Question

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

• A. A has one vibrational mode and B has two
• B. Both A and B have a vibrational mode each
• C. A is rigid but B has a vibrational mode
• D. A has a vibrational mode but B has none

Answer 1

Answer: (D)

For A
$R = C_p - C_v = 7$
$C_{V} = \frac{fR}{2} = 22 \Rightarrow f= \frac{44}{7} = 6.3 $
$ f \simeq6 \begin{matrix} \to &5 \left(\text{Rotation}+\text{Translatioal}\right)\\ \to &1 \left(\text{Vibration}\right)\end{matrix} $
For B
$ R = C_{P} -C_{V} =9 $
$ C_{V} = \frac{fR}{2} = 21 \Rightarrow f= \frac{42}{9} $
$ f \simeq 5 \begin{matrix} \to &5 \left(\text{Rotation}+\text{Translatioal}\right)\\ \to &0 \left(\text{Vibration}\right)\end{matrix}$