HW#$7-4(15$ pt$)$ A gas$-$turbine power plant operates on the simple Brayton cycle between the pressure limits of $100$ and $1600$ kPa $.$ The working fluid is air, which enters the compressor at $40C$ at a rate of $850\frac{m^3}{m}in$ and leaves the turbine at $650C($actual$).$ Assuming a compressor isentropic efficiency of $85\%$ and a turbine isentropic efficiency of $90\%,$ determine $[($a$)$ the net power output, $($b$)$ the back work ratio, and $($c$)$ the thermal efficiency$]$ of ideal and actual cycles $($ideal: isentropic$,$ actual: considering isentropic efficiency$).$ Assume constant specific heats and use air properties at $1000$ K in Table A$-2($b$).$