$8-78.$ Figure P$8\mathrm{.}78$ shows a vapor power cycle with reheat and regeneration. The steam generator produces vapor at $6\mathrm{.}9$ MPa, $430\backslash$deg C$.$ Some of this steam expands through the first turbine stage to $690$ kPa 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 $690$ kPa exit the flash chamber as separate streams. The vapor is reheated in the heat exchanger to $277\backslash$deg C before entering the second turbine stage. The open feedwater heater operates at $690$ kPa, and the condenser pressure is $6\mathrm{.}9$ kPa. Each turbine stage has an isentropic efficiency of $88\%$ and the pumps operate isentropically$.$ For a net power output of $5\mathrm{.}27$ X $109$ kJ$/$h$,$ determine $($a$)$ the mass flow rate through the steam generator, in kg$/$h$.($b$)$ the thermal efficiency of the cycle. $($c$)$ the rate of heat transfer to the cooling water passing through the condenser, in kJ$/$h$.$