5A?C1;8:0=A:0O D878G5A:0O >;8<?8040
(III MB0?).
2005 3>4.
9 :;0AA.
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;O ?>3@C7:8 <0AA82=KE 1>G5: =0
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@048CA 20;0 ;5154:8 r . 5154:0 ?>4=8<05B 1>G:C <0AA>9 m =0 2KA>BC h ?> =0:;>==>9
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345 Ä… =07K205BAO :>MDD8F85=B>< ;8=59=>3> @0AH8@5=8O.
G5284=>, GB> ?@8 =03@520=88 C25;8G8205BAO 8 >1J5< 1@CA:0, ?@8G5< 53> >1J5< 7028A8B
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#25@5=K, GB> 2K 7=0:><K A CAB@>9AB2>< @BCB=>3> B5@<><5B@0:
4;8==0O AB5:;O==0O F8;8=4@8G5A:0O B@C1:0 A>548=5=0 A =51>;LH8<
AB5:;O==K< 10;;>=><, 70?>;=5==K< @BCBLN. @8 =03@520=88 @BCBL
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87<5@O5BAO ?> H:0;5, :>B>@0O ?@>3@04C8@>20=0 2 3@04CA0E &5;LA8O.
 @0AA<0B@8205<>< B5@<><5B@5 ?@8 B5<?5@0BC@5 t0 = 0,0°C :
- 2=CB@5==89 >1J5< 10;;>=0 V0 = 200<<3 ;
- 2=CB@5==89 480<5B@ B@C1:8 d0 = 0,20<< ;
- @BCBL ?>;=>ABLN 70?>;=O5B 10;;>=G8:, => =5 70E>48B 2 B@C1:C;
- :>MDD8F85=B >1J5<=>3> @0AH8@5=8O @BCB8 @025= ² = 1,8Å"10-4°C-1 ;
-1
- :>MDD8F85=B ;8=59=>3> @0AH8@5=8O AB5:;0 Ä… = 3,0 Å"10-6°C .
3.3 @5=51@530O B5?;>2K< @0AH8@5=85< AB5:;0, ?>AB@>9B5 3@0D8:
7028A8<>AB8 2KA>BK C@>2=O @BCB8 2 B@C1:5 h (2 <<) >B 87<5@O5<>9 B5<?5@0BC@K t° (2
3@04CA0E &5;LA8O).
3.4 CABL B5@<><5B@ ?@>3@04C8@>20= 157 CG5B0 B5?;>2>3> @0AH8@5=8O AB5:;0 (:0: C:070=>
2 ?@54K4CI5< ?C=:B5 3.2). 0948B5 >B=>A8B5;L=CN ?>3@5H=>ABL ?>:070=8O B0:>3>
B5@<><5B@0, A2O70==CN A B5?;>2K< @0AH8@5=85< AB5:;0, ?@8 B5<?5@0BC@5 t1 = 10°C .
040G0 4. «><>65< "5E0AC
 "5E0A5 2K?0; A=53, 8 «>=8 =5 7=0NB, GB> A =8< 45;0BL!
;O ?;02;5=8O A=530 A>740=> A;54CNI55 A=53>?;028;L=>5
CAB@>9AB2>.  3;C1>:CN O<C H8@8=>9 a =1,0< 8 4;8=>9
b = 5,0< ?>AB>O==> 70AK?0NB A=53, =0E>4OI89AO ?@8 B5<?5@0BC@5
?;02;5=8O. 25 ?@>B82>?>;>6=K5 1>:>2K5 AB5=K O<K
<5B0;;8G5A:85 8 ?>4A>548=5=K : 8AB>G=8:C ?>AB>O==>3> =0?@O65=8O
U = 1,0 : .  4=5 O<K 8<55BAO :@0= 4;O A;820 B0;>9 2>4K 8
?>445@60=8O 53> =0 ?>AB>O==>< C@>2=5 h =1,5< .
%0@0:B5@8AB8:8 2>4K 8725AB=K:
:3
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<3
2
46
- C45;L=0O B5?;>B0 ?;02;5=8O A=530  = 3,3Å"105 ;
:3
- C45;L=>5 M;5:B@8G5A:>5 A>?@>B82;5=85 B0;>9 2>4K Á =1,0 < Å" < ;
- ?@>2>48<>ABLN A=530 <>6=> ?@5=51@5GL.
