Amira, a first-year chemistry student, is studying oxygen gas in a closed, fixed-volume container. Using the formula \(Q=mc\Delta T\), she heats the gas with *exactly* the amount of energy needed to raise the temperature of the gas from \(300K\) to \(325K\), forgetting that gases can also use this energy for work, or adiabatic expansion. After running the experiment, she is extremely surprised to find that the temperature of the gas itself is exactly the same! However, the gas has expanded by a certain volume, due to the increase in energy.

Find \(\frac { { P }_{ i } }{ { P }_{ f } }\), the ratio of the gas's initial pressure to final pressure, assuming that the specific heat capacity of oxygen gas is constant at \(C=920J{ kg }^{ -1 }{ K }^{ -1 }\). Round your answer to three decimal places.

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