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⚛️ Physics  ·  Kinetic Theory  ·  NEET & JEE

A vessel contains N<sub>2</sub> gas at temperature T. If the temperature is raised such that the gas molecules begin to dissociate into individual N atoms at very high T, the degrees of freedom of the system effectively:

Answer: Decreases from 5 to 3 per resulting particle, since atoms only have translational degrees of freedom.

  • A Increases from 5 to 6, since atoms mainly have translational freedom but more molecules exist in routine practice
  • B Decreases from 5 to 3 per resulting particle, since atoms only have translational degrees of freedom
  • C Stays at 5 overall in most cases under typical conditions according to standard textbooks in general practice
  • D Becomes 7 as frequently described in most textbook accounts during normal conditions as generally observed

Correct answer: B. Decreases from 5 to 3 per resulting particle, since atoms only have translational degrees of freedom

Explanation: Diatomic N<sub>2</sub> molecules have f=5 (translational+rotational). After dissociation into individual N atoms, each atom (monatomic) only has translational freedom, f=3 per atom.

Maxwell-Boltzmann Speed Distributionspeed (v)fraction of moleculesv_pv_avgv_rmsv_p < v_avg < v_rms always, for any gas at any temperature

Not all gas molecules move at the same speed - the Maxwell-Boltzmann distribution shows the spread, with the most probable speed vp slightly less than the average vavg, which is slightly less than the root-mean-square speed vrms used in the pressure formula.

Concept context

Kinetic theory of gases connects molecular motion to pressure and temperature, explaining gas laws, specific heats, and molecular speeds.

Read the full Kinetic Theory notes →