Конспект лекций по статистической физике. Коренблит С.Э - 53 стр.

                               |53|
d( 1= ln Q) ¤«ï áâ âá㬬ë Q = Q( ; V ;  ) ¢¨¤ (5.6), (5.10) ¤¥©á⢨-
⥫쭮 ï¥âáï ¤¨ää¥à¥­æ¨ «®¬ ¡®«ì讣® â¥à¬®¤¨­ ¬¨ç¥áª®£® ¯®â¥­-
æ¨ « , ¯®áª®«ìªã, ¤«ï ­¥§ ¢¨á¨¬ëå ¯¥à¥¬¥­­ëå ; ; V , ¨¬¥¥¬:
           !
d    1 ln Q = 1 d(ln Q) + ln Q d  kTd(ln Q) (ln Q)kdT;         (5.29)
         @ ln Q      @ ln Q
d(ln Q) = @ d + @ d + @V dV = @ ln Q      X N N 1ZN
                                             N    Q d +
  XX              exp( EmN )          X X N exp( EmN )      @E   !
                N                                             mN
       ( EmN )                d +         
+
   N m                  Q              N m        Q !        @V dV
        NwmN d
   XX               XX                   X X @EmN
=                         EmN wmN d +             @V   wmN dV =)
   N m              N m      ** @E ++    N  m
=) <>  d
            <>d +           @V dV = d(ln Q);                (5.30)
£¤¥ á।­¨¥ ®¯à¥¤¥«¥­ë ᮣ« á­® (5.22), (5.28), ¨ ¢­®¢ì, ­ «®£¨ç­® (4.37):
    ** @E ++ X   1 X     @E    !                @< > !
        @V  N=0 m         @V wmN =)
                            mN
                                                   @V S;N = P; (5.31)
{ ¥áâì ¤ ¢«¥­¨¥ ¢ á¨á⥬¥. ®¤áâ ¢¨¢ (5.30) ¨ (5.27) ¢ (5.29), ­ ©¤¥¬:
          Q !
  d    ln     = <> d ln  + <> d PdV + <> + S +
                 !d                                             k
        + <>       = <>
                                 d ln  PdV + S d + <> d ;
                                                    k 2       2

¨ â ª ª ª d ln  = d = d( ) = d + d , d = k 2 dT , ¯®«ã稬:
     d    1 ln Q! = <>d PdV           SdT =) dJ (T; V; ):      (5.32)
’.¥. á¯à ¢ ¢ (5.32) ¨¬¥¥¬ ¨§¢¥áâ­®¥ ¨§ â¥à¬®¤¨­ ¬¨ª¨ ¢ëà ¦¥­¨¥ ¤«ï
¤¨ää¥à¥­æ¨ « ¡®«ì讣® â¥à¬®¤¨­ ¬¨ç¥áª®£® ¯®â¥­æ¨ « , ¯®â®¬ã:
     J = kT ln Q =!J (T; V; ) = ! PV;  = exp( )  exp( ); (5.33)
     P = kT @ @V
              ln Q
                        =
                              @J
                              @V       J =) P (T; );
                                        V   !!!
                                                             (5.34)
                    T;           T;
     <> = kT @ ln Q ! = 1 @J ! = @P ! =) n(T; ); (5.35)
       V      V @ T;V           V @ T;V @ T !!!