A new approach to the adiabatic piston problem through the arduino board and innovative frequency analysis procedures

The adiabatic piston problem is the subject of great attention for the involved education aspects in advanced thermodynamics curricula. The aim of this work, which for the theoretical section is mainly based on the work published in 1996 by Crosignani B. and Di Porto P., is to examine the adiabatic piston time evolution towards the mechanical equilibrium (final pressure determination) and towards the thermal equilibrium (final temperature determination). In particular, it will be shown how, by means of a thermodynamics analysis is not possible to univocally determine the final state of the system; it will be shown how this indeterminacy can be overcome by using an appropriate kinetic model. In particular, the motion equations derived from a kinetic model allow to define the final equilibrium state once that the initial value of the piston position and the initial temperatures of the two component subsystems are defined. In this framework it will be shown how it is possible to evaluate the phase relations between the temperatures and the piston displacement by applying the Wavelet Cross Correlation approach. Finally the gas specific heat ratio is experimentally evaluated by measuring the oscillation period of an adiabatic piston, where the relevant physical parameters are collected through sensors connected to an Arduino board, by applying a Fourier transform approach.