$($b$)$ A tank whose volume is unknown is divided into two parts by a partition. One side of the tank contains $\backslash (0\mathrm{.}01\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ of refrigerant$-134$a that is a saturated liquid at $0\mathrm{.}8$ MPa $,$ while other side is evacuated. The partition is now removed, and the refrigerant fills the entire tank. If the final state of the refrigerant is $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $500$ kPa $,$ determine the volume of the tank and entropy change of refrigerant$-134$a$.$

$(8$ marks$)$