 Otto cycle

The ideal Otto cycle consists of reversible adiabatic compression, constant-volume heat addition, reversible adiabatic expansion and constant-volume heat rejection. For a fixed amount of ideal gas with constant heat capacity ratio $\gamma =C_p/C_V>1$ and compression ratio $r=V_1/V_2>1$, its thermal efficiency isThe reversible adiabats are isentropic processes; merely preventing heat exchange would not make an irreversible compression obey the same relations.

To derive the formula, number the four states in cycle order. The adiabats giveWith constant whole-sample heat capacity at constant volume $C_V$, the absorbed and rejected heat magnitudes areSubstitution into $\eta =1-Q_{\mathrm{out}}/Q_{\mathrm{in}}$ cancels the heat-addition temperature difference and yields the stated result.

Within this model, larger $r$ increases thermal efficiency. Real engines also depend on combustion, heat transfer, friction and the temperature dependence of heat capacities; the formula does not predict those losses.