Irreversibility I = W_{max} – W_{act}

– W_{max }= Change in internal energy – T_{0} × Change in entropy

– W_{max} = (u_{2} – u_{1}) – T_{0}(s_{2} – s_{1}) = W_{rev}

– W_{max} = c_{v}(T_{2} – T_{1}) – T_{0}[c_{p} ln (T_{2}/T_{1}) – R ln (p_{2}/p_{1})]

= 0.716(370 – 300) – 293 × [1.005 ln (370/300) – 0.287 ln (6.8/1)]

W_{max} = –149.53 kJ/kg = W_{rev}

(negative sign indicates that work is done on air)

The index of compression ‘n’ is given by