Consider an ideal gas refrigeration cycle using helium as the working fluid. Helium enters the compressor at 100 kPa and -20°C and is compressed to 220 kPa. Helium is then cooled to 20°C before it enters the turbine. For a mass flow rate of 0.22 kg/s, the net power input required is

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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=5.1926 "kJ/kg.K"
P1= 100 "kPa"
T1=-20+273 "K"
P2=220 "kPa"
T3=20+273 "K"
m=0.22 "kg/s"
"Mimimum temperature is the turbine exit temperature"
T2=T1*(P2/P1)^((k-1)/k)
T4=T3*(P1/P2)^((k-1)/k)
W_netin=m*Cp*((T2-T1)-(T3-T4))
"Some Wrong Solutions with Common Mistakes:"
W1_Win = m*Cp*((T22-T1)-(T3-T44)); T22=T1*P2/P1; T44=T3*P1/P2 "Using wrong relations for temps"
W2_Win = m*Cp*(T2-T1) "Ignoring turbine work"
W3_Win=m*1.005*((T2B-T1)-(T3-T4B)); T2B=T1*(P2/P1)^((kB-1)/kB); T4B=T3*(P1/P2)^((kB-1)/kB); kB=1.4 "Using air properties"
W4_Win=m*Cp*((T2A-(T1-273))-(T3-273-T4A)); T2A=(T1-273)*(P2/P1)^((k-1)/k); T4A=(T3-273)*(P1/P2)^((k-1)/k) "Using C instead of K"

Consider an Ideal Gas Refrigeration Cycle Using Helium as the Working