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**DEGREE OF FREEDOM**

Number of independent variables or coordinates needed to describe motion of a particle is called degree of freedom.

- Total number of dof = 3N (where N = atomicity)
- No. of translational dof (f
_{t}) = 3 (for all gases) - No. of rotational dof (f
_{r}) = 0 (for monoatomic gas)

= 2 (for diatomic gas)

= 2 (for polyatomic linear molecules)

= 3 (for polyatomic nonlinear molecule) - No. of vibrational dof (f
_{v}) = 3N - f_{t }- f_{r}

In a monoatomic species, rotational and vibrational modes of motion are absent. Hence three degree of freedom correspond to three translational motion along three different axes.

For a diatomic molecule, total degree of freedom = 3 Ã— 2 = 6

**Break up: ****(i) **3 translation degree of freedom representing translation motion of centre of mass in three independent directions.**(ii)** Two possible axes of rotation, hence two rotational degree of freedom.**(iii)** One vibration degree of freedom.

**Vibrational dof is active only at high temperatures.****Q. Find total degree of freedom and break up as translational, rotational or vibrational dofs in following cases.****(i)** O = C = O**(ii)****(iii)** He**(iv)** NH_{3}**Solution.****(i)** CO_{2}: Total dof = 3 x 3 = 9

Translational = 3

Rotational = 2 (âˆµ linear molecule)

Vibrational = 4

Total = 9

**(ii)** SO_{2}: Total dof = 3 x 3 = 9

Translational = 3

Rotational = 3 (âˆµ Bent molecule)

Vibrational = 3

Total = 9

**(iii) **He: Total dof = 3

Translational = 3

**(iv) **NH_{3}: Total dof = 3 x 4 = 12

Translational = 3

Rotational = 3 (âˆµ non linear molecule)

Vibrational = 6

Total = 12**LAW OF EQUIPARTITION OF ENERGY**

Energy equal to Â½ kT is associated with each translational and rotational degree of freedom per ideal gas molecule.

Energy equal to kT is associated with each vibrational degree of freedom per ideal gas molecule.

Where k = R/N_{A} Boltzmann constant

âˆ´ For n moles,

On ignoring vibrational degree of freedom

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