PROBLEM $3$:

$[30$ points$]$

An air compressor and a steam turbine are connected directly to work together. The combined system sends its net output power to a generator to produce electricity.

Steam turbine: Steam enters the turbine at $12$ MPa and $520C$ at a flow rate of $25k\frac{g}{s}.$ The steam exits the turbine at $10$ kPa with a quality of $0\mathrm{.}92.$

Air compressor: Air enters the compressor at $98$ kPa and $22C$ at a flow rate of $10k\frac{g}{s}.$ The air exits the compressor at $1$ MPa $.$ The isentropic efficiency of the compressor is $85\%.$

For air, use the ideal gas model with the gas constant R$=0\mathrm{.}287$ kJ$/$kg$.$K$.$ Assume the air's specific heats vary with temperature. Calculate the following for the system:

$($a$)$ Sketch the actual and isentropic air compression processes between the inlet and outlet pressures on the T$-$s diagram. Show details and directions on the sketch.

$(3$ points$)$

$(7$ points$)$

$($b$)$ The temperature of air at compressor exit, in $K.$

$($c$)$ The power input to the compressor, in $[$kW$].$

$($d$)$ the net power delivered to the generator, in $[$kW$].$

$(7$ points$)$

$(7$ points$)$

$($e$)$ the rate of entropy generation within the compressor, in $k\frac{W}{K}.$

$(6$ points$)$

$,$

$1$MPa,$12$MPa

$,520C$