Question:
why do we relate rotational degree of freedom with energy
Answer:
- The 3n degrees of freedom describe the translational, rotational, and vibrational motions of the molecule. The rotations occur around the two axes perpendicular to the line between the two atoms. The Rotational degree of freedom happens only in diatomic gas. It is possible in diatomic molecules as two atoms are connected together by a bond. So the rotation of one atom with respect to other atom results in rotational degree of freedom.
- Consider an oxygen molecule. The two oxygen atoms are joined together by a bond and there are two perpendicular axis. There are two rotations possible along the two axis.
- There are 3 translational degree of freedom and two rotational degrees of freedom in the above case which contributes to the energy.
- Let the linear velocity be vx, vy and vz and the angular velocity be ωx , ωy and ωz
- Total energy = (1/2)mxvx2 + (1/2)myvy2 + (1/2)mzvz2) which are translatory in nature plus (1/2)I12ω12 + (1/2)I22ω22 which are rotational
- As angular momentum is involved, we associate rotational degree of freedom with energy.
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