Simple realization of the polytropic process with a finite-sized reservoir

In most thermodynamics textbooks, polytropic processes are introduced by defining the process equation rather than explaining their physical origin. In this paper, we propose a simple model to realize a polytropic process for an ideal gas. The ideal gas is compressed or expanded quasi-statically while in thermal contact with a finite reservoir with constant heat capacity, and the entire system is thermally isolated from the outside environment. We propose an experimental implementation of our model with realistic parameters.