4.1 ?@545;8B5 ?@>872>48B5;L=>ABL (>1J5< B0;>9 2>4K 2 548=8FC 2@5<5=8) 40==>9
CAB0=>2:8.
 =5:>B>@K9 <><5=B 2@5<5=8
A;82=>9 :@0= 70A>@8;AO, 8 C@>25=L
2>4K 2 O<5 AB0; @57:> =0@0AB0BL.
028A8<>ABL C@>2=O 2>4K >B 2@5<5=8
h(t) ?>:070=0 =0 3@0D8:5.
4.2 1JOA=8B5 ?@82545==CN
7028A8<>ABL, 409B5 55 >?8A0=85 =0
«O7K:5 D>@<C; 8 C@02=5=89.
4.3 0 :0:>5 2@5<O 2>40 70?>;=8B 2AN
O<C, 5A;8 55 3;C18=0 H = 6,0< ?
5A?C1;8:0=A:0O D878G5A:0O >;8<?8040
(III MB0?).
2005 3>4.
10 :;0AA.
040G0 1. «"@0=A?>@B5@
;O <5E0=8G5A:>3> A=OB8O 3>B>2KE 8745;89 A
;5=BK B@0=A?>@B5@0, 4286CI59AO 3>@87>=B0;L=> A>
A:>@>ABLN V , 8A?>;L7C5BAO =5?>4286=0O
25@B8:0;L=0O =0?@02;ONI0O ?5@5:;048=0,
CAB0=>2;5==0O ?>4 C3;>< Ä… =0 ;5=B5. >MDD8F85=B
B@5=8O 8745;89 > ;5=BC B@0=A?>@B5@0 @025= µ1, 0 > =0?@02;ONICN ?5@5:;048=C  µ2 .
1.1 @8 :0:>< <8=8<0;L=>< C3;5 Ä…min 8745;8O 1C4CB A>A:0;L7K20BL A ;5=BK
B@0=A?>@B5@0?
1.2 0948B5 CAB0=>282HCNAO A:>@>ABL u 42865=8O 8745;89 24>;L =0?@02;ONI59.
040G0 2. «8?5=85
@8 B5<?5@0BC@5 100°C 8 =>@<0;L=>< 0B<>AD5@=>< 402;5=88 A ?>25@E=>AB8
2>4K 70 2@5<O t =1,0c 8A?0@O5BAO N = 5 Å"106 <>;5:C;O@=KE A;>52 2>4K. ;>B=>ABL
:3 :3
2>4O=>3> ?0@0 ?@8 MB8E CA;>28OE @02=0 Á = 0,60 , ?;>B=>ABL 2>4K Á0 = 1,0 Å"103 .
<3 <3
@8 :8?5=88 8A?0@5=85 ?@>8AE>48B =5 B>;L:> A> A2>1>4=>9 ?>25@E=>AB8, => 8
«2=CB@L 684:>AB8, B.5. 2 ?C7K@L:8.
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2
345 Á0 - ?;>B=>ABL 2>4K, v - A:>@>ABL 42865=8O ?C7K@L:0 S - <0:A8<0;L=0O ?;>I04L
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2.2 >AB@>9B5 3@0D8: 7028A8<>AB8 A:>@>AB8 2A?;KB8O ?C7K@L:0 >B 2@5<5=8 v(t), =0G8=0O
>B <><5=B0 53> 70@>645=8O.
2.3 CABL ?C7K@5: 70@>48;AO 21;878 4=0 :0AB@N;8 A :8?OI59 2>4>9, C@>25=L :>B>@>9
h = 25A< . F5=8B5 @048CA rmax ?C7K@L:0 C ?>25@E=>AB8 2>4K.
040G0 3. «8M;5:B@8:, 8;8 ?@>2>4=8:?
