Scientific Notes of V.I. Vernadsky Crimean Federal University. Biology. Chemistry Scientific Notes of V.I. Vernadsky Crimean Federal University. Biology. Chemistry Ученые записки Крымского федерального университета имени В.И. Вернадского. Биология. Химия. 2413-1725 91896 10.29039/2413-1725-2024-10-3-341-348 ХИМИЧЕСКИЕ НАУКИ CHEMICAL SCIENCES ХИМИЧЕСКИЕ НАУКИ APPROXIMATION BY ANALYTICAL FUNCTIONS OF THE TEMPERATURE DEPENDENCE COPPER ATOMIC HEAT CAPACITY IN THE INTRVAL 50-1300 K АППРОКСИМАЦИЯ АНАЛИТИЧЕСКИМИ ФУНКЦИЯМИ ТЕМПЕРАТУРНОЙ ЗАВИСИМОСТИ АТОМНОЙ ТЕПЛОЁМКОСТИ МЕДИ В ИНТЕРВАЛЕ 50–1300 K Шейх-Заде М. И. Sheyh-Zade M. I. Крымский инженерно-педагогический университет Crimean Engineering and Pedagogical University 12 12 2024 12 12 2024 10 3 341 348 12 12 2024 https://sn-biolchem.cfuv.ru/approksimacziya-analiticheskimi-funkcziyami-temperaturnoj-zavisimosti-atomnoj-teployomkosti-medi-v-intervale-50-1300-k/

Рассмотрена задача об аппроксимации аналитическими функциями температурной зависимости атомной теплоёмкости при постоянном давлении Cpm меди в интервале температур 50–1300 K. Экспериментальные значения Cpm в указанном интервале температур заимствованы из литературных источников. Показано, что в интервале 300–1300 K зависимость Cpm от температуры удовлетворительно описывается линейной зависимостью. Параметры этой зависимости найдены методом наименьших квадратов. В интервале 50–300 K зависимость Cpm от температуры имеет нелинейный характер и для описания этой зависимости использованы интерполяционный полином Лагранжа L3(T) и интерполяционный кубический сплайн S3(T). Показано, что при использовании сплайна S3(T) качество аппроксимации лучше, чем при использовании полинома L3(T).

Theory and experiment show that the atomic heat capacities at constant volume and constant pressure depend on temperature. In a theoretical consideration of heat capacity, it is easier to calculate , since depends only on the change in internal energy, and also depends on the work of expansion. The dependence of on temperature for bodies with an atomic lattice was theoretically considered by Debye, who obtained a formula that correctly conveys this dependence. In an experimental determination of heat capacity, it is easier to measure the values of . In this paper, the problem of approximating the temperature dependence of the copper atomic heat capacity in the temperature interval 50–1300 K by analytical functions is considered. It is shown that in the temperature interval 300–1300 K, this dependence is satisfactorily described by the linear function, the parameters of which are determined by the least squares method; the standard deviation was found to be equal to s = 4·10–3. In the interval 50–300 K, the dependence of on temperature is nonlinear and the Lagrange interpolation polynomial and cubic spline S3(T) were used to describe this dependence. It is shown that when using the spline S3(T) with the confidant a,j, given in the table it is possible to obtain a better approximation quality than when using the Lagrange interpolation polynomial L3(T).

 теплоёмкость температурная зависимость аппроксимация. heat capacity temperature dependence approximation.

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