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An engineering method for calculating the air element is offered with air damping due to the discrete switching of active and additional gas volumes. Heat exchange with the environment is described with the polytropic process law. The analytical dependence determining the growth of entropy in irreversible processes during volumes switching is described. The thermodynamic parameters of gas in general case are functionals from change history of the active volume. It is shown that steady operating mode is feasible under the assumptions made, if the polytropic index is equal to one. For other polytropic index values at a periodic variation of the active volume the indicator diagram is not closed due to the continuous increase in pressure and temperature from cycle to cycle

Gas-dynamic Processes Mathematical Modeling in Pneumatic Components with Air Damping