;>A:89 :>=45=A0B>@ >1@07>20= 42C<O ?0@0;;5;L=K<8 ?;0AB8=0<8
?;>I04LN S = 25A<2 :0640O, @0A?>;>65==K<8 =0 @0AAB>O=88 h = 2,0<<
4@C3 >B 4@C30. 564C >1:;04:0<8 :>=45=A0B>@0 @0A?>;>65=0 ?;0AB8=:0
h
B>;I8=>9 , 8<5NI0O BC 65 ?;>I04L, 873>B>2;5==0O 87 <0B5@80;0 A
2
48M;5:B@8G5A:>9 ?@>=8F05<>ABLN µ = 2,5 8 C45;L=K< M;5:B@8G5A:8<
A>?@>B82;5=85< Á = 1,0 Å"1010 < Å" < . >=45=A0B>@ ?>4:;NG5= : 8AB>G=8:C
?>AB>O==>3> =0?@O65=8O U0 = 5,0: G5@57 GC2AB28B5;L=K9 0<?5@<5B@.
3.1 >AB@>9B5 ?@8<5@=K5 3@0D8:8 7028A8<>AB8 70@O40 :>=45=A0B>@0 8 A8;K B>:0 G5@57
0<?5@<5B@ >B 2@5<5=8 ?>A;5 70<K:0=8O :;NG0.
3.2 F5=8B5 E0@0:B5@=>5 2@5<O ACI5AB2>20=8O B>:0 2 F5?8.
3.3 0:>5 :>;8G5AB2> B5?;>BK 2K45;8BAO 2 ?;0AB8=:5 2=CB@8 :>=45=A0B>@0 70 2@5<O
ACI5AB2>20=8O B>:0 2 F5?8?
$
-;5:B@8G5A:0O ?>AB>O==0O µ0 = 8,85 Å"10-12 .
<
040G0 4. «;>A:0O 5<;O
@52=85 3@5:8 AG8B0;8, GB> 5<;O O2;O5BAO
?;>A:8< 48A:><, 2@0I0NI8<AO 2>:@C3 A2>59 >A8.
@8<5< 8 <K, GB> 5<;O O2;O5BAO ?;>A:8< 48A:><
4>AB0B>G=> 1>;LH>3> @048CA0 (A:065<, 1>;55 40 000 :<).
C45< B0:65 AG8B0BL, GB> ?5@8>4 >1@0I5=8O 48A:0
2>:@C3 A2>59 >A8 @025= >4=8< ACB:0<. !@54=NN
?;>B=>ABL <0B5@80;0 48A:0 ?@8<5< @02=>9 A@54=59
:3
?;>B=>AB8 5<;8 Á = 5,5 Å"103 .
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@028B0F8>==0O ?>AB>O==0O @02=0 G = 6,67 Å"10-11 .
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4
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F5=B@5. ">G:0 ?5@5A5G5=8O >A8 2@0I5=8O ?;0=5BK A ?>25@E=>ABLN
48A:0 O2;O5BAO A525@=K< ?>;NA>< N . 0;55 0=0;>38G=>: ;N1CN
@0480;L=CN ?@O<CN, 2KE>4OICN 87 A525@=>3> ?>;NA0 1C45<
=07K20BL <5@8480=><. 53:> 4>3040BLAO, GB> N6=>3> ?>;NA0 S , :0: B0:>2>3>, =0 ?;>A:>9
?;0=5B5 =5B  53> @>;L 83@0NB 2A5 B>G:8 :@0O 48A:0. !>>B25BAB25==>, >:@C6=>AB8, B>G:8
:>B>@KE =0E>4OBAO =0 @02=>< @0AAB>O=88 >B ?>;NA0, =07>25< ?0@0;;5;O<8. 2865=85 ?>
?0@0;;5;O< 2 =0?@02;5=88 2@0I5=8O 5<;8 1C45B A>>B25BAB2>20BL 42865=8N =0 2>AB>:
( E ), 0 2 ?@>B82>?>;>6=>< =0?@02;5=88  =0 70?04 (W ). CABL D8=K =0E>4OBAO 2 B>G:5
A , @0A?>;>65==>9 =0 @0AAB>O=88 r0 = 4,0 Å"103 :< >B A525@=>3> ?>;NA0 N .
4.1 0:>9 4>;6=0 1KBL B>;I8=0 h MB>3> 48A:0, GB>1K CA:>@5=85 A2>1>4=>3> ?045=8O =0
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A525@=>< ?>;NA5 N 1K;> g = 9,8 ?
