Problem $5(10\mathrm{.}121)$

The power plant shown in Fig. $10\mathrm{.}24$ combines a gas$-$turbine cycle and a steam$-$turbine cycle. The following data are known for the gas$-$turbine cycle. Air enters the compressor at $100$kPa,$25C,$ the compressor pressure ratio is $14,$ the heater input rate is $60$ MW ; the turbine inlet temperature is $1250C,$ the exhaust pressure is $100$ kPa ; the cycle exhaust temperature from the heat exchanger is $200C.$ The following data are known for the steam$-$turbine cycle. The pump inlet state is saturated liquid at $10$ kPa $,$ the pump exit pressure is $12\mathrm{.}5$ MPa ; turbine inlet temperature is $500C.$ Determine

a$.$ The mass flow rate of air in the gas$-$turbine cycle.

b$.$ The mass flow rate of water in the steam cycle.

c$.$ The overall thermal efficiency of the combined cycle.

Answer: $m_{\text{A}\text{I}\text{R}}=58\mathrm{.}28k\frac{g}{s},m_{\text{w}\text{a}\text{t}\text{e}\text{r}}=6\mathrm{.}259k\frac{g}{s},{}_{th}=0\mathrm{.}634$