The computational investigation is performed to find out the interaction of arc plasmas with surrounding materials and the thermal flow characteristics in a PASB (Puffer-Assisted Self-Blast) chamber, which is one of new breaking concepts in $SF_6$ switchgears. It is very important to define the flow and mass transfer happened during the full arcing history for further understanding complex physics inside the chamber. In this study, we have considered two diffusion processes by the hot arc plasma, one is PTFE nozzle ablation and the other is Cu electrode evaporation, simultaneously. It was found that the principle of the pressure-rise inside the chamber is confirmed by the computational results and the increase of the electrical conductivity of the residual gas near current zero is critical to the chamber design.