Regarding the application limitations of the Carnot, s theorem

The purpose of this article is to perform a comparative study of a reversible heat engine with an ideal or real gas as a working fluid and to determine the change in its efficiency depending on the thermodynamic characteristics of the working fluid. The main research method is the method of thermodynamic potentials, based primarily on the analysis of changes in the free and internal energy of an ideal and real gas in a cyclic process. The theory of thermodynamic potentials is used to consider the Carnot quasistatic heat engine. A comparative analysis of its operation is carried out, for a cycle with both an ideal and a real gas as a working fluid. The possibility of analyzing cyclic processes occurring in heat engines using the method of thermodynamic potentials has been identified and substantiated. The study has shown that the existing formulation of the Carnot’s theorem is valid only for ideal gas as a working fluid. Based on the work carried out, the Carnot’s theorem in the general case can be formulated, for example, as follows: the efficiency of the heat engine ηr, when it operates at the reversible Carnot cycle with real gas as a working fluid, is determined by the following expression:

h_r= 1 - T_B /T_A + ε,

where T_A and T_B are the temperatures of the upper and lower isotherms of the Carnot cycle, respectively; 
ε is the correction term (positive or negative), depending on the thermodynamic properties of a real gas, which tends to zero as the properties of a real gas approach the properties of an ideal gas.

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