Simplification and determination of polytropic exponent of thermodynamic process in the filling and exhausting process in a pneumaitic system

A pneumatic system consisted of a relatively large container and a short tube is interviewed. The system is carefully modeled and heat transfer is taken into account. Then simplification is done based on the theoretical calculation and experiments, which shows that both filling and exhausting process could be divided into two stages according to the value of the pressure. The first stage is that the pressure rises or drops 99% of the whole value that to rise or drop, the polytropic exponent could be treated as a constant between 1.0 and 1.4, the rest of the filling or exhausting process is the second stage, and the polytropic exponent could be treated as 0 since the second stage could be treated as isobaric one. This method takes both heat transfer and the varying of polytropic exponent into account, and thus is more precious to describe a pneumatic system.