Question:
Match the $\mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}}$ ratio for ideal gases with different type of molecules:
Correct Option: , 3
Solution:
(3) As we know,
$\gamma=\frac{C_{p}}{C_{v}}=1+\frac{2}{f}$, where $f=$ degree of freedom
(A) Monatomic, $f=3$
$\therefore \gamma=1+\frac{2}{3}=\frac{5}{3}$
(B) Diatomic rigid molecules, $f=5$
$\therefore \gamma=1+\frac{2}{5}=\frac{7}{5}$
(C) Diatomic non-rigid molecules, $f=7$
$\therefore \gamma=1+\frac{2}{7}=\frac{9}{7}$
(D) Triatomic rigid molecules, $f=6$
$\therefore \gamma=1+\frac{2}{6}=\frac{4}{3}$
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