 2KA>BK C@>2=O 2>4K 2 :N25B5.
#45;L=>5 M;5:B@8G5A:>5 A>?@>B82;5=85 =0;8B>9 2>4K @02=> Å‚ = 20Å"102 < Å" <
,
:3
8 =5 7028A8B >B B5<?5@0BC@K, ?;>B=>ABL 2>4K Á = 10Å"103 , 55 C45;L=0O
,
<3
6
B5?;>5<:>ABL c = 42 Å"103 , C45;L=0O B5?;>B0 ?0@>>1@07>20=8O
,
:3 Å" 3 @04
6
= 23Å"106 , 0B<>AD5@=>5 402;5=85 =>@<0;L=>5, 8A?0@5=85< 2>4K 4>
,
:3
=0G0;0 :8?5=8O <>6=> ?@5=51@5GL.
4. «0B>:
0H8=0 4;O C?;>B=5=8O 3@C=B0 A>AB>8B 8 :>@?CA0 8 42CE >48=0:>2KE
>4=>@>4=KE F8;8=4@8G5A:8E :0B:>2. 0AA0 :>@?CA0 (A 8<5NI8<AO 2=CB@8
>1>@C4>20=85<) @02=0 M , <0AA0 :064>3> :0B:0 m , @048CA :0B:0 - R ,
@0AAB>O=85 <564C >AO<8 :0B:>2 - L , F5=B@ <0AA :>@?CA0 =0E>48BAO =0 A5@548=5
@0AAB>O=8O <564C >AO<8 :0B:>2, =0 2KA>B5 @02=>9 @048CAC :0B:>2 >B 8E >A59.
E>45 A1>@:8 <0H8=K 1K;0 4>?CI5=0 >H81:0, 2 @57C;LB0B5 :>B>@>9 >:070;>AL,
GB> :0B:8 2@0I0NBAO 2 ?@>B82>?>;>6=K5 AB>@>=K (=0?@02;5=85 2@0I5=8O
<>6=> ?5@5:;NG0BL). #3;>20O A:>@>ABL 2@0I5=8O :0B:>2 ?>AB>O==0 8 @02=0 É0 .
>MDD8F85=B B@5=8O <564C :0B:0<8 8 ?>25@E=>ABLN ?>AB>O=5= 8 @025= µ .
0. 0H8=0 @0A?>;>68;8 =0 3>@87>=B0;L=>9
?>25@E=>AB8, =0 :>@?CA CAB0=>28;8 =51>;LH>9
3@C7 (=0?@8<5@, 2>48B5;L) <0AAK m0 , =0
@0AAB>O=88 x >B >A8 <0H8=K. 0948B5 70:>=
42865=8O <0H8=K.
1. 0H8=C @07<5AB8;8 =0 A:;>=, A>AB02;ONI59
<0;K9 C3>; Ä… A 3>@87>=B><, B0: GB> >A8 :0B:>2
3>@87>=B0;L=K. @8 :0:8E CA;>28OE <0H8=0
A<>65B ?>4=8<0BLAO ?> A:;>=C?
2. 0H8=0 >:070;0AL =0 4;8==>< A:;>=5,
A>AB02;ONI5< C3>; <0;K9 Ä… A
3>@87>=B><, B0:, GB> >A8 :>;5A =0?@02;5=K
24>;L A:;>=0. @57C;LB0B5 G5@57
=5:>B>@K9 ?@><56CB>: 2@5<5=8 <0H8=0
=0G0;0 A>A:0;L7K20BL A ?>AB>O==>9
A:>@>ABLN. ?@545;8B5 MBC A:>@>ABL.
8=A:0O 3>@>4A:0O >;8<?8040
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11 :;0AA.
