= Brayton cycle
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The ideal Brayton cycle consists of <adiabatic compression>, constant-pressure <heat> addition, <adiabatic expansion>, and constant-pressure heat rejection. Its ideal working substance is an <ideal gas> with constant <heat capacities>, and the insulated stages are <reversible thermodynamic processes>.
For pressure ratio $r_p=p_h/p_l$ and <heat capacity ratio> $\gamma=C_p/C_V$, a <reversible ideal-gas adiabat> has $T\propto p^{(\gamma-1)/\gamma}$. Thus $T_2/T_1=T_3/T_4=k=r_p^{(\gamma-1)/\gamma}$, and the constant-pressure heat transfers have $Q_{\rm out}/Q_{\rm in}=(T_4-T_1)/(T_3-T_2)=1/k$. The <thermal efficiency> is
$$
\boxed{\eta=1-r_p^{-(\gamma-1)/\gamma}.}
$$
This formula requires constant <heat capacities> and internally reversible insulated stages. An arbitrary dissipative <adiabatic process> does not satisfy the same pressure-temperature relation.
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