# If entropy of a closed system decreases by a certain amount, why does not the entropy of the surroundings increase by the same amount? [duplicate]

As said by the Second law of thermodynamics,

Energy spontaneously disperses from being localized to being spread out if not hindered from doing so.

Now, for systems other than isolated one, and for the surroundings , the net entropy change always is greater than $0$ . $$\Delta{S_{sys}} + \Delta{S_{surr}} > 0$$ . Net entropy of the universe always increases. As my book says

Entropy change of the universe must be positive and for this entropy change of the surroundings must be greater than that of the system when it releases thermal energy.

But, can't net entropy of the universe be $0$ ? That is, can't the entropy change in the system be equal to entropy change of the surroundings?? If not, why???

Can't the entropy change in the system be equal to entropy change of the surroundings?

Yes, it can be in a reversible process. Although most spontaneous processes in nature are irreversible, so that only happens in a minority of cases. One example is the Carnot cycle which is a reversible process with heat exchange between two sources. It is used in refrigerators for instance. You can see a more detailed description in the link, and the graphs are pretty explanatory. Of course, any reversible process is ideal, no one exactly happens in nature. Any thing in nature that looks like the step three would be an example (but see the webpage for details):

isothermal heat rejection: a reversible isothermal compression of the gas, where the surroundings do work on the gas, causing an amount of heat energy and of entropy to flow out of the gas to a low temperature reservoir.

Can't net entropy of the universe be 0 ?

For it to be zero you need all the energy concentrated at a single place, but this will not last much, because as you quoted: Energy spontaneously disperses from being localized to being spread out if not hindered from doing so.

• Thanks! So, the entropy of the universe either doesn't or will increase but not decrease, right? – user36790 Nov 30 '14 at 8:57
• Just can you give me an example of spontaneous reversible reaction where the entropy of the universe remains same? – user36790 Nov 30 '14 at 8:58
• @user36790 sure, I'll do it later (gotta go work now) , the only ones I have in mind now are the ones where there is no change in entropy in either system (such as an adiabatic expansion or contraction). But I want to find an example where the entropy decrease in one and increases on the other. – Wolphram jonny Nov 30 '14 at 12:45
• @user36790 I updated my answer with an example. But I encourage you to read the link for more details. – Wolphram jonny Nov 30 '14 at 14:42