Question

Air at the rate of 25 kg/min is compressed in a centrifugal air compressor from 1 bar to 2 bar. The temperature increases from 15°C to 100°C during compression. Determine actual and minimum power required to run the compressor. The surrounding air temperature is 15°C. 

Neglect the heat interaction between the compressor and surroundings and changes in potential and kinetic energy. 

Take for air, c_p = 1.005 kJ/kg K, R = 0.287 kJ/kg K

Answer 1

Rate of flow of air, m = 25 kg/min. 

Initial pressure, p₁ = 1 bar 

Final pressure, p₂ = 2.0 bar 

Initial temperature, T₁ = T₀ = 15 + 273 = 288 K 

Final temperature, T₂ = 100 + 273 = 373 K. 

Applying energy equation to compressor

W_actual = h₂ – h₁ [as Q = 0, ∆PE = 0, ∆KE = 0] 

= c_p (T₂ – T₁) = 1.005 (373 – 288) = 85.4 kJ/kg

Total actual work done/min 

= 25 × 85.4 = 2135 kJ/min

= \(\cfrac{2135}{60}\) = 35.58 kJ/s = 35.58 kW

The minimum work required is given by the increase in availability of the air stream.

= 85.4 – 288 × 0.061 = 67.8 kJ/kg

Minimum work required

\(\cfrac{25\times67.8}{60}\) = 28.25 kJ/s = 28.25 kW