Methane gas is continually fed into a steady$-$state isothermal compressor at

an inlet absolute pressure of $500$ bar and temperature of $200K.$ The gas

exits the compressor at an absolute pressure of $750$ bar. The compressibility

factor of methane in this range of conditions obeys the following equation:

$Z=a+bP$

with the constants taking the values $a=0\mathrm{.}28$ and $b=0\mathrm{.}00208$ bar ${?}^{-1}.$

Calculate the final volume of the gas in $c{m}^3$ and the molar work of

compression in $k\frac{J}{m}ol.($the answer should be $1\mathrm{.}05$ kj$/$mol$)$