For the Brayton cycle, the maximum temperature in the cycle is limited to T3 by metallurgical conditions. The minimum temperature is set to T1 by the temperature of inlet air. 

1

The optimum pressure ratio for fixed values of T1 and T3, for which work is maximum is given by \({\left( {\frac{{{T_3}}}{{{T_1}}}} \right)^{\frac{\gamma }{{2\left( {\gamma - 1} \right)}}}}\)

2

At that optimum pressure ratio, thermal efficiency of the brayton cycle is given by \(1 - \sqrt {\frac{{{T_3}}}{{{T_1}}}} \)

3

At that optimum pressure ratio, heat rejected during the brayton cycle is given by \(m{C_p}\left[ {\sqrt {{T_1}{T_3}} - {T_1}} \right]\) 

4
The maximum work for fixed values of T1 and T3  is given by \(m{C_P}{\left[ {\sqrt {{T_1}} - \sqrt {{T_3}} } \right]^2}\)

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