Mass of air, m = 1 kg
Initial temperature, T1 = T0 = 290 K
Final temperature, T2 = 400 K
Initial pressure, p1 = p0 = 1 bar
Final pressure, p2 = 6 bar.
(i) The irreversibility, I :
We know that reversible work,
Wrev. = Change in internal energy – T0 × Change in entropy
= 134.37 kJ/kg (–) [–ve sign indicates that work is done on the air] Actual work is given by
The index n for the compression is given by :
(–ve sign means that the work is done on the air)
Now, irreversibility = Wrev – Wactual
= – 134.37 – (– 144.8) = 10.43 kJ.
(ii) The effectiveness, ∈ :
∈ = \(\cfrac{W_{rev}}{W_{actual}}\)= \(\cfrac{-134.37}{-144.8}\) = 0.928 or 92.8%.