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Bulletin of the National Engineering Academy of the Republic of Kazakhstan
ISSN
2709-4693
2709-4707
2 результаты
Показано: 1 - 2 из 2
- Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Mathematical model of an ideal gas(2025-06-30); ; ; ; К. К. ЖантлеуовThe peculiarity of this article is that the model of an ideal gas is based on the principle of one molecule, one mole, unit volume and the entire gas, that is, it is proposed to determine such quantities as mass, number of molecules, energy and average velocity that characterize the gas, relative to such a sequence. The method of averaging and doubling was used as a mathematical apparatus. While the volume of gas is taken as the total number of unit volumes, the pressure of the gas is considered as the energy accumulated in unit volumes. The value “number of moles per unit volume” has been introduced, which determines the concentration of molecules and the total number of moles. The relations between the state parameters are realized on the basis of Kelvin and Joule energy measurements. The ways of determining the energy of an ideal gas according to the positions of B. Clapeyron and D. Mendeleev are shown, the role of the equation of state is determined. At the same time, a theoretical justification for changing the state of the gas using dynamic and thermal effects (approaches) was developed. The patterns of generalized changes in the gas state and the ideological significance of isoprocesses were discussed in detail. Mathematical proofs of the idea of applying the first principle of thermodynamics to an ideal gas are presented. - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Variational modeling method in mathematical physics(2026-03-30); ; D. DauletbekThis article examines the application of the non-alternative variational principle to environmental mechanics under conditions of strong interactions of various physical fields. More precisely, this principle is considered as the main modeling method used to obtain the equations of motion of conservative and dissipative systems. Variations of functionals, conditions of stationarity of integral functionals, and variational principles in optics are presented. Calculations related to the principle of least action, Hamilton’s stationary action principle, Bernoulli’s variational equations, D’Alembert’s principle, and the variational equation of mechanics were carried out. It is shown that when transitioning from systems with a limited number of degrees of freedom to the environment, the kinetic and internal energies of the medium become functionals of the defining functions. It is proven that the first law of thermodynamics also represents a variational equation written through functionals in accordance with the variational principle. Variational approaches of analytical mechanics to discrete particles were applied to the study of oscillations of a thin string. By applying the stationarity condition for actions, the equation of string oscillation was obtained.