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By convention, we make work "negative" PΔV because we are looking at the work done by a system. If it were work done on a system, then it would just be PΔV without the negative sign. This is because, from the standpoint of the system, when it expands, hence when ΔV is positive, the system loses energy by doing work on the surroundings. Energy lost is, by convention, given a negative sign, which is why the work done by a system equals -PΔV.
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