Consider a two$-$stage steam power cycle. The high$-$temperature cycle $($topping cycle$)$ is a standard Brayton cycle. Air enters the compressor at $100$ kPa and $300$ K and is compressed to a pressure ratio of $8$ before entering the turbine at $1300$ K$.$ The isentropic efficiency of the compressor is $80\%,$ and the isentropic efficiency of the gas turbine is $85\%.$

The low$-$temperature cycle $($bottoming cycle$)$ is an ideal Rankine cycle. Steam enters the turbine at $7$ MPa and exits at $5$ kPa as a mixture of vapor and liquid. Finally, water enters the pump as a saturated liquid at $5$ kPa. The steam is reheated to $500$C using exhaust gas in the heat exchanger and exits the heat exchanger at $450$ K$.$

Answer the following:

$($a$)$ Draw a schematic diagram. $(15$ points$)$

$($b$)$ Draw a T$-$s diagram. $(15$ points$)$

$($c$)$ Calculate the mass flow rate ratio $($mv$/$mgm$\_$v $/$ m$\_$gmv$/$mg$)$ between the steam and exhaust gas. $(15$ points$)$

$($d$)$ Evaluate the thermal efficiency of the combined cycle based on the mass flow rate ratio. $(10$ points$)$