Problem: For gasoline engines, a larger compression ratio, defined as Vmax / Vmin for the piston, means a greater efficiency. In a typical engine, air is mixed with fuel at atmospheric pressure (1x105 Pa) and 0.5 L of this mixture is drawn into a piston, compressed to Vmin, and then ignited. However, a piston can only compress the mixture so much before the fuel can be ignited by the increase in temperature of the air alone, usually at a temperature of 250oC. If we consider the compression to be very rapid, we can say PVγ is a constant, where γ = 1.24 for a fuel-air mixture. If the fuel-air mixture is drawn into the piston at 27oC, what would the maximum theoretical compression ratio be for this engine?

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For gasoline engines, a larger compression ratio, defined as Vmax / Vmin for the piston, means a greater efficiency. In a typical engine, air is mixed with fuel at atmospheric pressure (1x105 Pa) and 0.5 L of this mixture is drawn into a piston, compressed to Vmin, and then ignited. However, a piston can only compress the mixture so much before the fuel can be ignited by the increase in temperature of the air alone, usually at a temperature of 250oC. If we consider the compression to be very rapid, we can say PVγ is a constant, where γ = 1.24 for a fuel-air mixture. If the fuel-air mixture is drawn into the piston at 27oC, what would the maximum theoretical compression ratio be for this engine?

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