Molar Specific Heat Ratio of Polyatomic Gas – Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

A polyatomic molecule has 3 translational, 3 rotational degrees of freedom. The molar specific heat ratio \((\gamma = \frac{C_p}{C_v})\) for this gas is
\(\frac{7}{5}\)
\(\frac{7}{6}\)
\(\frac{4}{3}\)
\(\frac{3}{2}\)

Solution Explained:

To solve this problem, we apply the core principles of Kinetic Theory of Gases. Understanding the underlying formula is key to arriving at the correct answer below:

Total degrees of freedom \(f = 3 + 3 = 6\). Thus, \(C_v = \frac{f}{2} R = 3R\), and \(C_p = C_v + R = 4R\). Therefore, \(\gamma = \frac{C_p}{C_v} = \frac{4}{3}\).

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