An isothermal gas turbine admits propane at $30$ atm and $26\mathrm{.}7\backslash$deg C and discharges it at $1$ atm, A fraction of the turbine work is used to drive a compressor that operates adiabatically and reversibly, in which a CO$2$ stream of $1$ atm and $250$K is compressed to $20$ atm.

$($a$)$ What is the gas temperature at the compressor outlet?

$($b$)$ what fraction of the total work delivered by the turbine should it be supplied to the compressor?