Air enters an insulated compressor operating at a steady sta

Air enters an insulated compressor operating at a steady state of 1.05 bars, 22C with a mass flow rate of 1.8kg/s and exits at 2.9 bars. KE and PE are negligible. If isentropic efficiency is 80% determine a) the outlet temperature b) minimum theoretical work input c) actual work input

Solution

at 1.05 bar and 22 C    h₁ = 295 kJ/kg   s₁ = 6.84 kJ/kgK

for 100 % isoentropic exit we have s₁ = s_2s

at 2.9 bar and s_2s   = 6.84   we get T_2s   = 121 C and h_2s   = 395 kJ/kg

isoentropic efficiency   = 0.8   = ( h_2s - h₁) / (h₂ - h₁ )

h₂   = 295 + (395 - 295) / 0.8   = 420 kJ/kg

a) Outlet temperature   = 145 C

b) theoretical work = mass flow rate * ( h_2s - h₁) = 1.8 * (100)   = 180 kW

c) actual work   = mass flow rate * (h₂ - h₁ ) = 1.8 * (420 - 295)   = 225 kW