Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): During the isothermal free expansion of an ideal gas, the entropy of the system increases even though no heat is exchanged with the surroundings. Reason (R): Entropy is a path function, and its change for the system depends on the actual irreversible path taken during the expansion. In the light of

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Assertion (A) is true: In an isothermal free expansion of an ideal gas, the external pressure is zero, so the work done W = 0 . Since the process is isothermal, the change in internal energy U = 0 . According to the first law of thermodynamics, q = U - W = 0 . However, because the volume increases, the entropy of the system increases ( S_ sys = nR (V₂/V₁) > 0 ). Reason (R) is false: Entropy is a state function, not a path function. The change in entropy of the system is independent of the actual irreversible path t