1. «$>B>B>: . ;8==0O ?;>A:0O ?;0AB8=:0
4;8=>9 l 8 H8@8=>9 a , A>?@>B82;5=85 :>B>@>9
@02=> R0 , 2:;NG5=0 ?>A;54>20B5;L=> 2
M;5:B@8G5A:CN F5?L, A>45@60ICN 8AB>G=8:
?>AB>O==>3> =0?@O65=8O U0 8 420 >48=0:>2KE
@578AB>@0 A>?@>B82;5=8O<8 R . ;0AB8=:0
>A25I05BAO ?0@0;;5;L=K< <>=>E@><0B8G5A:8<
A25B>2K< ?>B>:>< A 4;8=>9 2>;=K , 8=B5=A82=>ABL :>B>@>3> @02=0 I0 . >4
459AB285< MB>3> 87;CG5=8O ?@>8AE>48B D>B>MDD5:B, :20=B>20O MDD5:B82=>ABL
:>B>@>3> @02=0 · . 0948B5 A8;K B>:>2 G5@57 :064K9 @578AB>@. =CB@5==8<
A>?@>B82;5=85< 8AB>G=8:0 ?@5=51@5GL; AG8B0BL, GB> ?;>B=>ABL D>B>B>:0
?>AB>O==0 =0 2A59 ?;0AB8=5, 8 2K;5B52H85 M;5:B@>=K =0 ?;0AB8=C =5
2>72@0I0NBAO. <:>ABL 8AB>G=8:0 <>6=> AG8B0BL 15A:>=5G=> 1>;LH>9.
@8<5G0=8O: - ?>4 8=B5=A82=>ABLN A25B0 2 40==>< A;CG05 ?>=8<05BAO
M=5@38O, ?5@5=>A8<0O A25B>2K< ?>B>:>< 2 548=8FK 2@5<5=8 G5@57 ?;>I04:C
548=8G=>9 ?;>I048, @0A?>;>65==CN ?5@?5=48:C;O@=> A25B>2><C ?>B>:C;
:20=B>20O MDD5:B82=>ABL D>B>MDD5:B0 - >B=>H5=85 G8A;0 M;5:B@>=>2,
2K;5B52H8E 87 ?;0AB8=K, : G8A;C D>B>=>2, ?>?02H8E =0 ?;0AB8=C.
2. «0AB>9. %>@>H> 8725AB=>, GB> 4;O 1>;LH8=AB20 B@CI8EAO ?>25@E=>AB59
:>MDD8F85=B B@5=8O ?>:>O ?@52KH05B :>MDD8F85=B B@5=8O A:>;L65=8O.
#25;8G5=85 A8;K B@5=8O ?>:>O ?> A@02=5=8N A A8;>9 B5@=8O A:>;L65=8O =>A8B
=0720=85 «O2;5=85 70AB>O. -B> O2;5=85 ?@82>48B : @O4C 8=B5@5A=KE
?>A;54AB289, =0?@8<5@, 53> =0;8G85< >1JOA=O5BAO A:@8? 425@=KE ?5B5;L,
72CG0=85 AB@C=K A:@8?:8 8 4@.
;O 87CG5=8O O2;5=8O 70AB>O A>740=0 A;54CNI0O CAB0=>2:0. 0
4286CICNAO A ?>AB>O==>9 A:>@>ABLN 3>@87>=B0;L=CN ;5=BC B@0=A?>@B5@0
?><5I5= 1@CA>:, ?@8:@5?;5==K9 A ?><>ILN ;5:3>@0ABO68<>9 ?@C68=K :
=5?>4286=><C C?>@C. @8 MB>< 1@CA>: A>25@H05B =570BCE0NI85 :>;510=8O.
). 1JOA=8B5 <5E0=87< 2>7=8:=>25=8O =570BCE0NI8E :>;510=89.
). 0948B5 <0:A8<0;L=CN 8 <8=8<0;L=CN 45D>@<0F88 ?@C68=K 2 ?@>F5AA5
42865=8O 1@CA:0.
). ?@545;8B5 ?5@8>4 :>;510=89 1@CA:0.
( )
). 0948B5 70:>= 42865=8O 1@CA:0 x t 8 ?>AB@>9B5 53> 3@0D8: (2 :0G5AB25
:>>@48=0BK x 8A?>;L7C9B5 45D>@<0F8N ?@C68=K).
0@0<5B@K CAB0=>2:8: <0AA0 1@CA:0 m = 1003 ; :>MDD8F85=B 65AB:>AB8
A<
,
?@C68=K k = 10 ; A:>@>ABL 42865=8O ;5=BK B@0=A?>@B5@0 v0 = 50 ;
< A
:>MDD8F85=B B@5=8O A:>;L65=8O 1@CA:0 > ;5=BC µ = 025; :>MDD8F85=B B@5=8O
,
?>:>O 1@CA:0 > ;5=BC µ0 = 030 .
,
3. «K;L. ;>A:89 :>=45=A0B>@ >1@07>20= 42C<O
?0@0;;5;L=K<8 <5B0;;8G5A:8<8 ?;0AB8=0<8.
