Match the List I with List II

	List - I		List - II
(A)	Triatomic rigid gas	(I)	$\frac{C_p}{C_v}=\frac{5}{3}$
(B)	Diatomic non-rigid gas	(II)	$\frac{C_p}{C_v}=\frac{7}{5}$
(C)	Monoatomic gas	(III)	$\frac{C_p}{C_v}=\frac{4}{3}$
(D)	Diatomic rigid gas	(IV)	$\frac{C_p}{C_v}=\frac{9}{7}$

Choose the correct answer from the options given below:

<p>The explanation uses the equation for the heat capacity ratio, $ \gamma = 1 + \frac{2}{\text{f}} $, where $ \text{f} $ is the degrees of freedom of the gas. Here's how it applies to different types of gases:</p> <p><strong>Triatomic Rigid Gas</strong>: </p> <p><p>Degrees of freedom ($ \text{f} $) = 6</p></p> <p><p>$ \gamma = 1 + \frac{2}{6} = \frac{4}{3} $</p></p> <p><strong>Diatomic Non-Rigid Gas</strong>: </p> <p><p>Degrees of freedom ($ \text{f} $) = 7</p></p> <p><p>$ \gamma = 1 + \frac{2}{7} = \frac{9}{7} $</p></p> <p><strong>Diatomic Rigid Gas</strong>: </p> <p><p>Degrees of freedom ($ \text{f} $) = 5</p></p> <p><p>$ \gamma = 1 + \frac{2}{5} = \frac{7}{5} $</p></p> <p><strong>Monoatomic Gas</strong>: </p> <p><p>Degrees of freedom ($ \text{f} $) = 3</p></p> <p><p>$ \gamma = 1 + \frac{2}{3} = \frac{5}{3} $</p></p> <p>Therefore, when matching List I with List II, the correct pairing is:</p> <p><p><strong>A</strong> (Triatomic rigid gas) - <strong>III</strong> $(\frac{4}{3})$</p></p> <p><p><strong>B</strong> (Diatomic non-rigid gas) - <strong>IV</strong> $(\frac{9}{7})$</p></p> <p><p><strong>C</strong> (Monoatomic gas) - <strong>I</strong> $(\frac{5}{3})$</p></p> <p><p><strong>D</strong> (Diatomic rigid gas) - <strong>II</strong> $(\frac{7}{5})$</p></p> <p>Thus, the correct answer from the options given is:</p> <p><strong>A-III, B-IV, C-I, D-II</strong></p>