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In my chemistry book, the formula for change in entropy is given as :

$$\int{dS} = \int{\frac{δq_{rev}}{T}}$$

What is the meaning of $δq_{rev}$? I know that it is the heat exchanged in a reversible process. But why $δq_{rev}$? Why not $dq_{rev}$? What is the difference between $δq_{rev}$ and $dq_{rev}$? What exactly is the meaning of $δ$ here and how is it different from $d$?

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$\delta Q$ represents the inexact differential that means a change in heat from one state to another depends on the path. $$\Delta Q=\int_{\mathcal{P}} \delta Q \not= Q(\text{Final})-Q(\text{Initial})$$

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  • $\begingroup$ Oh damn, learn something new everyday. Didn't know that notation before :) $\endgroup$ – Buraian Apr 23 at 16:39
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It’s an inexact differential because, unlike properties like internal energy, pressure, temperature etc. heat (like work) is not a property so heat doesn’t “change” . The $\delta$ means amount of energy transferred in the form of heat. The amount transferred may then result in a change in the properties ($dT$, $dp$, $dU$, etc.) of the entities between which energy is transferred.

Hope this helps

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