0AAB>O=85 <564C ?;0AB8=0<8 h 7=0G8B5;L=> <5=LH5
@07<5@>2 ?;0AB8=. ;>I04L :064>9 ?;0AB8=K @02=0
S . >=45=A0B>@ ?>4:;NG5= : 8AB>G=8:C ?>AB>O==>3>
=0?@O65=8O, 25;8G8=0 :>B>@>3> @02=0 U . 564C
?;0AB8=0<8 =0E>48BAO <5;:0O <5B0;;8G5A:0O ?K;L. 064CN ?K;8=:0
?@54AB02;O5B A>1>9 <5B0;;8G5A:89 H0@8: @048CA0 r 8 <0AAK m , A@54=OO
:>=F5=B@0F8O ?K;8=>: <564C ?;0AB8=0<8 @02=0 n .
) 0948B5 7=0G5=85 A8;K B>:0 2 F5?8.
) F5=8B5 2@5<O, 2 B5G5=85 :>B>@>3> =0?@O65=85 <564C ?;0AB8=0<8
C<5=LH8BAO =0 · = 1% ?>A;5 @07<K:0=8O F5?8.
59AB285< A8;K BO65AB8 ?@5=51@5GL, 2>74CE <564C ?;0AB8=0<8
>BACBAB2C5B. #40@K ?K;8=>: > ?;0AB8=K AG8B0BL 01A>;NB=> =5C?@C38<8.
4. «2>9=0O 8=B5@D5@5=F8O
;>A:0O <>=>E@><0B8G5A:0O A25B>20O 2>;=0 A 4;8=>9 2>;=K ?0405B
=>@<0;L=> =0 =5?@>7@0G=K9 M:@0= 2 :>B>@>< ?@>45;0=K 425 C7:85
?0@0;;5;L=K5 I5;8, =0E>4OI85AO =0 @0AAB>O=88 2h1. 0 @0AAB>O=88 l1 >B
?5@2>3> M:@0=0 @0A?>;>65= 2B>@>9 =5?@>7@0G=K9 M:@0=, 2 :>B>@>< B0:65
?@>45;0=K 425 ?0@0;;5;L=KE I5;8, =0E>4OI85AO =0 @0AAB>O=88 2h2 4@C3 >B
4@C30, ?@8G5< MB8 I5;8 ?0@0;;5;L=K I5;O< 2 ?5@2>< M:@0=5. 0 @0AAB>O=88 l2
>B 2B>@>3> M:@0=0 @0A?>;>65= M:@0=, =0 :>B>@>< =01;N40NB
8=B5@D5@5=F8>==CN :0@B8=C. A5 M:@0=K ?0@0;;5;L=K 4@C3 4@C3C, I5;8
@0A?>;>65=K A8<<5B@8G=> >B=>A8B5;L=> >A8 A8AB5<K.
) 0948B5 @0A?@545;5=85 >A25I5==>AB8 =0 A25B0 =0 ?>A;54=5< M:@0=5, :0:
DC=:F8N :>>@48=0BK x - @0AAB>O=8O >B >A8 A8AB5<K.
) >?CAB8<, GB> >?B8G5A:0O A8AB5<0 8A?>;L7C5BAO 4;O 87<5@5=8O 4;8=K 2>;=K
?040NI53> A25B0, 4;O G53> ?@>2>48BAO 87<5@5=85 7028A8<>AB8 A25B0 =0
?>A;54=5< M:@0=5 2 D8:A8@>20==>9 B>G:5 x 2 7028A8<>AB8 >B @0AAB>O=8O 2h2
<564C I5;O<8 2> 2B>@>< M:@0=5. :0:>9 B>G:5 x 2K 1K @5:><5=4>20;8
?@>2>48BL B0:85 87<5@5=8O, GB>1K, A >4=>9 AB>@>=K, ?>3@5H=>ABL >?@545;5=8O
4;8=K 2>;=K 1K;0 <8=8<0;L=0, 0 A 4@C3>9, 8=B5@?@5B0F8O @57C;LB0B>2 1K;0 =5
A;8H:>< A;>6=0?
@8 @0AG5B0E CG8BK209B5, GB> @0AAB>O=8O <564C I5;O<8 A>AB02;ONB 4>;8
<8;;8<5B@0, 0 @0AAB>O=8O <564C M:@0=0<8 - =5A:>;L:> <5B@>2.
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