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Консультация № 138444
29.05.2008, 10:03
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Доброго времени суток! Уважаемые эксперты, помогите пожалуйста решить задачу –
Молярная теплоемкость Сm серебра при температуре Т = 20 К оказалась равной 1,65 Дж/(моль•К). Вычислить по значению теплоемкости характеристическую температуру ΘD. Условие Т<<ΘD считать выполненным.
Примного благодарен.
Молярная теплоемкость Сm серебра при температуре Т = 20 К оказалась равной 1,65 Дж/(моль•К). Вычислить по значению теплоемкости характеристическую температуру ΘD. Условие Т<<ΘD считать выполненным.
Примного благодарен.
Обсуждение
Неизвестный
29.05.2008, 15:13
общий
это ответ
Здравствуйте, Петров Василий Алибабаевич!
Случай Т << Θ, где Θ - характеристическая температура Дебая, - это случай низких температур, для которого теплоекость C<sub>v</sub> изменяется пропорционально кубу абсолютной температуры Т:
C<sub>v</sub>=12*pi<sup>4</sup>*N<sub>a</sub>*k*(Т/Θ)<sup>3</sup>/5 (1)
где k=1,38*10<sup>-23</sup> Дж/К - постоянная Больцмана, N<sub>a</sub>=6,022*10<sup>23</sup> - число Авогадро, C<sub>v</sub>=1,65 Дж/(моль•К) -молярная теплоемкость, Т=20 К - температура
Выражая Θ из (1) имеем:
Θ=T*(12*pi<sup>4</sup>*N<sub>a</sub>*k/(5*C<sub>v</sub>))<sup>1/3</sup>=206,13 K
Случай Т << Θ, где Θ - характеристическая температура Дебая, - это случай низких температур, для которого теплоекость C<sub>v</sub> изменяется пропорционально кубу абсолютной температуры Т:
C<sub>v</sub>=12*pi<sup>4</sup>*N<sub>a</sub>*k*(Т/Θ)<sup>3</sup>/5 (1)
где k=1,38*10<sup>-23</sup> Дж/К - постоянная Больцмана, N<sub>a</sub>=6,022*10<sup>23</sup> - число Авогадро, C<sub>v</sub>=1,65 Дж/(моль•К) -молярная теплоемкость, Т=20 К - температура
Выражая Θ из (1) имеем:
Θ=T*(12*pi<sup>4</sup>*N<sub>a</sub>*k/(5*C<sub>v</sub>))<sup>1/3</sup>=206,13 K
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