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Problem: Chemical engineers often have to design their synthesis process using a vessel at high pressure. A given reaction vessel contains 492cm³ of air at atmospheric pressure (1.01 × 10⁵ Pa) and a temperature of 27.0 µC. The next step in a given synthesis process compresses this air to a volume of 46.9cm3 and the gauge pressure has increased to 2.80 × 10⁶ Pa.

Part I: Compute the final temperature of the air after this compression?

Please also explain, thank you in advance.

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