# Air at the rate of 25 kg/min is compressed in a centrifugal air compressor from 1 bar to 2 bar.

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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, cp = 1.005 kJ/kg K, R = 0.287 kJ/kg K

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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

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

= cp (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