Brayton cycle

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 $Q_{\mathrm{out}}/Q_{\mathrm{in}}=(T_4-T_1)/(T_3-T_2)=1/k$. The thermal efficiency isThis formula requires constant heat capacities and internally reversible insulated stages. An arbitrary dissipative adiabatic process does not satisfy the same pressure-temperature relation.

For constant-pressure heat addition $A\to B$ and two reversible ideal-gas adiabats, set $r=(p_h/p_l{)}^{(\gamma -1)/\gamma }$. The Brayton cycle has ${\eta }_B=1-1/r$, maximum temperature $T_B$ and minimum $T_D=T_A/r$. A Carnot cycle using those extreme temperatures has the strictly greater efficiency displayed whenever $T_B>T_A$. Reversibility of the isobaric heating requires continuously matched reservoir temperatures, rather than heat transfer solely at the maximum temperature.