Quantitative analysis of a non-adiabatic process undergone by a gas in a piston-cylinder assembly

Abstract

The influence of the finite values of piston speed as well as the thermal conductivity and capacity of the cylinder and piston walls on the connection between the thermodynamic parameters is investigated on a quantitative level. There are two possible qualitatively different types of evolution of thermodynamic processes for both the compression and expansion of gas due to the presence of heat transfer through the confining shell. Among them there may be cases where gas compressing (expanding) in the cylinder will cool (heat) during a certain interval of its volumes. Moreover, due to the presence of the dissipative process of heat transfer through the cylinder walls, the compression and expansion of gas should pass along the different T–V curves. The analytical expressions for such processes in one important limiting case are also derived. We show that the polytropic model is actually only able to take into account the process of absorption of heat by the walls and not the dissipative heat transfer through the walls. In the presence of heat transfer an exactly polytropic process is possible only under very specific conditions.