An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains $6kg$ of air at $500$kPa and $50C,$ and the other part is evacuated. The partition is now removed, and the air expands into the entire tank. Determine $($a$)$ the volume of the tank, $($b$)$ the final temperature and pressure in the tank, and $($c$)$ the total entropy change during this process.