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### Thermodynamics Problem: Adiabatic Expansion of an Ideal Diatomic Gas

**1. Problem Statement:**

An ideal diatomic gas at 65 K is slowly expanded adiabatically and reversibly to twice its original volume. What is its final temperature?

\[ \text{Final temperature} = \_\_\_\_ \sqrt{\ } K \]

**Think:**
Should the gas cool down or heat up during the adiabatic expansion? Does your answer validate your prediction?

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