$7\mathrm{.}16.$ A turbine operates adiabatically with superheated steam entering at $T_1$ and $P_1$ with a mass flow rate $m^{}.$ The exhaust pressure is $P_2$ and the turbine efficiency is $.$ For one of the following sets of operating conditions, determine the power output of the turbine and the enthalpy and entropy of the exhaust steam.

$($a$){}_1=450C,P_1=8000$kPa,$m^{}=80kg*s^{-1},P_2=30$kPa,$=0\mathrm{.}80.$

$($b$)T_1=550C,P_1=9000$kPa,$m^{}=90kg*s^{-1},P_2=20$kPa,$=0\mathrm{.}77.$

$($c$)T_1=600C,P_1=8600$kPa,$m^{}=70kg*s^{-1},P_2=10$kPa,$=0\mathrm{.}82.$

$($d$)T_1=400C,P_1=7000$kPa,$m^{}=65kg*s^{-1},P_2=50$kPa,$=0\mathrm{.}75.$

$($e$)T_1=200C,P_1=1400$kPa,$m^{}=50kg*s^{-1},P_2=200$kPa,$=0\mathrm{.}75.$

$($f$)T_1=900(F),P_1=1100(a),m^{}=150(l{b}_m)(s{)}^{-1},P_2=2(a),=0\mathrm{.}80.$

$($g$)T_1=800(F),P_1=1000(a),m^{}=100(l{b}_m)(s{)}^{-1},P_2=4(a),=0\mathrm{.}75.$