$8\mathrm{.}78$ Figure P$8\mathrm{.}78$ shows a vapor power cycle with reheat and

regeneration. The steam generator produces vapor at $1000$

$lb\frac{f}{i}{n}^2{?}^2,800F.$ Some of this steam expands through the first

turbine stage to $100lb\frac{f}{i}n.{?}^2$ and the remainder is directed to

the heat exchanger. The steam exiting the first turbine stage

enters the flash chamber. Saturated vapor and saturated

liquid at $100lb\frac{f}{i}n.{?}^2$ exit the flash chamber as separate

streams. The vapor is reheated in the heat exchanger to

$530F$ before entering the second turbine stage. The open

feedwater heater operates at $100lb\frac{f}{i}{n}^2{?}^2,$ and the condenser.

pressure is $1$ lbf$/$in$\mathrm{.}2$ Each turbine stage has an isentropic

efficiency of $88\%$ and the pumps operate isentropically$.$ For

a net power output of $53109$ Btu$/$h$,$ determine

$($a$)$ the mass flow rate through the steam generator, in lb$/$h$.$

$($b$)$ the thermal efficiency of the cycle.

$($c$)$ the rate of heat transfer to the cooling water passing

through the condenser, in Btu$/$h$.$