Class 11 Physics Kinetic Theory Rotational Degree of freedom

Rotational Degree of freedom

  • Independent rotations that specify the orientation of a body or system.
    • There is rotation of one part of the body with respect to the other part.
  • Rotational degree of freedom happens only in diatomic gas.
  • Diatomic molecules have rotational degrees of freedom in addition to translational degrees of freedom.
  • It is possible in diatomic molecules as 2 atoms are connected together by a bond.So the rotation of one atomw.r.t to other atom.
  • In diatomic there is translational in addition to that they have rotational degree of freedom also.
    • For example: - Two oxygen atoms joined together by a bond. There are two perpendicular axes.
    • There are 2 rotations possible along the two axes.
    • They have 3 translational degrees of freedom and also 2 rotational degree of rotation.
  • Therefore Rotational degree of freedom contributes a term to the energy that contains square of a rotational variable of motion.
  • Rotational variable of motion comes from angular momentum ω.
    • Linear velocity is vx,vy,vz. Whereas angular velocity is wx,wy,wz.
    • ER(rotational) = (1/2)(I1ω1)+(1/2)I2 ω2. These are 3 rotationaldegrees of freedom along the 2 perpendicular axes.
  • The total energy contribution due to the degrees of freedom for oxygen molecule.
    • There will be 3 translational degree of freedom (1/2)mxvx2,(1/2)myvy2,(1/2)mzvz2)
    • 2 rotational degree of freedom (1/2)I12ω12,(1/2)I22ω22

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