ࡱ> cy2EbjbjB{{_ mmmmm8 ;!(!!!""# #b:d:d:d:d:d:d:$c=@:m#""##:mm!!4i;_4_4_4#m!m!b:_4#b:_4_466!-ܵ*6N:;0;6,@0 @6@m6x_4###::2~###;####@######### ? 3:$545@0;L=>5 035=BAB2> ?> >1@07>20=8N >AC40@AB25==>5 >1@07>20B5;L=>5 CG@5645=85 2KAH53> ?@>D5AA8>=0;L=>3> >1@07>20=8O "C;LA:89 3>AC40@AB25==K9 C=825@A8B5B 0D54@0 >1>@C4>20=85 8 B5E=>;>38O A20@>G=>3> 8 ;8B59=>3> ?@>872>4AB20 $ %'! !+ "  !" 5B>48G5A:85 C:070=8O ?> ?@>2545=8N ?@0:B8G5A:8E 70=OB89 4;O ABC45=B>2 =0?@02;5=8O: 150200  0H8=>AB@>8B5;L=K5 B5E=>;>388 8 >1>@C4>20=85 A?5F80;L=>AB8: 150204  0H8=K 8 B5E=>;>38O ;8B59=>3> ?@>872>4AB20 >G=>9 D>@<K >1CG5=8O "C;0 2005 3. 07@01>B0;: .. 0;5=:> :0=4840B B5E=8G5A:8E =0C:, 4>F5=B  #G51=0O 48AF8?;8=0  $878:>-E8<8G5A:85 >A=>2K ;8B59=>3> ?@>872>4AB20  87CG05BAO ABC45=B0<8 A?5F80;L=>AB8 150204 2 9->< A5<5AB@5 :0: ?@>4>;65=85 :C@A0  "5@<>48=0<8G5A:85 8 D878:>-E8<8G5A:85 >A=>2K 2KA>:>B5<?5@0BC@=KE <5B0;;C@38G5A:8E ?@>F5AA>2  . @0:B8G5A:85 70=OB8O ?> MB>9 48AF8?;8=5 ?@>2>4OBAO A F5;LN 1>;55 3;C1>:>3> CA2>5=8O ABC45=B0<8 <0B5@80;0, 87;0305<>3> 2 ;5:F8>==>< :C@A5, ?@8>1@5B5=8O =02K:>2 >?@545;5=8O >A=>2=KE B5@<>48=0<8G5A:8E ?0@0<5B@>2 8 DC=:F89 D878:>-E8<8G5A:8E ?@>F5AA>2 ;8B59=>3> ?@>872>4AB20. @8 A>AB02;5=88 <5B>48G5A:8E C:070=89 : ?@0:B8G5A:8< 70=OB8O< CGB5=>, GB> ABC45=BK >A2>8;8 >A=>2K ?@>3@0<<8@>20=8O =0 -.  "'! /" !1   -"  / ,    '+%  &!!% 1. &5;L 8 7040G8 ?@0:B8G5A:>3> 70=OB8O. @0:B8G5A:>5 >7=0:><;5=85 A <5B>4>< >?@545;5=8O M=B@>?88 <>;O 8450;L=>3> 3070 ?@8 @07;8G=KE ?@>F5AA0E. 2. A=>2=K5 B5>@5B8G5A:85 ?>;>65=8O. -=B@>?8O S O2;O5BAO >4=>7=0G=>9 DC=:F859 A>AB>O=8O B5@<>48=0<8G5A:>9 A8AB5<K: S = f (T, , V(. 7<5=5=85 M=B@>?88 dS 2 @02=>25A=>< 87>B5@<8G5A:>< ?@>F5AA5 @02=> >B=>H5=8N 87<5=5=8O B5?;>BK A8AB5<K (Q : B5<?5@0BC@5 A8AB5<K ", B.5. dS = (Q / ". 5@02=>25A=K5 ?@>F5AAK 2 87>;8@>20==>9 A8AB5<5 A>?@>2>640NBAO @>AB>< M=B@>?88, >=8 ?@81;860NB A8AB5<C : A>AB>O=8N @02=>25A8O, 2 :>B>@>< M=B@>?8O <0:A8<0;L=0. "0: :0: dS O2;O5BAO ?>;=K< 48DD5@5=F80;><, B> 87<5=5=85 M=B@>?88 2 ;N1>< D878:>-E8<8G5A:>< ?