Q140 / 160 · TS EAMCET 2018 (07 May Shift 1) · Physics

A polyatomic gas has $f$ vibrational degrees of freedom, then the ratio of the specific heat at constant pressure to that at constant volume will be

  • Correct answer
    A
    $\frac{4+f}{3+f}$
  • B
    $\frac{4-f}{3-f}$
  • C
    $\frac{3+f}{4+f}$
  • D
    $\frac{3-f}{4-f}$

Solution

For a polyatomic atom value of specific heat at constant volume, $C_V=(3+f) R$ where, $f=$ vibration degree of freedom and $R=$ gas constant. Now, $$ \begin{aligned} & C_p=C_V+R \\ & C_p=(3+f) R+R \\ & C_p=(4+f) R \end{aligned} $$ Now, ratio of $C_p$ and $C_V$ $$ \frac{C_p}{C_V}=\frac{4+f}{3+f} $$

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

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