Question

Air enters an adiabatic compressor at atmospheric conditions of 1 bar, 15°C and leaves at 5.5 bar. The mass flow rate is 0.01 kg/s and the efficiency of the compressor is 75%. After leaving the compressor, the air is cooled to 40°C in an after-cooler. Calculate

(a) The power required to drive the compressor

(b) The rate of irreversibility for the overall process (compressor and cooler).

Answer 1

For minimum work required to compressor is isentropic

∴ Actual work required

W_act = \(\frac{181.55}{0.75}\) = 242 kJ/kg

(a) ∴ Power required driving the compressor

= \(\overset • m\) W_act 

= 2.42 kW

Extra work added in 2′ to 2 is (242 – 181.55) = 60.85 kJ/kg

∴ If C_P (T₂ -  T'₂) = 60.85

or T₂ = \(\frac{60.85}{1.005}\)

= 529.25 K

∴ Availability loss due to cooling

∴ Total available energy loss = (60.85 + 65.302) kJ/kg 

= 126.15 kJ/kg

∴ Power loss due to irreversibility = 1.2615 kW