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CGP EDU Academic Team
Published on: September 12, 2026
An ideal gas is originally confined to a volume V 1 in an insulated container of volume V 1 + V 2 . The remainder of the container is evacuated. The partition is then removed and the gas expands to fill the entire container. If the initial temperature of the gas was T, what is the final temperature? Justify your answer.

Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: In the initial state, the gas occupies volume V_1 at temperature T.
Step 2: When the partition is removed, the gas expands into the total volume of (V_1 + V_2).
Step 3: Since the container is insulated, no heat is exchanged with the surroundings; therefore, the process is adiabatic.
Step 4: For an ideal gas undergoing free expansion, there is no work done on or by the gas, and no heat is exchanged.
Step 5: Thus, the internal energy of the gas remains constant, which implies that the final temperature remains the same.
Step 6: Thus, the final temperature after the expansion is still T.
Therefore, the final temperature is T.
Step 2: When the partition is removed, the gas expands into the total volume of (V_1 + V_2).
Step 3: Since the container is insulated, no heat is exchanged with the surroundings; therefore, the process is adiabatic.
Step 4: For an ideal gas undergoing free expansion, there is no work done on or by the gas, and no heat is exchanged.
Step 5: Thus, the internal energy of the gas remains constant, which implies that the final temperature remains the same.
Step 6: Thus, the final temperature after the expansion is still T.
Therefore, the final temperature is T.
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