Диэлектриктердің жылу сиымдылығы (Дебай теориясы)
Диэлектриктерде (және жоғары атомдық жартылай өткізгіштерде) еркін заряд тасушылар жоқ немесе өте аз. Кристалдың энергиясы тек қана кристалдық тордың энергиясымен анықталады. Жылу сиымдылық ᄉ ᄃ. Сонымен, кристалдық тордың энергиясын анықтау керек.
ᄉ ᄃ, (5.11)
мұндағы
ᄉ ᄃ (5.12)
ᄉ ᄃ. (5.13)
Теңдеудің бірінші мүшесі – кристалдық тордың нөлдік энергиясы.
ᄉ ᄃ.
Заттың бір молі үшін ᄉ ᄃ және ᄉ ᄃ деп ауыстырамыз.
ᄉ ᄃ. (5.14)
Ендеше: ᄉ ᄃ (5.15)
Өлшемсіз айнымалыға ауысу ыңғайлы, сонда
ᄉ ᄃ ( ᄉ ᄃ; (5.16)
ᄉ ᄃ, ᄉ ᄃ ( (5.17)
ᄉ ᄃ. (5.18)
Жоғары және төменгі температуралар аймақтарын жеке түрді қарастырамыз.
Жоғары температуралар аймағы, ᄉ ᄃ.
ᄉ ᄃ болады, яғни ᄉ ᄃ – аз шама.
Қатарға жіктеуді қолданамыз:
ᄉ ᄃ ( (5.19)
ᄉ ᄃ;
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)
ᄉ ᄃ (5.20)
Бір моль үшін ᄉ ᄃ: ᄉ ᄃ
ᄉ ᄃ; ᄉ ᄃ (5.21)
Дюлонг және Пти заңын алдық: ᄉ ᄃ және температураға байланысты емес. Қатты дене атомында 6 еркіндік дәрежесі бар: үш өлшемді координата осьтері бойындағы серпімді тербелістер кинетикалық және потенциалық энергияларға байланысты. Сонымен: ᄉ ᄃ.
(Қатты денені қыздырғандағы көлем өзгерісін ескермеуге болады, ᄉ ᄃ).
Төменгі температуралар аймағы, ᄉ ᄃ.
Бұл кезде ᄉ ᄃ. Ендеше
ᄉ ᄃ (
ᄉ ᄃ (5.22)
ᄉ ᄃ (5.23)
– бұл төменгі температураларға арналған Дебай заңы.
Дебай теориясының экспериментпен сәйкестілігі 5.4-суретте көрсетілген. Дебай өз теориясын 1912 жылы ұсынды. Бұдан ертерек (1908 жылы) А.Эйнштейн өзінің жылу сиымдылық теориясын ұсынған. Ол ең алғаш рет осциллятор энергиясы мәндерінің дискреттілігін қолданды және олар бір-біріне тәуелсіз деп алып, мына заңды алды: ᄉ ᄃ. Бұл заң төменгі температуралар аймағында эксперимент нәтижелерімен сәйкес келмейді.
Әртүрлі температураларда ᄉ ᄃ тәуелділігі неге әртүрлі? ᄉ ᄃ болған кезде, ᄉ ᄃ артқанда тербелістер амплитудалары ғана артады: ᄉ ᄃ, ᄉ ᄃ. Төменгі температуралар аймағында тербелістер амплитудалары артады және ᄉ ᄃ; (ᄉ ᄃ, ᄉ ᄃ, ендеше, ᄉ ᄃ); ᄉ ᄃ (5.9), ᄉ ᄃ.
Достарыңызбен бөлісу: |