A $40,000-kW$ straight$-$flow condensing industrial steam turbogenerator unit is supplied steam at

$800l\frac{b}{i}{n}^2($abs$)(5512$kPa$)$ and $800F(426\mathrm{.}7C)$ and is to exhaust at $3in(76cm)Hg$ absolute$.$

The half$-$load and full$-$load throttle steam flows are estimated to be $194,000l\frac{b}{h}(88,076k\frac{g}{h})$ and

$356,000l\frac{b}{h}(161,624k\frac{g}{h}),$ respectively. The mechanical efficiency of the turbine is $99$ percent and

the generator efficiency is $98$ percent. Find $($a$)$ the no$-$load throttle steam flow; $($b$)$ the heat rate of

the unit expressed as a function of the kW output; $($c$)$ the internal steam rate of the turbine at

$30$ percent of full load.