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CGP EDU Academic Team
Published on: September 12, 2026
An insulated chamber is divided into two halves of volumes. The left half contains an ideal gas at temperature T 0 and the right half is evacuated. A small hole is opened between the two halves, allowing the gas to flow through, and the system comes to equilibrium. No heat is exchanged with the walls, Find the final temperature of the system.
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Consider the initial and final states of the system. Initially, the left half contains gas at temperature T0, while the right half is a vacuum (evacuated).
Step 2: When the hole is opened, the gas begins to expand into the evacuated half. This is a free expansion process, which is an irreversible process.
Step 3: Since the chamber is insulated, there is no heat exchange with the walls (Q = 0). As the gas undergoes free expansion, no work is done on or by the system (W = 0) because it expands into a vacuum.
Step 4: According to the first law of thermodynamics, \Delta U = Q - W. Since Q = 0 and W = 0, we have \Delta U = 0. This means the internal energy remains constant.
Step 5: For an ideal gas, the internal energy is a function of temperature. Thus, if the internal energy is constant, the temperature must also remain constant.
Therefore, the final temperature of the system, after reaching equilibrium, remains T0.
Step 2: When the hole is opened, the gas begins to expand into the evacuated half. This is a free expansion process, which is an irreversible process.
Step 3: Since the chamber is insulated, there is no heat exchange with the walls (Q = 0). As the gas undergoes free expansion, no work is done on or by the system (W = 0) because it expands into a vacuum.
Step 4: According to the first law of thermodynamics, \Delta U = Q - W. Since Q = 0 and W = 0, we have \Delta U = 0. This means the internal energy remains constant.
Step 5: For an ideal gas, the internal energy is a function of temperature. Thus, if the internal energy is constant, the temperature must also remain constant.
Therefore, the final temperature of the system, after reaching equilibrium, remains T0.
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