1. Tardigrade
  2. Question
  3. Physics
  4. Statement I: Each vibrational mode gives two degrees of freedom Statement II: By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is 2kB T.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Statement I : Each vibrational mode gives two degrees of freedom
Statement II : By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is $2k_B T$.

Kinetic Theory

Solution:

By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is $\frac{1}{2} k_B T$.
Each quadratic term form in the total energy expression of a molecules is to be counted as a degree of freedom. Thus each vibrational mode gives $2$ degree of freedom
i.e, kinetic and potential energy modes, corresponding to the energy $2\left(\frac{1}{2} k _{ B } T \right)= k _{ B } T$