Конспект лекций по статистической физике. Коренблит С.Э - 89 стр.

                                 |89|
           0      1                  0      1        0          1
         1 @ @ 2Q A      1 @Q !2 @ @ 2 ln Q A      1 @ @ 2 ln Q A
D2(N ) = Q @ 2                     =             = 2                =)
                   T;V   Q @   T;V     @ 2
                                              T;V        @  2
                                                                 T;V
     @<>  !        1 @<> !            @n  !
=)
         @      T;V
                    =
                           @ T;V = kTV @ T ;                      (9.9)
{ ¢ ᨫã (9.7). ’ਠ¨­â¥­á¨¢­ëå ¯ à ¬¥âà T; P;  ïîâáï § ¢¨á¨¬ë¬¨
ᮣ« á­® ãà ¢­¥­¨î ƒ¨¡¡á -„¬ ,  = (T; P ), ¨«¨ (5.34), P = P (T; ),
  ¯® ãà ¢­¥­¨î á®áâ®ï­¨ï ¢ ¢¨¤¥ (5.35), n = n(T; ) = n(T; P ), á¢ï§ ­ë
¬¥¦¤ã ᮡ®© âਠ¨­â¥­á¨¢­ëå ¢¥«¨ç¨­ë T; P; n, ¯®í⮬ã:
     @n ! = @n @P ! = @P ! @n ! = n @n ! = n2K ;                   (9.10)
                                                         T
    @ T @P @ T           @ T @P T ! @P T            !
                      N
   â ª ª ª, ¯à¨ n  V : KT = V @P  1 @V         1  @n
                                          T;N
                                              =
                                                n @P T ;           (9.11)
{ ª®íää¨æ¨¥­â ¨§®â¥à¬¨ç¥áª®© ᦨ¬ ¥¬®áâ¨. ’® ¥áâì (áà ¢­¨ á (9.38)):
    D2(N ) = <<(
N )2>> = n2kTV KT  (<>)2 kTK   T
                                                  V :              (9.12)
’®£¤ , ­ «®£¨ç­ ï (9.4) ®â­®á¨â¥«ì­ ï ä«ãªâã æ¨ï â ª¦¥ áâ६¨âáï ª
­ã«î ¢ â¥à¬®¤¨­ ¬¨ç¥áª®¬ ¯à¥¤¥«¥, ¯à¨ N; V ! 1:
                       v
                       u                 v
                                         u
                       u
                       u <
                         <  (
 N ) 2>>   t kTKT  p1 ! 0:
                                         u
              2(N )  t             2 =
                                             V                 (9.13)
                          (<>)                   V
Œ «®áâì 2(N ) 㪠§ë¢1 ¥â, çâ® ®¯à¥¤¥«ïî騩 ¡®«ìèãî áâ â¨áâ¨ç¥áªãî
á㬬ã àï¤ Q( ) = N=0 P  N Z ; ᮤ¥à¦¨â ¬ ªá¨¬ «ì­ë© ç«¥­, ª®â®àë©,
                              N
¯à¨ wfN  1, ¤ ¥â ®á­®¢­®© ¢ª« ¤, áãé¥á⢥­­® ¯à¥¢ëè î騩 ¢ª« ¤ë
¢á¥å ®áâ «ì­ëå ç«¥­®¢, ¢ë¤¥«ïï ¨§ í⮩ á㬬ë á« £ ¥¬®¥ á ­ ¨¡®«¥¥
¢¥à®ïâ­ë¬ §­ 祭¨¥¬ (¯à ªâ¨ç¥áª¨ ®­® ¦¥, { á।­¥¥) ç¨á« ç áâ¨æ ¢
á¨á⥬¥ <> = N  1. “á«®¢¨¥ â ª®£® ¬ ªá¨¬ã¬ ®¯à¥¤¥«ï¥â , ª ª:
                     N 
   @ wN = 0; 7! e ZN = 0;  = kT @ ln ZN = @F ! : (9.14)
     f            @
   @N                 @N                        @N    @N T;V
‚ëç¨á«¨¬ ª®­âãà­ë© ¨­â¥£à « (5.11) ¯®  = exp( ), ®¯à¥¤¥«ïî騩 ª -
­®­¨ç¥áªãî áâ âá㬬ã ZN ç¥à¥§ ¡®«ìèãî áâ âá㬬ã Q( ) = exp( J ),
¨á¯®«ì§ãï ¬¥â®¤ ¯¥à¥¢ « ¢ ª®¬¯«¥ªá­®© ¯«®áª®á⨠, ¯à¨ N  1:
            1 I Q( )            I
      ZN = 2i  N+1 d = 2i d exp [ (J (T; V; ) + N)] :   (9.15)