Degrees of Freedom and Heat Capacity Ratio – Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

Assertion (A): The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas. Reason (R): The ratio of \(\frac{C_p}{C_v}\) for an ideal diatomic gas is more than that for an ideal monoatomic gas (where \(C_p\) and \(C_v\) have usual meaning).  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

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:

Monoatomic gas has 3 degrees of freedom, diatomic has 5 (or 7). So (A) is true. The ratio \(\gamma = 1 + \frac{2}{f}\) is \(5/3\) for monoatomic and \(7/5\) for diatomic. Since \(5/3 > 7/5\), (R) is false.

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