What happens to the internal energy of a gas when it is allowed to expand freely

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Question: What happens to the internal energy of a gas when it is allowed to expand freely into a vacuum?

Options:

Correct Answer: Remains constant

Solution:

In free expansion, no work is done and no heat is exchanged, so the internal energy remains constant.

What happens to the internal energy of a gas when it is allowed to expand freely into a vacuum?

What happens to the internal energy of a gas when it is allowed to expand freely into a vacuum?

Step 1: Understand what free expansion means. It is when a gas expands into a space with no other gas (a vacuum).
Step 2: Recognize that during free expansion, the gas does not push against anything, so it does not do any work.
Step 3: Note that there is no heat exchange with the surroundings because the gas is expanding into a vacuum, which has no heat to transfer.
Step 4: Since no work is done and no heat is exchanged, the internal energy of the gas does not change.
Step 5: Conclude that the internal energy of the gas remains constant during free expansion.

Internal Energy – The total energy contained within a system, related to the temperature and state of the gas.
Free Expansion – A process where a gas expands into a vacuum without doing work or exchanging heat.
First Law of Thermodynamics – States that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.