Steps of the Otto cycle:

• Fuel injection at 1
• 1 → 2 compression
• 2 → 3 spark + combustion
• 3 → 4 power
• 4 → 1 exhaust

Combustion step (2 → 3):   Q_h = n C_V(T_C-T_B)

Exhaust step (4 → 1): Q_c = n C_V(T_D-T_A)

The efficiency is:   η

= 1 -

Qc Qh

= 1 -

TD - TA TC - TB

Now use adiabatic rule:   TV^γ-1 = const. ≡ K   or   T = K V^1-γ

The efficiency becomes:   η

= 1 -

KhVD1-γ - KcVA1-γ KhVC1-γ KcVB1-γ

= 1 -

Vmax1-γ Vmin1-γ

Rewrite as:   η = 1 - r^1-γ   with r = V_max/V_min the compression ratio.