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The value of $γ (= \frac{C_{p}}{C_{v}})$ , for hydrogen, helium, and another ideal diatomic gas X (Whose molecules are not rigid but have an additional vibrational mode), are respectively equal to

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$\frac{7}{5}, \frac{5}{3}, \frac{9}{7}$

$\frac{5}{3}, \frac{7}{5}, \frac{9}{7}$

$\frac{5}{3}, \frac{7}{5}, \frac{7}{5}$

$\frac{7}{5}, \frac{5}{3}, \frac{7}{5}$

answer is A.

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Detailed Solution

$γ = 1 + \frac{2}{f}$

For $H_{2}, γ = 1 + \frac{2}{5} = \frac{7}{5}$

For $H e, γ = 1 + \frac{2}{3} = \frac{5}{3}$

For $X, γ = 1 + \frac{2}{7} = \frac{9}{7}$

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