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 $b=($