A2
4.2 ;O A2O78 A 68B5;O<8 «4@C3>9 AB>@>=K ?;>A:>9 5<;8 24>;L >A8 55 2@0I5=8O
?@>1C@5=0 A:2>7=0O B>=:0O H0EB0. A;8 157 =0G0;L=>9 A:>@>AB8 2 H0EBC >?CAB8BL
:0<5H5:, B> >=, ?@>94O A:2>7L H0EBC, >:065BAO =0 4@C3>9 AB>@>=5 5<;8. 0948B5
<0:A8<0;L=CN A:>@>ABL Åmax :0<5H:0 ?@8 B0:>< 42865=88. !8;>9 A>?@>B82;5=8O 2>74CE0
?@5=51@5GL.
4.3 ;O A2O78 A 68B5;O<8 «A2>59 AB>@>=K ?;>A:>9 5<;8 87 D8= A ?><>ILN
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AC?5@:0B0?C;LBK ?@>872>48BAO 2KAB@5; «A=0@O4>< A =0G0;L=>9 A:>@>ABLN Å0 = 100
A
?>4 C3;>< Ä… = 45° : 3>@87>=BC. !8;>9 A>?@>B82;5=8O 2>74CE0 ?@5=51@5GL.
0) =0948B5 25;8G8=C 8 =0?@02;5=85 A<5I5=8O " S A=0@O40 >B <5@8480=0 70 2@5<O
53> ?>;5B0 ?@8 2KAB@5;5 24>;L <5@8480=0 (@0AA<>B@8B5 420 A;CG0O).
1) =0948B5 25;8G8=C 8 =0?@02;5=85 A<5I5=8O " S A=0@O40 >B ?0@0;;5;8 70 2@5<O
53> ?>;5B0 ?@8 2KAB@5;5 24>;L ?0@0;;5;8 (@0AA<>B@8B5 420 A;CG0O).
5A?C1;8:0=A:0O D878G5A:0O >;8<?8040
(III MB0?).
2005 3>4.
11 :;0AA.
040G0 1. «%>@>H> ;8 K 7=05B5 A8;C B@5=8O?
1.0 ">=:>AB5==K9 F8;8=4@ @048CA0 R 8 <0AAK m (:>B>@0O
@02=><5@=> @0A?@545;5=0 ?> 1>:>2>9 ?>25@E=>AB8 F8;8=4@0)
<>65B 2@0I0BLAO 157 2>:@C3 =5?>4286=>9 >A8.  1>:>2>9
r
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=0?@02;5==CN ?> :0A0B5;L=>9 : ?>25@E=>AB8. >:068B5, GB>
87<5=5=85 C3;>2>9 A:>@>AB8 É 2@0I5=8O F8;8=4@0 ?>4G8=O5BAO
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8A?>;L7>20BL 53> 2 40;L=59H5<. @><5 B>3>, =0?><8=05<, GB> ?;>A:>?0@0;;5;L=>5
42865=85 B25@4>3> B5;0 <>6=> ?@54AB028BL 2 2845 AC<<K ?>ABC?0B5;L=>3> 42865=8O
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5
1.1 ">=:>AB5==CN F8;8=4@8G5A:CN B@C1:C @048CA0 R @0A:@CB8;8 4> C3;>2>9 A:>@>AB8
É0 8 0::C@0B=> ?>;>68;8 =0 3>@87>=B0;L=CN ?>25@E=>ABL
(157 =0G0;L=>9 ?>ABC?0B5;L=>9 A:>@>AB8). 0948B5 A:>@>ABL
CAB0=>282H53>AO 42865=8O >A8 F8;8=4@0. "@5=85< :0G5=8O
?@5=51@5GL.
1.2 51>;LH>9 ?@O<>C3>;L=K9 1@CA>: <0AAK m =1,0:3 =0E>48BAO =0 3>@87>=B0;L=>9
?>25@E=>AB8. >MDD8F85=B B@5=8O <564C 1@CA:>< 8
?>25@E=>ABLN @025= µ = 0,20 .  1@CA:C ?@8:;04K20NB
?>AB>O==CN 3>@87>=B0;L=> =0?@02;5==CN A8;C F .
