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1

I'm taking this out of wikipedia: the molar specific heat at constant pressure, $C_p$ of oxygen is 29.4 J/(mol K). Other values from standard tables say 0.92J/gK at 298K, and we can check that this is the same thing. Dividing by the gas constant R=8.314 J/(mol K), we get $\frac{C_p}{nR}=3.5$, which tells us that $\frac{C_V}{nR}=2.5$, so we indeed have five ...

0

I Worte the equations for your case Where S is the rotation matrix between body fixed system and Inertial system

4

Because translational and angular velocities for such a system are tied together; once you know one, you can directly tell the other. Therefore the system has only three degrees of freedom.

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