work & expansion

Question

For reversible isothermal expansion of an ideal gas, work done is maximum because:

RankGuru · Accepted Answer

1. **Reversibility**: A process is reversible if it is conducted so slowly that the system remains in **equilibrium** with its surroundings at all times.
2. **Pressure Factor**: In a reversible expansion, the external pressure ($P_{ext}$) is always infinitesimally less than the internal gas pressure ($P_{int}$).
3. **Work Formula**: $W = -\int P_{ext} \, dV$. 
4. **Work Magnitude**: Since $P_{ext} \approx P_{int}$ throughout the entire path, we integration along the highest possible pressure values for the entire volume change.
5. **Result**: This yields the **maximum possible work** that can be extracted from the system (negative work value with max magnitude).

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work & expansion

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