Question

A small air turbine with an isentropic efficiency of 80% should produce 270 kJ/kg of work. The inlet temperature is 1000 K and it exhausts to the atmosphere. Find the required inlet pressure and the exhaust temperature. 

Answer 1

C.V. Turbine actual energy Eq.  

w = h_i - h_e,_ac = 270 kJ/kg 

h_i = 1046.22 ⇒ h_e,ac = 776.22 kJ/kg, T_e = 757.9 K

C.V. Ideal turbine, Eq. and energy Eq 

w_s = w/η_s = 270/0.8 = 337.5 = h_i - h_e,s ⇒ h_e,s = 708.72 kJ/kg From T_e,s = 695.5 K

Entropy Eq.  s_i = s_e,s adiabatic and reversible 

To relate the entropy to the pressure use Eq  inverted and standard entropy