@>F5AA5 7028A8B B>;L:> >B =0G0;L=>3> 8 :>=5G=>3> A>AB>O=8O A8AB5<K 8 =5 7028A8B >B ?CB8 ?5@5E>40: "S = S2  S1. -=B@>?8O O2;O5BAO 0448B82=>9 25;8G8=>9, B.5. M=B@>?8O A;>6=>9 A8AB5<K @02=0 AC<<5 M=B@>?89 55 >B45;L=KE G0AB59. A=>2=>5 C@02=5=85 4;O >?@545;5=8O M=B@>?88 <>;O 8450;L=>3> 3070 dS= Cv* dT/ T+ R* dV/ V 8;8 dS= Cv* dlnT+ R*dlnV (1) ;O 87>10@=>3> ?@>F5AA0 (p = const, dp = 0): dS= Cv*dln T+ R*dln V; EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 "0: :0: ?@8 ?>AB>O==>< @ 4;O 8450;L=KE 307>2 dT/ T= dV/V, B> EMBED Equation.3 dS= CP* dlnT (2) 8;8 EMBED Equation.3 dS= CP*dlnV (3) EMBED Equation.3EMBED Equation.3EMBED Equation.3 EMBED Equation.3EMBED Equation.3 ;O 87>E>@=>3> ?@>F5AA0 / V= const, dV=0/: EMBED Equation.3 "0: :0: dV= 0 , B> EMBED Equation.3 (4) EMBED Equation.3EMBED Equation.3 EMBED Equation.3 (87: @V= RT ; T=@V/ R= V/ R* @= const* @ ). ;O 87>B5@<8G5A:>3> ?@>F5AA0 / T= const, dT= 0 /: EMBED Equation.3 . "0: :0: dT= 0, B> EMBED Equation.3 (5) EMBED Equation.3EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 (6) (87: pV= RT; RT= const; pV= p1V1= p2V2= const ; V2/ V1= p1/ p2). 3. K?>;=5=85 ?@0:B8G5A:>9 @01>BK. 040=85: >?@545;8BL M=B@>?8N <>;O 2>4>@>40 :0: 8450;L=>3> 3070 ?@8 1000  8 87<5=5=85 M=B@>?88 S0 = S01000 - S0298: 1- 2 87>10@=>< ?@>F5AA5 / p= 0,10= const /; 2- 2 87>E>@=>< ?@>F5AA5 / V0= 22, 43*10-3=<3 / <>;L 2= const; 3- 2 87>B5@<8G5A:>< ?@>F5AA5 / T= 1000 K= const / ?@8 ?>2KH5=88 402;5=8O A 0,1 /<2 8;8 ?@8 C<5=LH5=88 >1J5<0 2 10 @07. ?@545;5=85 M=B@>?88 <>;O 2>4>@>40 ?@8 1000  8 87<5=5=85 53> M=B@>?88 2 8=B5@20;5 >B 298  4> 1000  2K?>;=ONBAO: 2 87>10@=>< ?@>F5AA5 ?> C@02=5=8N (1) 8;8 (2) , (3); 2 87>E>@=>< ?@>F5AA5 ?> C@02=5=8N (4); 2 87>B5@<8G5A:>< ?@>F5AA5 ?> C@02=5=8N (5) 8;8 (6), 0 B0:65 ?> A?@02>G=K< 40==K< [2, 3]. 57C;LB0BK >?@545;5=8O >1J5<0 2>4>@>40 ?@8 298 , A@54=59 B5?;>5<:>AB8 2>4>@>40 2 B5<?5@0BC@=>< 8=B5@20;5 298  - 1000 , M=B@>?88 2>4>@>40 ?@8 298 , 0 B0:65 ?