The maximum net specific work obtainable in an ideal Brayton cycle for T_max = 900 K and

T­_min = 400 K is given by

Concept:

A gas turbine works upon the Brayton cycle.

In order to achieve maximum work, the temperature after compression (T₂) and after exhaust from the turbine (T₄) is given by

\({{\rm{T}}_2} = {{\rm{T}}_4} = {\rm{\;}}\sqrt {{{\rm{T}}_{{\rm{max}}}} \times {\rm{\;}}{{\rm{T}}_{{\rm{min}}}}} = \sqrt {{{\rm{T}}_3} \times {\rm{\;}}{{\rm{T}}_1}}\)

Where T₃ is the temperature at the turbine inlet and T₁ is the temperature of the air before compression

Since compressor also consumes the work, therefore, the net work is the difference between the work done by the turbine and the work consumed by the compressor

Maximum net specific work obtainable = Turbine work – Compressor work

W_net = w_T - w_C

w_T = C_p (T₃ – T₄)

W_C = C_p (T₂ – T₁)

Calculation:

Given, T_max = 900 K, T_min = 400 K

∴ \({{\rm{T}}_2} = {{\rm{T}}_4} = \sqrt {{{\rm{T}}_3} \times {\rm{\;}}{{\rm{T}}_1}} = \sqrt {900\; \times 400} = 600\;K\)

\({{\rm{w}}_{{\rm{net}}}} = {\rm{\;}}{{\rm{C}}_{\rm{p}}}{\rm{\;}}\left[ {\left( {{{\rm{T}}_3} - {{\rm{T}}_2}} \right) - \left( {{{\rm{T}}_4} - {{\rm{T}}_1}} \right)} \right]\)

\({{\rm{w}}_{{\rm{net}}}} = {\rm{\;}}{{\rm{C}}_{\rm{p}}}\left[ {\left( {900 - 600} \right) - \left( {600 - 400} \right)} \right]\)

w_net = C_p (300 – 200) = 100 C_p