At the design speed, following data is applied to a gas turbine plant incorporating a separate power turbine, heat exchanger, re$-$heater and intercooler between two stage compression:

Isentropic efficiency of the compressor $($each stage$)$: $84\%$

Isentropic efficiency of the compressor turbine and power turbine: $0\mathrm{.}9$ and $0\mathrm{.}85$ respectively

Turbine to compressor transmission efficiency: $99\%$

Compressor pressure ratio in each stage: $2$:$1$

Temperature after intercooler: $295$ K

Air mass flow rate! $13\mathrm{.}65k\frac{g}{s}$

Heat exchanger effectiveness: $0\mathrm{.}75$

Maximum turbine temperature $($both$)$: $900$ K

Ambient temperature and pressure: $288\mathrm{.}15K,\frac{1\mathrm{.}013}{b}ar$

LCV of fuel: $43100k\frac{J}{k}g$

Calculate the following:

a$)$ Net output of the plant b$)$ specific fuel consumption c$)$ Thermal efficiency

b$)$ Assume $C_{pa}=1\mathrm{.}005k\frac{J}{k}gK,C_{pg}=1\mathrm{.}147k\frac{J}{k}gK,rg=1\mathrm{.}33$