@8 1000  8 87<5=5=85 M=B@>?88 2>4>@>40 2 8=B5@20;5 >B 298  4> 1000  70=5AB8 2 B01;.1. "01;8F0 1 @>F5AAK EMBED Equation.3*103, =<3/<>;L EMBED Equation.3, 6/(<>;L*)EMBED Equation.3 ?@8 298-1000 , 6/(<>;L*)S01000, 6/(<>;L*)EMBED Equation.3=S01000- -S0298 , 6/(<>;L*)7>10@=K97>E>@=K97>B5@<8- G5A:89  "'! /" ! 2   -"  / ,   !! 1. &5;L 8 7040G8 ?@0:B8G5A:>3> 70=OB8O. @0:B8G5A:>5 >7=0:><;5=85 A <5B>4>< >?@545;5=8O M=B@>?88 <>;O 8450;L=>3> 3070 2 A<5A8. 2. A=>2=K5 B5>@5B8G5A:85 ?>;>65=8O. 1@07>20=85 307>2>9 A<5A8 2 @57C;LB0B5 A0<>?@>872>;L=>3> =5>1@0B8<>3> ?@>F5AA0 2708<=>9 48DDC788 8AE>4=KE 307>2 A>?@>2>6405BAO C25;8G5=85< M=B@>?88: SA<=-R*(NA*lnNA+NB*lnNB) , (1) SA< = 4.69 345 SA<  87<5=5=85 M=B@>?88 ?@8 A<5H820=88 307>2  8  =0 >48= <>;L A<5A8 MB8E 307>2, 6/ (<>;L*); R  C=825@A0;L=0O 307>20O ?>AB>O==0O, R= 8,31434 6/<>;L*; NA 8 NB  <>;L=K5 4>;8 :><?>=5=B>2  8  2 307>2>9 A<5A8: NA=nA/nA+nB; NB=nB/nA+nB; NA+ NB=1 ;O n <>;59 307>2>9 A<5A8: SA<=-n*R*(NA*lnNA+NB*lnNB) (2) -=B@>?8O <>;O 307>2>9 A<5A8 @02=0: SA<=NA* S+NB* S+ SA<= = NA* S+NB* S  R*(NA*lnNA+NB*lnNB), (3) SA<=152 345 S 8 S  M=B@>?8O <>;O 3070  8  A>>B25BAB25==>, 6/(<>;L*). -=B@>?8O n <>;59 307>2>9 A<5A8: SA<=n*(NA* S+NB* S+ SA<)= =n*[ NA* S+NB* S  R*(NA*lnNA+NB*lnNB)] (4) ;O M:28<>;O@=>9 307>2>9 A<5A8 NA= NB= 0,5 8 ?>MB><C 4;O =55 SA< <0:A8<0;L=0 8 A>AB02;O5B 5,77 6/(<>;L* )  @8A.2.1. ;O <>;O 307>2>9 A<5A8, A>45@60I59 ;N1>5 G8A;> :><?>=5=B>2, SA< @02=>: SA<=-R*(NA*lnNA+NB*lnNB + N!*lnN! +& ) , (5) 345 NA=nA/(nA+nB+nC+& ); NB=nB/(nA+nB+nC +& ); N!=n!/(nA+nB+nC+& ); NA+ NB +NC+& =1 ;O n <>;59 A<5A8, A>45@60I59 ;N1>5 G8A;> :><?>=5=B>2, SA< @02=>: SA<=-n*R*(NA*lnNA+NB*lnNB + N!*lnN! +& ) (6)  8A.1. 028A8<>ABL 87<5=5=8O M=B@>?88 A<5A8 8450;L=KE 307>2 >B A>AB020 A<5A8 3. K?>;=5=85 ?@0:B8G5A:>9 @01>BK. 040=85: >?@545;8BL SA< 8 M=B@>?8N SA< <>;O 307>2>9 A<5A8, A>45@60I59 0,25 4>;8 >:8A8 C3;5@>40 ! 8 0,75 <>;L=>9 4>;8 2>4>@>40 2, ?@8 1000 2 87>10@=>< ?@>F5AA5 /@ = 0,1 =/<2= const/. "0:0O A<5AL >1@07C5BAO ?@8 :>=25@A88 ?@8@>4=>3> 3070 ?> @50:F88 !4+2=!+32. ?@545;5=8O SA< 8 SA< <>;O 307>2>9 A<5A8 ! 8 2 ?