A gas consisting of rigid diatomic molecules (degrees of freedom r = 5) under standard conditions `(P_(0) = 10^(5)` Pa and `T_(0) = 273 K`) was compressed adiabatically `eta = 5` times. Find the mean kinetic energy of a rotating molecule in the final state.

Explanation

To solve the problem step by step, we will follow the outlined approach in the video transcript.

### Step 1: Understanding the Degrees of Freedom
For a rigid diatomic molecule, the degrees of freedom (r) are given as 5. This includes:
- 3 translational degrees of freedom (movement in x, y, z directions)
- 2 rotational degrees of freedom (rotation about two axes perpendicular to the bond axis)

### Step 2: Mean Kinetic Energy of a Rotating Molecule
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