Question

Air at 1 atm, 60 F is compressed to 4 atm, after which it is expanded through a nozzle back to the atmosphere. The compressor and the nozzle both have efficiency of 90% and kinetic energy in/out of the compressor can be neglected. Find the actual compressor work and its exit temperature and find the actual nozzle exit velocity. 

Answer 1

Steady state separate control volumes around compressor and nozzle. For ideal compressor we have inlet : 1 and exit : 2 

Adiabatic : q = 0.

Reversible: s_gen = 0

Energy Eq.: h₁ + 0 = w_C + h₂;

Entropy Eq.: s₁ + 0/T + 0 = s₂

Ideal compressor: w_c = h₁ - h₂ , s₂ = s₁ 

The constant s from Eq