Show that the efficiency of this engine, which only relies on the expansion and compression ratios

A cycle starts with an adiabatic compression of the air from state a with a volume V₃ to state b with volume V₁. At the end of the compression, heat is added (absorbed), resulting in an isobaric expansion to state c with volume V₂ followed by an adiabatic expansion back to volume V₃ at state d. Finally, heat is expelled, corresponding to an isochoric reduction completing the cycle and bringing air back to state a.

The ratio between the initial and final temperatures for the adiabatic compression is T_a / T_b = 1 / r_c^γ-1, and the adiabatic expansion is T_c / T_d = r_e^γ-1, where the compression ratio r_c = V₃ /V₁ and the expansion ratio r_e = V₃ /V₂.

Show that the efficiency of this engine, which only relies on the expansion and compression ratios, is as proved as in figure 1.
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