A sealed insulated flask of gas (fixed N, V, E) and a test tube in a constant-temperature water bath (fixed N, V, T) are studied. (a) Which ensemble describes each? (b) In which can the system's energy fluctuate? (c) If the test tube could also exchange molecules with the bath, which ensemble applies? Solution: (a) Flask: microcanonical (isolated). Test tube: canonical (thermal contact, fixed T). (b) The test tube's energy fluctuates as heat flows to/from the bath; the flask's energy is strictly fixed. (c) Grand canonical - both energy and particle number fluctuate, controlled by T and chemical potential mu.