A piston$-$cylinder device below initially contains Oxygen $($O$2)$ at $160$ kPa and $200$C$.$ At this stage, the

piston rests on a pair of stops, as shown in the figure below, and the enclosed volume is $200$ litres. The

mass of the piston is such that a $240$ kPa inside pressure is required to move it$.$ The O$2$ gas is now

heated until its volume has doubled.

Determine $($a$)$ the final temperature, $($b$)$ the total work done by the gas, and $($c$)$ the total heat transferred

to the gas.

Assuming:

$1)$ O$2$ is a perfect gas, and its molecular mass is $32$ kg$/$kmol$.$ The ratio of specific heat capacities,

$($gamma$),$ is $1\mathrm{.}4.$

$2)$ There is no friction between the piston and cylinder walls, and the piston moves slowly at the

same speed when it happens $($no acceleration$).$

$3)$ Ignore the volume occupied by the stoppers.

$4)$ There is no leakage.

$5)$ Use $273$ for the conversion between Celsius and Kelvin degrees.

$6)$ Use $8314\mathrm{.}5$ J$/$kmol$.$K for the universal gas constant.