An engine runs an ideal gas round an Otto-type cycle: an adiabatic compression, heating at constant volume, an adiabatic expansion, and cooling at constant volume. The lowest temperature in the cycle (at the start of the compression) is $300\ \text{K}$, and the highest (at the end of the heating) is $1200\ \text{K}$. The compression ratio is chosen so that the engine does the most work per cycle. What is then the efficiency of the cycle?