>AB@>9B5 3@0D8: 7028A8<>AB8 <>4C;O CA:>@5=8O 1@CA:0 >B
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1.3 0 3>@87>=B0;L=>9 ?>25@E=>AB8 @0A?>;>65= 1@CA>: >MDD8F85=B B@5=8O <564C
1@CA:>< 8 ?>25@E=>ABLN @025= µ = 0,20 . O4>< A
1@CA:>< @0A?>;030NB A8;L=> @0A:@CG5==K9
B>=:>AB5==K9 F8;8=4@ <0AAK m1 = 1,0:3 , 480<5B@
:>B>@>3> @025= 2KA>B5 1@CA:0. >MDD8F85=B
B@5=8O <564C 1>:>2>9 ?>25@E=>ABLN F8;8=4@0 8
3>@87>=B0;L=>9 ?>25@E=>ABLN, 0 B0:65 A ?>25@E=>ABLN 1@CA:0 @025= µ = 0,20 .
@8 :0:>9 <0:A8<0;L=>9 <0AA5 1@CA:0 F8;8=4@ A<>65B A428=CBL 53> A <5AB0?
'5<C 1C45B @02=> CA:>@5=85 1@CA:0, 5A;8 53> <0AA0 m2 = 0,10:3 ?
1.4 0 3>@87>=B0;L=>9 ?>25@E=>AB8 ?>:>8BAO
B>=:>AB5==K9 F8;8=4@. O4>< A =8< 0::C@0B=> :;04CB
B0:>9 65 F8;8=4@, => A8;L=> @0A:@CG5==K9 2>:@C3
A>1AB25==>9 >A8. >MDD8F85=BK B@5=8O <564C
F8;8=4@0<8 8 ?>25@E=>ABLN, 0 B0:65 <564C 1>:>2K<8
?>25@E=>ABO<8 F8;8=4@>2 >48=0:>2K 8 @02=K
µ = 0,20 . ! :0:8<8 CA:>@5=8O<8 =0G=CB 42830BLAO MB8 F8;8=4@K?
040G0 2. «%>@>H> ;8 K 7=05B5 70:>= ?@5;><;5=8O A25B0?
2.1 >:070B5;L ?@5;><;5=8O 2>74CE0 7028A8B :0: >B B5<?5@0BC@K, B0: 8 >B
402;5=8O. C45< AG8B0BL, GB> 2 =0H8E CA;>28OE ?>:070B5;L ?@5;><;5=8O 7028A8B B>;L:>
>B B5<?5@0BC@K, ?@8G5< MB0 7028A8<>ABL 8<55B 284
a
n = 1+ , (1)
T
;O 2>74CE0 ?@8 =>@<0;L=>< 402;5=88 ?>AB>O==0O a H" 8,6 Å"10-2 K .
>74CE =04 4>@>3>9 ?>4 459AB285< A>;=5G=KE ;CG59 @07>3@5205BAO, 87-70 G53>
ACE>9 0AD0;LB <>65B :070BLAO «<>:@K<. CABL 2 4>AB0B>G=> B>=:>< A;>5 =04 4>@>3>9
B5<?5@0BC@0 2>74CE0 ?@52KH05B A@54=NN B5<?5@0BC@C t0 = 17°C =0 25;8G8=C "t . 0
=5:>B>@>< <8=8<0;L=>< @0AAB>O=88 S >B A51O =01;N40B5;L <>65B 2845BL «;C68 =0
4>@>35.
1JOA=8B5 ?>O2;5=85 «;C6.
>AB@>9B5 3@0D8: 7028A8<>AB8 S("t).
;07 =01;N40B5;O =0E>48BAO =0 2KA>B5 h = 1,0< >B 4>@>38
6
 ;O <>45;8@>20=8O <8@060 2 ;01>@0B>@88 55 @07<5@K O2=> =54>AB0B>G=K,
?>MB><C 2>74CE «>AB@>C<=> <>6=> 70<5=8BL =0 :CA>: >@30=8G5A:>3> AB5:;0,
?>:070B5;L ?@5;><;5=8O :>B>@>3> 3>@074> A8;L=55 7028A8B >B B5<?5@0BC@K.
 :0G5AB25 8AB>G=8:0 A25B0 8A?>;L7C5BAO B>=:0O A25BOI0OAO =8BL S .  40;L=59H5<
@0AA<0B@8209B5 ;CG8:
0) 84CI85 ?>4 <0;K<8 C3;0<8 : >A8 A8AB5<K 8 =0 <0;>< @0AAB>O=88 >B =55
(?0@0:A80;L=>5 ?@81;865=85);
1) ;CG8 2 ?;>A:>AB8, A>45@60I59 >AL A8AB5<K, 8 ?5@?5=48:C;O@=>9 =8B8.
