$2.$ A gas turbine cycle operates with two compression stages and two expansion stages. In each compression stage the pressure ratio is $2\mathrm{.}4$ and the thermal efficiency is $0\mathrm{.}81,$ the inlet temperature to the compressor is $25$C$,$ but the intercooler only cools the stream entering the second stage to $40$C$.$ The inlet temperature to each expansion stage is $890$C$,$ but a pressure drop between the compressor and the turbine reduces the pressure ratio in each expansion stage to $1\mathrm{.}9.$ The adiabatic efficiency of the expansion stages is $0\mathrm{.}87.$ The regenerator has an efficiency of $0\mathrm{.}75$ determine a$)$ The compression work in KJ$/$kg b$)$ The heat extracted in the intercooler c$)$ The thermodynamic efficiency d$)$ The temperature of the air leaving the regenerator and entering the combustion chamber in Kelvin.