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An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If Ti is the initial temperature and Tf is the final temperature, which of the following statements is correct?

1. (Tf)rev = (Tf)irrev
2. Tf = Ti for both reversible and irreversible processes
3. (Tf)irrev > (Tf)rev
4. Tf > Ti for reversible process but Tf = Ti for irreversible process

Correct answer: (Tf)irrev > (Tf)rev

Solution

In an irreversible expansion, the gas does work on the surroundings without the ability to return to equilibrium, resulting in a higher final temperature compared to a reversible process where the system remains in equilibrium throughout. This leads to the conclusion that the final temperature after irreversible expansion is greater than that after reversible expansion.

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