Boyle’s Law and Molecular Velocity – Rankers Physics

Thermodynamics: Practice Problem & Solution

Assertion (A): For an ideal gas, at constant temperature, the product of the pressure and volume is constant. Reason (R): The mean square velocity of gas molecules is inversely proportional to mass of molecule.  
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 Thermodynamics. Understanding the underlying formula is key to arriving at the correct answer below:

Boyle's Law states that for an ideal gas at constant T, \( PV = \text{constant} \). So (A) is true. The mean square velocity \( = \frac{3kT}{m} \), so it is inversely proportional to molecular mass m.

So (R) is true. However, (R) does not explain Boyle's law (A).

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