2.2 0 @0AAB>O=88 a = 40A< >B 8AB>G=8:0
@0A?>;>68;8 B>=:CN A>18@0NICN ;8=7C A
D>:CA=K< @0AAB>O=85< F = 20A< . 0 :0:><
@0AAB>O=88 b >B ;8=7K A;54C5B
@0A?>;>68BL M:@0=, GB>1K =0 =5< 1K;>
G5B:>5 87>1@065=85 =8B8?
2.3 5 <5=OO ?>;>65=85 8AB>G=8:0 8 ;8=7K,
2?;>B=CN : 8AB>G=8:C @0A?>;>68;8
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3> 4;8=0 l = 20A< , ?>:070B5;L
?@5;><;5=8O n0 = 1,5 .
0 :0:>< @0AAB>O=88 b >B ;8=7K A;54C5B @0A?>;>68BL M:@0=, GB>1K >?OBL =0 =5<
?>;CG8;>AL G5B:>5 87>1@065=85 8AB>G=8:0?
2.4 @CA>: AB0;8 >A25I0BL ?0@0;;5;L=K< ?CG:><
A25B0. -:@0= @0A?>;>68;8 2 D>:0;L=>9 ?;>A:>AB8
;8=7K. >A;5 G53> 1@CA>: AB0;8 =03@520BL A >4=>9
AB>@>=K.  @57C;LB0B5 =5@02=><5@=>3> =03@520
?>:070B5;L ?@5;><;5=8O 1@CA:0 AB0; 87<5=OBLAO
;8=59=> >B n0 = 1,5 =0 >4=>9 AB>@>=5 4>
n1 = n0 + ´n , 345 ´n = 2,0 Å"10-4 =0 4@C3>9. 0?@02;5=85 87<5=5=8O B5<?5@0BC@K
?5@?5=48:C;O@=> =0?@02;5=8N @0A?@>AB@0=5=8O A25B0. 0: 87<5=8;0AL :0@B8=0 =0 M:@0=5
?>A;5 C:070==>3> =03@520 1@CA:0? ">;I8=0 1@CA:0 d = 4,0A< .
040G0 3. «'B> 2K 7=05B5 > !>;=F5?
 Å" <2
@028B0F8>==0O ?>AB>O==0O G = 6,67 Å"10-11 ;
:32
<
!:>@>ABL A25B0 c = 3,0Å"108 ;
A
!@54=55 @0AAB>O=85 >B 5<;8 4> !>;=F0 L = 1,5 Å"108 :< ;
2
#3;>2>9 @07<5@ !>;=F0, 2848<K9 A 5<;8 Ä… = 32 ;
0AA0 5<;8 m = 6,0 Å"1024 :3 ;
5@8>4 >1@0I5=8O 5<;8 2>:@C3 !>;=F0 1 3>4 (B>G=>);
!>;=5G=0O ?>AB>O==0O (:>;8G5AB2> A>;=5G=>9 M=5@388 !>;=F0, ?040NI59 2 B5G5=85 1A =0
?;>I04:C ?;>I04LN 1<2 , ?>AB02;5==CN =0 3@0=8F5 0B<>AD5@K, ?5@?5=48:C;O@=> :
:B
A>;=5G=K< ;CG0<) Å‚ = 1,4 ;
<2
B
>AB>O==0O !B5D0=0->;LF<0=0 Ã = 5,7 Å"10-8 ;
4
<2
7
6
#=825@A0;L=0O 307>20O ?>AB>O==0O R = 8,31 .
<>;L Å" 
A?>;L7CO MB8 40==K5, >F5=8B5:
3.1. "5<?5@0BC@C ?>25@E=>AB8 !>;=F0.
3.2. '5@57 :0:>9 ?@><56CB>: 2@5<5=8 <0AA0 !>;=F0 C<5=LH8BAO =0 10%.
3.3. !G8B0O, GB> A>;=5G=0O 0B<>AD5@0 A>AB>8B 87 0B><0@=>3> 2>4>@>40, >F5=8B5
MDD5:B82=CN B>;I8=C !>;=5G=>9 0B<>AD5@K.
8