@8 1000 2 87>10@=>< ?@>F5AA5 2K?>;=ONBAO A>>B25BAB25==> ?> C@02=5=8O< (1) 8 (3) ?>A;5 ?@5420@8B5;L=>3> >?@545;5=8O M=B@>?88 ! 8 2 ?@8 B>9 65 B5<?5@0BC@5 ?> C@02=5=8N (1) 8;8 ?> C@02=5=8O< (2), (3) 87 ?@0:B8G5A:>3> 70=OB8O ! 1, 0 B0:65 ?> A?@02>G=K< 40==K< [2,3]. 57C;LB0BK 2K1>@0 8 >?@545;5=8O AB0=40@B=KE 7=0G5=8O M=B@>?88 :><?>=5=B>2 307>2>9 A<5A8, M=B@>?88 MB8E :><?>=5=B>2 ?@8 1000, 0 B0:65 S0A< 8 S0A< ?@8 1000 70=5AB8 2 B01;.1. "01;8F0 1 @>F5AA !B0=40@B=0O M=B@>?8O :><-B>2 307>2>9 A<5A8, 6/(<>;L*)-=B@>?8O :><-B>2 307>2>9 A<5A8 ?@8 1000, 6/(<>;L*) S0A<, 6/(<>;L*) S0A<, 6/ (<>;L*) !H2!2 7>10@=K9197.54130.57234.43166.144.69 152  "'! /" ! 3 !'"+ !/ $-%'!%  &!! "  !" ! ),. !."+% ' -",  -"  1. &5;L 8 7040G8 ?@0:B8G5A:>3> 70=OB8O. @0:B8G5A:>5 >7=0:><;5=85 A <5B>4>< @0AG5B>2 @02=>25A8O D878:>-E8<8G5A:8E ?@>F5AA>2 ;8B59=>3> ?@>872>4AB20 A ?><>ILN 01A>;NB=KE 7=0G5=89 M=B0;L?88 8 M=B@>?88. 2. A=>2=K5 B5>@5B8G5A:85 ?>;>65=8O. 0 >A=>25 M:A?5@8<5=B0;L=KE 8 B5>@5B8G5A:8E @01>B A>740=K A?@02>G=K5 B01;8FK B5@<>48=0<8G5A:8E A2>9AB2 <=>38E M;5<5=B>2 8 8=48284C0;L=KE 25I5AB2 (307>2 8 E8<8G5A:8E A>548=5=89) 4;O B5<?5@0BC@ >B 293 4> 3000 8 2KH5 [4]. 7<5=5=85 M=5@388 811A0 @50:F88 0+2=A!+dD ?@8 7040==>9 B5<?5@0BC@5 A 8A?>;L7>20=85< MB8E A?@02>G=KE 40==KE >?@545;ONB ?> A;54CNI5<C C@02=5=8N: G0T = 0" - S0" *T , (1) 345 GoT - 87<5=5=85 M=5@388 811A0 @50:F88 ?@8 7040==>9 B5<?5@0BC@5 ", 6/<>;L; 0" - 87<5=5=85 M=B0;L?88 @50:F88 ?@8 7040==>9 B5<?5@0BC@5 ", 6/<>;L; S0" - 87<5=5=85 M=B@>?88 @50:F88 ?@8 7040==>9 B5<?5@0BC@5 ", 6/(<>;L*); T - 7040==0O B5<?5@0BC@0 @50:F88, . 7<5=5=85 M=B0;L?88 @50:F88 (B5?;>2>9 MDD5:B @50:F88) ?@8 7040==>9 B5<?5@0BC@5 " >?@545;ONB ?> C@02=5=8N: 0" = A0"! + d0"D - a 0"A - b0"B , (2) 345 ,  8 C, D - 8AE>4=K5 8 :>=5G=K5 25I5AB20 @50:F88 A>>B25BAB25==>; 0, 2 8 c, d -AB5E8><5B@8G5A:85 :>MDD8F85=BK C 8AE>4=KE 8 :>=5G=KE 25I5AB2 @50:F88 A>>B25BAB25==>; 0"A, 0"B 8 0"!, 0"D - ?>;=K5 M=B0;L?88 8AE>4=KE 8 :>=5G=KE 25I5AB2 @50:F88 A>>B25BAB25==>, 6/<>;L (2 A?@02>G=8:5 [4] ?