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A tire is filled with air at 13 ∘C to a gauge pressure of 230 kPa . \ \ \ \ If the tire reaches a temperature of 40 ∘C, what fraction of the original air must be removed if the original pressure of 230 kPa is to be maintained? \ \ \ \ Initial temperature $\"\"$ of the air = 13°C = 13+273 = 286 K.

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Final temperature $\"\"$ of the air = 40°C = 40+273 = 313 K.

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Equation of the ideal gas: $\"\"$ .

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Guage pressure is maintained constant.

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Hence volume and pressure are constant. \ \

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$\"\"$

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Find the fraction of air which will be removed.

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Let $\"\"$ be fraction of air which will be removed.

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$\"\"$

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$\"\"$ is inversely proportional to temperature $\"\"$ , therefore $\"\"$

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$\"\"$

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$\"\"$

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The amount of fraction of air which will be removed is 0.0863.

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