Helium gas expands in an adiabatic turbine steadily from 700°C and 900 kPa to 70 kPa at a rate of 0.15 kg/s. For an isentropic efficiency of 82%, the power produced by the turbine is
A)398 kW
B)286 kW
C)592 kW
D)2650 kW
E)239 kW

Question

Quizplus · Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
Cp=5.1926 "kJ/kg-K"
k=1.667
m=0.15 "kg/s"
T1=700 "C"
P1=900 "kPa"
P2=70 "kPa"
Eta_turb=0.82 
T2s=(T1+273)*(P2/P1)^((k-1)/k)-273
Eta_turb=(Cp*(T2-T1))/(Cp*(T2s-T1))
W_out=m*Cp*(T1-T2)
"Some Wrong Solutions with Common Mistakes:"
T2sW1=T1*(P2/P1)^((k-1)/k) "Using C instead of K to find T2s"
Eta_turb=(Cp*(T2W1-T1))/(Cp*(T2sW1-T1))
W1_Wout=m*Cp*(T1-T2W1)
Eta_turb=(Cp*(T2s-T1))/(Cp*(T2W2-T1)) "Using wrong definition for isentropic efficiency, and using C"
W2_Wout=m*Cp*(T1-T2W2)
W3_Wout=Cp*(T1-T2) "Not using mass flow rate"
Cv=3.1156 "kJ/kg.K"
W4_Wout=m*Cv*(T1-T2) "Using Cv instead of Cp"

Helium Gas Expands in an Adiabatic Turbine Steadily from 700°C