QUASILINEAR DIFFERENTIAL EQUATIONS FOR THE DESCRIPTION OF THE SPACE OF IDEAL GAS CONDITIONS
Abstract
Relevance
Today the classical thermodynamics as fundamentals of many physical sciences does not possess the finished and accurate axiomatic creation of the theory. Its many provisions and ratios are based on the empirical facts which are recognized as apriori and are not proved in terms of theoretical parcels.
Problem
In this paper the problem of a wording of thermodynamic provisions and ratios for spaces of ideal gas conditions is considered on the basis of analysis of solutions of partial differential equations of the first order.
Methods
In this work the method of characteristics for the solution of the quasilinear differential equations of the first order was used. And also formulas and dependences of differential geometry and means of computer mathematics are applied.
Results
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.
Conclutions
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.
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