Question

Air at 100 kPa, 17°C is compressed to 400 kPa after which it is expanded through a nozzle back to the atmosphere. The compressor and the nozzle are both reversible and adiabatic and kinetic energy in and out of the compressor can be neglected. Find the compressor work and its exit temperature and find the nozzle exit velocity. 

Answer 1

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 - w_C

= h₂ - h₁ , s₂ = s₁ 

Propertiesair: C_Po = 1.004 kJ/kg K, R = 0.287 kJ/kg K, k = 1.4 

Process gives constant s (isentropic) which with constant C_Po gives

The ideal nozzle then expands back down to P1 (constant s) so state 3 equals state 1. The energy equation has no work but kinetic energy and gives: