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What's the difference between $W$ and $dW$? They are both work done and have similar formulae (same dimension). But I don't know the difference between them.

$dW$ here ISN'T power.

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The difference is that $dW$ is an infinitesimal ''quantity'', whilst $W$ is not. I assume the context here is thermodynamics, which make use of calculus. In calculus there is the concept of the infinitesimal. I suggest, for you, to concern yourself with the structure of calculus if you are to tackle thermodynamics.

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  • $\begingroup$ One should keep in mind that in thermodynamics work $W$ is not a thermodynamical potential (TP) of a thermodynamical system, so the "d" is not a total differential. Therefore one should better writte $\delta W$. Remark: Work is not a TP, because the loop integral $\oint \delta W \neq 0$ in general if the system moved away and back from its original state. The inner energy $U$, e.g. is a thermodynamical potential, i.e. $\oint dU = 0$ $\endgroup$ – Frederic Thomas Mar 24 '17 at 14:38

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