Concept:The mathematical sign for work (W) depends heavily on the convention used. In many chemistry textbooks, work done
by the system (expansion) is negative, and work done
on the system (compression) is positive.
Formula:$$ W = -P_{ext} \Delta V $$
Solution:- When work is done on the system, the surroundings compress the gas, resulting in a decrease in volume (\( \Delta V = -\text{ve} \)).
- Substituting a negative \( \Delta V \) into the IUPAC work equation yields: \( W = -P \times (-\text{value}) = +P\Delta V \).
- Thus, the net mathematical term for compression work is positive: \( W = P\Delta V \).
Why other options are incorrect:Option B (\( -P\Delta V \)) represents the work term for expansion (work done BY the system). Options A and C contain division by volume, which is dimensionally incorrect for energy.
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