Which statements are correct about degrees of freedom?
A. A molecule with $n$ degrees of freedom has $n^2$ different ways of storing energy.
B. Each degree of freedom is associated with $\dfrac12RT$ average energy per mole.
C. A monoatomic gas molecule has $1$ rotational degree of freedom where as diatomic molecule has $2$ rotational degrees of freedom
D. $\text{CH}_4$ has a total to $6$ degrees of freedom.
Choose the correct answer from the option given below:
Answer: (B) B and D only
A: False. $n$ degrees of freedom mean $n$ independent ways of storing energy.
B: True. Equipartition gives $\dfrac12k_BT$ per molecule, i.e. $\dfrac12RT$ per mole, for each degree of freedom.
C: False. A monoatomic molecule has no rotational degrees of freedom.
D: True. $\text{CH}_4$ is a non-linear molecule: 3 translational + 3 rotational = 6.
B and D only.
Solution by Sreeraj P, M.Sc Physics