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There must be a negative sign since our system is the gas inside the piston. When we compress the gas, we do work on the gas and increase its internal energy. However, the final volume minus the initial volume would give us a negative number (because the gas is compressed). Without a negative sign, our value would be negative, implying that work is done by the system, where in fact, work is done on the system. Therefore, we need a negative sign to give us the right direction of work.
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