A spherical tank of $10m$ diameter contains $6000kg$ of oxygen $(O_2)$ gas at $-40C.$ Determine the pressure, in bar, exerted by the gas using:

$($a$)$ The ideal gas equation of state;

$(5$ marks$)$

$($b$)$ The van der Waals equation of state;

$(5$ marks$)$

$($c$)$ The Peng$-$Robinson equation of state;

$(5$ marks$)$

$($d$)$ The generalized compressibility chart $($Appendix Q$2)$;

$(5$ marks$)$

$($e$)$ The residue of the results from $($b$)$ to $($d$),$ and comment on it$.$

$(5$marks$)$