Конспект лекций по статистической физике. Коренблит С.Э - 44 стр.

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4      Ž¯à¥¤¥«¥­¨¥ â¥à¬®¤¨­ ¬¨ç¥áª¨å ¢¥«¨ç¨­
   ‘â àâãï ⥯¥àì á ®¯à¥¤¥«¥­¨ï í­âய¨¨ (3.39), ¯®¤áâ ¢¨¬ ¢ ­¥£® «®-
£ à¨ä¬ ¢¥à®ïâ­®á⨠ª ­®­¨ç¥áª®£® à á¯à¥¤¥«¥­¨ï ƒ¨¡¡á (4.15):
         X              X                        X
  S = k wm ln wm = k wm ( Em + ln ZN ) = k wmEm + k ln ZN :
         m              m                        m
                                                                  (4.32)
® ®á­®¢­®¬ã ¯®áâã« âã ¢­ãâ७­ïï í­¥à£¨ï ¥áâì ãá।­¥­­ ï ¯® ­á ¬-
¡«î í­¥à£¨ï ¬ˆªà®á®áâ®ï­¨© á¨á⥬ë, ¨ (4.32) ¯¥à¥¯¨è¥âáï ¢ ¢¨¤¥:
     1 ln Z = U S ; £¤¥: X w = 1; X w E  <> = U; (4.33)
            N                        m          m m
                     k          m            m
‚ í⮩ ä®à¬ã«¥ «¥£ª® 㧭 âì ¢ëà ¦¥­¨¥ ¤«ï ᢮¡®¤­®© í­¥à£¨¨, ¥á«¨:
  F = U TS; k1 = T; = kT           1
                                      ; F = 1 ln ZN = kT ln ZN : (4.34)
’.¥. ᢮¡®¤­ãî í­¥à£¨î á¨áâ¥¬ë ¬®¦­® ­ ©â¨, ¢ëç¨á«¨¢ áâ â¨áâ¨ç¥-
áªãî á㬬ã, ¢ëç¨á«¥­¨¥ ¦¥ ¢á¥å ®áâ «ì­ëå â¥à¬®¤¨­ ¬¨ç¥áª¨å å à ª-
â¥à¨á⨪ á¨á⥬ë 㦥 ­¥ ¯à¥¤áâ ¢«ï¥â âà㤠. Žá­®¢­®¥ ãà ¢­¥­¨¥ â¥à-
¬®¤¨­ ¬¨ª¨ ¯®«ãç ¥âáï ¨§ ¯®«­®£® ¤¨ää¥à¥­æ¨ « í­âய¨¨ (4.32):
         dS = kd( U ) + kd ln ZN = Ukd + k dU + kd ln ZN :        (4.35)
„«ï ä㭪樨 ZN ( ; V ) ­¥§ ¢¨á¨¬ëå ¯¥à¥¬¥­­ëå ; V , ¯à¨ N = const,
­ 室¨¬:
                       X E 1m !
      d ln ZN = d ln e           = 1 @ZN d + 1 @ZN dV =
                       m             ZN @         ZN !@V
                                            X @Em
      = 1 ( Em ) exp( Em )d +
              X
                                                       exp( Em )dV 
         ZN m             ** @E ++      Z N m     @V
       <> d +            @V dV = d ln ZN ;                    (4.36)
£¤¥, ¯à¨ ª¢ ­â®¢ ­¨¨ í­¥à£¨¨ ¢ ï騪¥, Em / qn2 , qn = 2n=L § ¢¨áïâ
⮫쪮 ®â ¥£® ®¡ê¥¬ V = L3: Em = Em(V ); â.ª. <> = U (S; V; N ),
â®2, ¢ ᨫã (3.8), §¤¥áì:
        ** @E ++ X @E !                       @<
                                                > !
             @V  m         @V wm =)
                              m
                                                @V S;N = P;       (4.37)
    2â.¥.   ¯à®¨§¢®¤­ ï <> = (4.33) ¯à¨ wm = const ¥áâì ¯à®¨§¢®¤­ ï ¯à¨ S = (4.32) = const.