A rigid vessel with a volume of $0\mathrm{.}75m^3$ contains steam at $1\mathrm{.}8MN{m}^{-2}$ and $450C.$ The vessel is cooled until the steam pressure is $8$ bar. Calculate:

$($a$)$ The mass of steam present.

$($b$)$ The final dryness fraction. Use the simplified method of calculation where $v_f$ is taken as zero.

$($c$)$ The heat transfer for the process.