Brayton-Carnot efficiency comparison (${\eta }_C-{\eta }_B=r^{-1}(1-T_A/T_B)>0$)

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.