An isothermal gas turbine admits a mixture of propane $(75$ mol$\%)$ and pentane $(25$ mol$\%)$ at $30$ atm and $26\mathrm{.}7$ C and discharges it at l atm. A fraction of the turbine's work is used to drive a compressor that operates adiabatically and reversibly, in which a stream of CO$2$ of l atm is compressed and $250$ K at $20$ atm. $($a$)$ What is the temperature of the gas at the outlet of the compressor?; $($b$)$ what fraction of the total work delivered by the turbine must be supplied to the compressor?; c$)$ Calculate the coefficient of fugacity of the mixture at the turbine inlet. ADDITIONAL INFORMATION: Assume as a solution ideal a mixture of ideal gases.