THE DIFFERENTIAL EQUATIONS FOR DESCRIPTION THE SPACE OF CONDITIONS OF IDEAL GAS

Author(s):  G.V. Averin, Dr., Prof., Belgorod National Research University, Belgorod, Russia, averin@bsu.edu.ru

M.V. Shevtsova, candidate of Sciences, associate Professor, Belgorod State Technological University named after V.G. Shoukhov, Belgorod , Russia, mashashev81@gmail.com

Issue:  Volume 51, № 2

Rubric:  Physics

Annotation:  In this article the problem of a wording of thermodynamic provisions and ratios for the spaces of ideal gas conditions is considered. The procedure of solving of this task is based on the analysis of solutions of partial differential equations of the first order. The solution of the equation is carried out by method of characteristics. It is shown that characteristics of partial differential equations are connected with entropy as a thermodynamic function of condition. Geometric presentation of the received integrated surfaces is executed. The connection between physical content of thermodynamic sizes (temperature, entropy, energy) and their mathematical analogs is established. By numerical methods using the means of computer mathematics it is illustrated the possibility of establishing consistent patterns of implementation of thermodynamic processes and cycles at the description them as functions of time. The assumption is formulated that irreversibility of thermodynamic processes can be connected with temporal features of implementation of these processes. The offered approach allows to give simple geometric interpretation of basic provisions and ratios of classical thermodynamics.

Keywords:  ideal gas, provisions and ratios of thermodynamics, geometric interpretation

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