Question

The specific heats, $C_P$ and $C_V$ of a gas of diatomic molecules, $A$, are given (in units of $Jmo{l}^{-1}{K}^{-1}$) 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
$R=C_p-C_v=7$
$C_V=\frac{fR}{2}=22\Rightarrow f=\frac{44}{7}=6.3$
$f\simeq 6\begin{array}{cc}\to & 5\left(\text{Rotation}+\text{Translatioal}\right)\\ \to & 1\left(\text{Vibration}\right)\end{array}$
For B
$R=C_P-C_V=9$
$C_V=\frac{fR}{2}=21\Rightarrow f=\frac{42}{9}$
$f\simeq 5\begin{array}{cc}\to & 5\left(\text{Rotation}+\text{Translatioal}\right)\\ \to & 0\left(\text{Vibration}\right)\end{array}$