>;=K5 M=B0;L?88 25I5AB2 >1>7=0G5=K :0: J0T); 0"= 0f298A+( 0"A-0OA)-(0298A-0OA)= = 0f298A +( 0"A -0298A), (3) 345 0f298A -B5?;>B0 >1@07>20=8O 25I5AB20  87 ?@>ABKE 25I5AB2 (=0?@8<5@, 2 87 2, 20 87 2 8 0,5 2 8 B.4.), 6/<>;L; 0OA -M=B0;L?8O 25I5AB20  ?@8 ,6/<>;L; 0"A-0OA -87<5=5=85 M=B0;L?88 25I5AB20  ?@8 ?>2KH5=88 B5<?5@0BC@K >B  4> " , 6/<>;L; 0298A-0OA -87<5=5=85 M=B0;L?88 25I5AB20  ?@8 ?>2KH5=88 B5<?5@0BC@K >B 0 4> 298 , 6/<>;L; 0"A -0298A -87<5=5=85 M=B0;L?88 25I5AB20  ?@8 ?>2KH5=88 B5<?5@0BC@K >B 298 4> ", 6/<>;L. 7<5=5=85 M=B@>?88 @50:F88 ?@8 7040==>9 B5<?5@0BC@5: S0"= cS0TC+ dS0"D-aS0TA-bS0TB , (4) 345 S0TA, S0TB, S0TC, S0"D - M=B@>?88 8AE>4=KE 8 :>=5G=KE 25I5AB2 @50:F88 ?@8 7040==>9 B5<?5@0BC@5 A>>B25BAB25==>, 6/(<>;L*). @8 >B@8F0B5;L=>< 7=0G5=88 G0" @50:F8O 845B A;520 =0?@02>, B.5. 2 cB>@>=C >1@07>20=8O :>=5G=KE 25I5AB2 ! 8 D, ?@8 ?>;>68B5;L=>< 7=0G5=88, =0>1>@>B- A?@020 =0;52>, B.5. 2 AB>@>=C 8AE>4=KE 25I5AB2  8 . '5< 1>;LH5 01A>;NB=>5 7=0G5=85 G0", B5< 1>;55 @50:F8O A<5I5=0 >B ?>;>65=8O @02=>25A8O. @8 G0" = 0 @50:F8O =0E>48BAO 2 A>AB>O=88 48=0<8G5A:>3> @02=>25A8O . "5<?5@0BC@0 @02=>25A8O @50:F88: "  = 0" /S0" (5) >=AB0=B0 @02=>25A8O @50:F88 >?@545;O5BAO ?> C@02=5=8N: ln@ = - G0"/ RT= -G0"/8,31434"; (6) ln@ = 2,30258 lg@ ; lg@ = ln@/ 2,30258 ; lg@ = - G0"/ 2,30258 RT = - G0"/ 19,14 " (7) 3. K?>;=5=85 ?@0:B8G5A:>9 @01>BK. 040=85: >?@545;8BL 87<5=5=85 M=5@388 811A0, B5<?5@0BC@C @02=>25A8O 8 :>=AB0=BC @02=>25A8O @50:F88 :>=25@A88 ?@8@>4=>3> 3070 !4+2 = = !+2 ?@8 1000 2 87>10@=>< ?@>F5AA5 (@= 0,1 M=/<2 = const) A 8A?>;L7>20=85< A?@02>G=KE B01;8F B5@<>48=0<8G5A:8E A2>9AB2 8=48284C0;L=KE 25I5AB2 [4]. ?@545;5=85 01000 @50:F88 :>=25@A88 ?@8@>4=>3> 3070 ?@8 1000 2K?>;=ONBAO ?> C@02=5=8N (2.2.), S01000 -?> (2.4.), G01000 -?> (2.1.) , "  - ?> (2.5.), @1000 -?> (2.6.) 8;8 (2.7.). 57C;LB0BK >?@545;5=89 87<5=5=8O M=B0;L?88, M=B@>?88, M=5@388 811A0, B5<?5@0BC@K @02=>25A8O 8 :>=AB0=BK @02=>25A8O @50:F88 :>=25@A88 ?@8@>4=>3> 3070 ?@8 1000 70=5AB8 2 B01;.1. 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