Problem$-3($Marks: $30+4$ for Cleanliness$)$

Consider a combined gas$-$steam power plant $($refer to the following figure$)$ has a net power output of $600$ MW $.$ The pressure ratio of the gas turbine cycle is $16.$ Air enters the compressor at $300$ K and turbine at $1600$ K $.$ The combustion gases leaving the gas turbine are used to heat the steam to $400C$ at $10$ MPa in a heat exchanger. The combustion gases leave the heat exchanger at $400$ K $.$ An open feedwater heater incorporated with the steam cycle operates at a pressure of $0\mathrm{.}6$ MPa $.$ The condenser pressure is $15$ kPa $.$ Assume, isentropic efficiencies of $100\%$ for the pump, $82\%$ for the compressor, and $86\%$ for the gas and steam turbines. The fuel$-$air ratio in the combustion chamber is $0\mathrm{.}03.$

Assume: for air: $k_a($specific heat ratio$)=1\mathrm{.}4,C_{p,a}=1\mathrm{.}005k\frac{J}{kg.K}$; for combustion gas: $k_g($specific heat ratio$)=1\mathrm{.}33,C_{p,g}=1\mathrm{.}150k\frac{J}{kg.K}.$

Draw the $T-$s diagram of the combined cycle showing all the state points.

Determine: $($a$)$ the mass flow rate of air and steam, in kg$/$s$,$ and $($b$)$ the thermal efficiency of the combined cycle.

Figure: Problem $3.$