$8\mathrm{.}64$ Figure P$8\mathrm{.}64$ shows a combined heat and power system $($CHP$)$ providing turbine power, process steam, and steam for a factory space heating load. Operating data are given on the figure at key states in the cycle. For the system, determine

$($a$)$ the rates that steam is extracted as process steam and for the heating load, each in $k\frac{g}{h}.$

$($b$)$ the rates of heat transfer for the process steam and the heating load, each in $k\frac{J}{h}.$

$($c$)$ the net power developed, in $k\frac{J}{h}.$

Devise and evaluate an overall energy$-$based efficiency for the combined heat and power system.