Конспект лекций по термодинамике. Коренблит С.Э. - 61 стр.

                                           |61|
P = npTE , ¯à¨ç¥¬, npT  const, ­¥ § ¢¨áïé ï ®â ⥬¯¥à âãàë, â.ª. â¥-
¯«®¢®¥ ¤¢¨¦¥­¨¥ ⮬®¢ ¯®ç⨠­¥ ¢«¨ï¥â ­ ¨å § à冷¢ãî ¤¥ä®à¬ æ¨î.
®«ïà­ë¥ ¤¨í«¥ªâਪ¨, ­ ¯à®â¨¢, á®áâ®ïâ ¨§ ¬­®¦¥áâ¢ í«¥¬¥­â à-
­ëå ¤¨¯®«ì­ëå ¬®¬¥­â®¢, å ®â¨ç¥áª¨ ®à¨¥­â¨à®¢ ­­ëå § áç¥â ⥯«®-
¢®£® ¤¢¨¦¥­¨ï ¢ ®âáãâá⢨¥ ¢­¥è­¥£® ¯®«ï. ®í⮬㠮­¨ ¯®«ïਧãîâáï
⮫쪮 ¢ ¯à¨áãâá⢨¨ ¢­¥è­¥£® ¯®«ï á P k E § áç¥â ¢ëáâà ¨¢ ­¨ï í«¥-
¬¥­â à­ëå ¤¨¯®«¥© ¢¤®«ì ¯®«ï, ¨ ¨å ⥮à¨ï ¤®á«®¢­® ¯®¢â®àï¥â ⥮à¨î
¯ à ¬ £­¥â¨ª®¢, á ­ «®£¨ç­ë¬ ãà ¢­¥­¨¥¬ á®áâ®ï­¨ï ¨¤¥ «ì­®£® ¤¨-
í«¥ªâਪ ¨ ⥬¨ ¦¥ ᢮©á⢠¬¨ (6.13) ä㭪樨 ‹ ­¦¥¢¥­ L(y):
       P = L P E ! ; £¤¥ ⥯¥àì: y = P E  0;
                    0
                                                              (6.39)
                                                                 0


       P  0    RT                     RT
                                                           f
           ¨, ¯à¨ y  1: P =) E ;    pT           pT =L) T ; f = L0 (0) PR ;
                                                                                                      2

                                                              (6.40)                                   0




¨ P { ¬ ªá¨¬ «ì­ ï ¯®«ïਧ æ¨ï ­ áë饭¨ï ­ ¥¤¨­¨æã ®¡ê¥¬ , ª®£¤
    0

¢á¥ ¤¨¯®«¨ 㦥 ¢ëáâ஥­ë ¢¤®«ì ¯®«ï (¨á. 6.1). ’ ª çâ® ¤«ï ®¡®¨å
⨯®¢ ¤¨í«¥ªâਪ®¢ ¢ á« ¡ëå ¯®«ïå ¢­®¢ì ¨¬¥¥¬ ã­¨¢¥àá «ì­ë¥ ãà ¢-
­¥­¨ï á®áâ®ï­¨ï á ᮮ⢥âáâ¢ãî饩 í«¥ªâà¨ç¥áª®© ¢®á¯à¨¨¬ç¨¢®áâìî
b (T; E ) ) T , ¨«¨ ¤¨í«¥ªâà¨ç¥áª®© ¯à®­¨æ ¥¬®áâìî (T ):
                   P = T E ; D = (T )E ; (T ) = 1 + 4T : (6.41)
 ª®­¥æ, ¤«ï ¤¨ää¥à¥­æ¨ «®¢ í­âய¨¨ ¨ ¢­ãâ७­¥© í­¥à£¨¨, ¨§ (6.37), ­ «®£¨ç­®
(6.15), (6.16), ­ 室¨¬:
                            !              !                         !
                        @S              @S
          dS (T; P )  @T dT + @ P dP = T dT @T dP ;  C P       @  E           (6.42)
                           !P            ! T                           P! !
                       @U            @U
         dU (T; P )  @T dT + @ P dP = CP dT + E T @T dP ;         @ E         (6.43)
                             P            T                              P
          çâ® ¤«ï á« ¡ëå ¯®«¥©: E =) P ; ¤ ¥â: dS =) CTP dT + T P dP ;
                                                                             0
                                                                               (6.44)              2
                                             T                               T
                              !        !
          CE CP = T @ P   @ E      @ P2

                                          = )  T (0T ) E = T (0T ) P ;
                                                         2
                                                                 2
                                                                               (6.45)
                                                                                       2
                                                                                           2

                               T @T E             T           T                  3



£¤¥ ¤«ï ­¥¯®«ïà­ëå ¤¨í«¥ªâਪ®¢ (Tnp )0 = 0, ¯®â®¬ã, ­ «®£¨ç­® (6.19){(6.21):
                                       (   )




                 S np S np = CPnp ln TT ; U  np U  np = CPnpT + 2Pnp ;      (6.46)
                                                                                               2
                                               (   )         (       )
                        0                                0
                                 0                                         T
                 S p S p =L) CPp ln TT Pe ; U  p U  p =L) CPp T;
                                           2

                    0
                                 0        2 
                                                       ( )
                                                                         0     (6.47)
                                                                             ( )



                 ¯à¨ç¥¬: CEnp CPnp = 0; CEp CPp > 0:                           (6.48)