$(4)$ A partition $($neglect its thickness$)$ was installed in a rigid tank to separate the tank into two spaces. One part contains the air $\backslash ((1\backslash$mathrm$\{$~kg$\})\backslash )$ and the other contains the $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}(3\backslash$mathrm$\{$~kg$\})\backslash ).$ The initial pressure and temperature are indicated in the figure. Now the partition moves freely, and the heat is transferred between two spaces to reach the same temperature and pressure. Determine $($a$)$ the final temperature $($in unit: K $)$ and pressure $($in unit: bar$),$ and $($b$)$ air to $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}\backslash )$ volume ratio at the final condition. Use constant specific heat at initial mean temperature of $400$ K $.(\backslash (15\backslash \%\backslash ))$