Choose the correct option for free expansion of an ideal gas under adiabatic condition:

Question

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Strategy:
 Free expansion occurs when a gas expands into a vacuum (). Combine this with the definition of adiabatic conditions to deduce the values of  and .

Step 1: Analyze the process conditions
- Adiabatic: By definition, .
- Free Expansion: Expansion against . Work .

Step 2: Apply the First Law
.

Step 3: Analyze Temperature change
For an ideal gas, internal energy is a function of temperature only (). Since , it follows that .
Summary: .

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