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Not sure how often we'll actually have to use these equations but we should probably understand the concept behind them. So work is one of the ways energy can be transferred from its system/surroundings. They're actually the same equation (you work it around the bit and one equals the other). If you think back to the model of a piston, there's a constant external pressure pushing down against the gas inside. The gas's own pressure will push against that external pressure, so you can think of Pex=Pgas. If these pressures are equal, the piston doesn't move and the volume stays the same, and no work is being done. However, when a system does work through expansion, the Pex will stay constant and the ΔV will increase because the gas inside is pushing against the external pressure causing a change in volume inside the piston. If you're confused about the signs associated with work, when a system expands (expansion) then the sign is negative because you're losing energy as work; thus the negative in front of the equation w = -Pex ΔV. You can look back to 8.3 in the textbook if you're not sure how the piston looks like or want to see how those equations equal each other. Hope I helped!
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