A coal fired power plant boiler B consumes coal with heating value $,$ at a rate of $,$ while of heat is expelled by the boiler as heat losses and hot gases from the chimney. The boiler is producing superheated steam at pressure P$3=5$MPa $(50$bar$)$ and temperature T$3=400$oC$.$ The steam is then lead to a turbine T operating with isentropic efficiency of $90\%$ and an outlet pressure of $50$KPa $(0\mathrm{.}5$bar$).$ The depleted steam is condensed to saturated liquid water at the condenser C which is then fed to a pump. The pressure of the saturated water is raised back to the operating high pressure by the pump P which operates isentropically $($ isentropic efficiency of $100\%).$Considering that all other processes correspond to an ideal operation of a Rankine Cycle, address the following:i$)$ Sketch the cycle on the T$-$s diagram provided. $(10-$marks$)$ii$)$ Calculate the mass flow rate of the steam produced by the boiler. $(10-$marks$)$iii$)$ Find the specific work and the mechanical power produced by the turbine. $(10$ marks$)$iv$)$ Calculate the overall plant efficiency. $(5$ marks$)$v$)$ Calculate the quality of the steam at the turbine exit. $(5-$marks$)$