GATE 2024 CY – Question 28
The correct statement(s) related to an ensemble is (are):
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Correct answer: (A) an ensemble is a collection of an infinite number of imaginary replications of the system of interest.; (C) an ensemble average of any macroscopic property of the system is equal to the value of the property averaged over a sufficiently long time.
Explanation
**Ensemble** (statistical mechanics): a large collection of imaginary copies of the system, each representing a possible state.
- **A. A collection of an infinite number of imaginary replications of the system.** True (the definition). ✓
- **B. All members are macroscopically identical and also have identical microstates.** False. The members share the same macroscopic variables but are in **different microstates**.
- **C. The ensemble average equals the long-time average.** True. This is the ergodic hypothesis. ✓
- **D. In a canonical ensemble, systems need not have the same composition.** False. In the canonical ensemble $N$, $V$ and $T$ are fixed, so every system has the same composition (only the grand canonical ensemble allows $N$ to vary).
Answer **A and C**.
Official GATE 2024 answer key: https://gate2026.iitg.ac.in/doc/download/2024/CYFinalAnswerKey.pdf