A physics student performs an experiment using a high$-$pressure gas cylinder which contains $58$ L of toxic gas at a pressure of $1\mathrm{.}3$ x$107$ N$/$m$2$ and a temperature of $20$C$.$ Due to use over time, a leak develops in the cylinder. A graduate student, desperate to reduce the rate of the leak, tries to cool the cylinder using dry ice $(-78\mathrm{.}5$ oC$)$ to reduce the pressure so that it can be safely repaired.

$($a$)$ What is the final pressure of the cylinder, assuming a negligible amount of gas leaks while being cooled and that there is no phase change?

$8\mathrm{.}63$E$6$

N$/$m$2$

$($b$)$ What is the final pressure if $15$ percent of the gas escapes?

$1\mathrm{.}11$E$7$

N$/$m$2$

$($c$)$ To what temperature should the cylinder be cooled to reduce the pressure to atmospheric pressure $($assuming the gas does not change phase and that there is no leakage during cooling$)?$

Number

K