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OJEE Degrees of Freedom — practice questions

Explore 3 free Degrees of Freedom questions in OJEE Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Degrees of Freedom questions and exercises with answers

Showing questions 1–3 of 3.

Number of degrees of freedom (DOF) of a monatomic gas (e.g. helium) molecule:Read the answer and worked solution →Number of degrees of freedom of a **rigid diatomic molecule** (e.g. O₂ at room temperature, vibrations not excited):Read the answer and worked solution →If vibrations are excited, a diatomic molecule has DOF:Read the answer and worked solution →

Worked practice questions

Number of degrees of freedom (DOF) of a monatomic gas (e.g. helium) molecule:

  1. 1
  2. 2
  3. 3 (translational only)
  4. 5
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Correct answer: C. 3 (translational only)

**Monatomic:** 3 translational DOF only. No rotation contributes (a point mass has zero moment of inertia), no vibrations (single atom). Internal energy per mole = (3/2)RT.

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Number of degrees of freedom of a **rigid diatomic molecule** (e.g. O₂ at room temperature, vibrations not excited):

  1. 3
  2. 5 (3 translational + 2 rotational)
  3. 6
  4. 7
Show answer and solution

Correct answer: B. 5 (3 translational + 2 rotational)

**Rigid diatomic:** 3 translational + 2 rotational (about two axes perpendicular to molecular axis; rotation about the axis itself contributes negligibly). $C_V = (5/2)R$, $C_P = (7/2)R$, $\gamma = 7/5 = 1.4$.

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If vibrations are excited, a diatomic molecule has DOF:

  1. 5
  2. 6
  3. 7 (3 trans + 2 rot + 2 vib (KE + PE))
  4. 9
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Correct answer: C. 7 (3 trans + 2 rot + 2 vib (KE + PE))

At high T, vibrational modes 'unlock' — diatomic vibration contributes 2 DOF (KE + PE both quadratic). Total = 3 + 2 + 2 = 7. $C_V = (7/2)R$. Realised only at high temperatures.

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