GATE 2009 AEROSPACE ENGINEERING (Q 21-30)

1. An ideal axial compressor is driven by an ideal turbine across which the total temperature ratio is 0.667. If the total temperature at turbine inlet is T₀ = 1500 K and specific heat of gas c_p= 1 kJ/kg/K, the power drawn by the compressor per unit mass flow rate of air is approximately,
   1. 300 kW/kg/s
   2. 1000 kW/kg/s
   3. 600 kW/kg/s
   4. 500 kW/kg/s

   Answer:- 500 kW/kg/s

   The units of the c_p are wrong. It should be 1 kJ/kgK.

   For ideal axial compressor and turbine system,

   Power required by the compressor = Power extracted by the turbine

   = c_p(T₀₁-T₀₂) (T₀₁ = Turbine inlet temperature T₀₂ = Turbine exit temperature)

   = c_p*T₀₁[1-(T₀₂/T₀₁)]

   = 1*1500(1-0.667)

   = 499.5 kW/kg/s ~ 500kW/kg/s