Argon gas enters an adiabatic nozzle steadily at 800°C and 700 kPa with a low velocity, and exits at a pressure of 120 kPa. The highest possible velocity of helium gas at the nozzle exit is
A)649 m/s
B)503 m/s
C)888 m/s
D)1070 m/s
E)752 m/s

Question

Quizplus · Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
k=1.667
Cp=0.5203 "kJ/kg.K"
Cv=0.3122 "kJ/kg.K"
T1=800 "C"
P1=700 "kPa"
Vel1=0
P2=120 "kPa"
"s2=s1 for maximum exit velocity"
"The exit velocity will be highest for isentropic expansion," 
T2=(T1+273)*(P2/P1)^((k-1)/k)-273 "C"
"Energy balance for this case is h+ke=constant for the fluid stream (Q=W=pe=0)"
(0.5*Vel1^2)/1000+Cp*T1=(0.5*Vel2^2)/1000+Cp*T2
 
"Some Wrong Solutions with Common Mistakes:"
T2a=T1*(P2/P1)^((k-1)/k) "Using C for temperature" 
(0.5*Vel1^2)/1000+Cp*T1=(0.5*W1_Vel2^2)/1000+Cp*T2a
T2b=T1*(P2/P1)^((k-1)/k) "Using Cv" 
(0.5*Vel1^2)/1000+Cv*T1=(0.5*W2_Vel2^2)/1000+Cv*T2b
T2c=T1*(P2/P1)^k "Using wrong relation" 
(0.5*Vel1^2)/1000+Cp*T1=(0.5*W3_Vel2^2)/1000+Cp*T2c

Argon Gas Enters an Adiabatic Nozzle Steadily at 800°C and 700