A simple ideal Rankine cycle with water as the working fluid operates between the pressure

limits of $15$MPa in the boiler and $100$kPa in the condenser. Saturated steam enters the

turbine. Following the conventional numbering of the processes, you are given the

following state properties $($these are obtained from the tables$/$ equations, so you don't have

to use them$).$

$h_1=417\mathrm{.}51k\frac{J}{k}g,v_1=0\mathrm{.}001043\frac{m^3}{k}g$

$h_2=433\mathrm{.}05k\frac{J}{k}g$

$h_3=2610\mathrm{.}8k\frac{J}{k}g,s_3=5\mathrm{.}3108k\frac{J}{k}gK$

$x_4=0\mathrm{.}6618,h_4=1911\mathrm{.}5k\frac{J}{k}g$

Determine the

$($a$)$ The heat transferred in the boilder: $q_{in}$ in $k\frac{J}{k}g$

$($b$)$ The thermal efficiency of the cycle: ${}_{th}$ in $\%$