Free Expansion of Ideal Gas – Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

Assertion (A): During free expansion of an Ideal gas, entropy is zero. Reason (R): Internal energy of an ideal gas is zero during free expansion.  
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:

Concept: Free expansion of an ideal gas. Entropy change. Internal energy.
Formula: For ideal gas, \( \Delta U = 0 \) (as \( Q=0, W=0 \)). Entropy change \( \Delta S > 0 \) for irreversible free expansion.
Solution: During free expansion of an ideal gas, \( \Delta U = 0 \) (meaning \( T \) is constant), but the internal energy itself is not zero. Also, free expansion is irreversible, so entropy *increases* (not zero). Both A and R are false.

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