$11$:$46$

$61$

Problem $2(20$ points$)$ Water is the working fluid in a reheat$-$regenerative Rankine cycle with one closed feedwater heater and one open feedwater heater. Steam enters the turbine at $1400lb\frac{f}{i}n.{?}^2$ and $1000$ F and expands to $500lbffi{n}^2,$ where some of the steam is extracted and diverted to the closed feedwater heater. Condensate exiting the closed feedwater heater as saturated liquid at $500lbf\frac{f}{i}n\mathrm{.}2$ undergoes a throttling process to $120$lbffin.${?}^2$ as it passes through a trap into the open feedwater heater. The feedwater leaves the closed feedwater heater at $1400lb\frac{f}{i}n.{?}^2$ and a temperature equal to the saturation temperature at $500lb\frac{f}{i}n.{?}^2$ The remaining steam is reheated to $900$ F before entering the second$-$stage turbine, where it expands to $120$ lbf$/$in$.{?}^2$ Some of the steam is extracted and diverted to the open feedwater heater operating at $120lb\frac{f}{i}n.{?}^2$ Saturated liquid exits the open feedwater heater at $120lb\frac{f}{i}n.{?}^2$ The rest expands through the third$-$stage turbine to the condenser pressure of $2lb\frac{f}{i}n.{?}^2$ All processes of the working fluid in the turbine stages and pumps are internally reversible. Flow through the condenser, closed feedwater heater, open feedwater heater, steam generator, and reheater is at constant pressure. The net power output of the cycle is $1{10}^9$ Btulh. Determine for the cycle

$($a$)$ the mass flow rate of steam entering the first stage of the turbine, in lb$/$h$.$

$($b$)$ the rate of heat transfer, in Btu$/$h$,$ to the working fluid passing through the steam generator, including the reheat section.

$($c$)$ the thermal efficiency.

$($d$)$ Determine the rate of exergy input, in Btu$/$h$,$ to the working fluid passing through the steam generator. Perform calculations to account for all outputs, losses, and destructions of this exergy. Let $T0=60F,p0=14\mathrm{.}7$ lbflin. ${?}^2$