Thermodynamics questions $12)$ A gas goes through some type of compression process. The initial conditions are $0\mathrm{.}95$ bar, $0\mathrm{.}75$ m$3,$ and $20\backslash$deg C$.$ The final pressure and volume are $5\mathrm{.}6$ bar and $0\mathrm{.}275$ m$3.$ What is the final temperature in Celsius? $(4)$

$13)$ A cylindrical gas receiver is $3$ meters tall and contains $250$ kg of a certain gas at $1250$ kPag and $22\backslash$deg C$.$ If $1$ m$3$ of the gas under atmospheric pressure and at $0\backslash$deg C has a mass of $3\mathrm{.}31$ kg$,$ find:

$($a$)$ the volume of the vessel $(6\mathrm{.}5)$

$($b$)$ the diameter of the vessel $(6\mathrm{.}5)$