The ratio of specific heat at constant pressure to specific heat at constant volume $(\gamma)$ for a gas is given by $\gamma = 1 + \frac{2}{f}$,where $f$ is the number of degrees of freedom of a molecule of the gas. What is the ratio of $\gamma_{d}$ for a rigid diatomic gas to $\gamma_{m}$ for a monoatomic gas?

  • A
    $\frac{14}{23}$
  • B
    $\frac{25}{21}$
  • C
    $\frac{21}{25}$
  • D
    $\frac{23}{14}$

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Match List-$I$ with List-$II$:
List-$I$ List-$II$
$(A)$ $3$ Translational degrees of freedom $(I)$ Monoatomic gases
$(B)$ $3$ Translational,$2$ rotational degrees of freedom $(III)$ Rigid diatomic gases
$(C)$ $3$ Translational,$2$ rotational and $1$ vibrational degrees of freedom $(IV)$ Non-rigid diatomic gases
$(D)$ $3$ Translational,$3$ rotational and more than one vibrational degrees of freedom $(II)$ Polyatomic gases

Choose the correct answer from the options given below:

For an ideal gas,$R = \frac{2}{3} C_v$. This suggests that the gas consists of molecules which are: $[R = \text{universal gas constant}]$

The ratio of specific heats at constant pressure and at constant volume is $\gamma$. To find out the degree of freedom,the expression is

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