The specific heats, ${\mathrm{C}}_p$ and ${\mathrm{C}}_v$ of a gas of diatomic molecules, $\mathrm{A},$ are given (in units of $\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}\mathrm{ }{\mathrm{K}}^{-1}$ ) by $29$ and $22,$ respectively. Another gas of diatomic molecules, $\mathrm{B},$ has the corresponding values $30$ and $21.$ If they are treated as ideal gases, then:

• A

  $\mathrm{A}$ has one vibrational mode and $\mathrm{B}$ has two
• Correct answer
  B

  $\mathrm{A}$ has a vibrational mode but $\mathrm{B}$ has none.
• C

  Both $\mathrm{A}$ and $\mathrm{B}$ have a vibrational mode each.
• D

  $\mathrm{A}$ is rigid but $\mathrm{B}$ has a vibrational mode.

Hence, the correct answer is option: 'B'.