hard · MCAT chem-phys
A rigid, perfectly insulated container is divided by a removable partition. One side holds 1 mol of an ideal gas at temperature T_0; the other side is fully evacuated. The partition is suddenly removed, and the gas expands irreversibly to fill the entire container. No stirring device or external motor is present, and the container exchanges no heat or matter with the surroundings.
How does the final gas temperature compare to T_0, and what is the correct justification?
- The temperature stays the same, since no heat enters and no work is done on anything, so internal energy cannot change
- The temperature falls, because the gas does work expanding into the larger available volume even though no piston is present
- The temperature rises, because the entropy increase of an irreversible process must be paid for by a rise in internal energy
- The temperature falls, because molecules collide less often at lower density, lowering their average kinetic energy
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