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In comparing the work of when a gas expands versus the work of isothermal expansion, I noticed a change carried out reversibly always does more work than a change carried out irreversibly but the values for the reversible process are technically lower. Why is it that the more negative the value, the greater the work done? Shouldn't it be the more the values are closer to positive the greater the work?
i think we look at the absolute values to determine which does more work. the sign is associated with what is doing the work; for example work is positive if its being done on a system and negative if its being done by a system.
When we look at work, the negative sign is just used to indicate which side of the system is doing work, not necessarily the amount of work. We would look at work's magnitude so we would disregard the sign change when comparing the two different systems.
In the example of irreversibility (isothermal expansion), the gas isn't doing work on its surroundings as the external pressure is zero. Therefore, P(ΔV) = 0. However, in the reversible example, the gas is doing work on its surroundings. Therefore, the reversible system is always doing more work than the irreversible system.
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