Consider a gas turbine cycle with two stage compression and two stage expansion. The inlet temperature of the first compressors is $300$ K and the second compressor inlet is at $350$C$.$ The first turbine inlet temperature is $1200$K and after reheat the temperature is $1100$K$.$ The pressure ratio across first compressor and turbine is $4$ and and pressure ratio across second compressor and turbine is $3.$ Determine the back work ratio and thermal efficiency of the cycle if a regenerator of $75\%$ effectiveness is employed. Use cold air standard analysis. Cp $=1\mathrm{.}005$ kJ$/$kgK

$($please draw PV and TS diagram and explain the steps to result very clearly please!$)$