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The Second Law of Thermodynamics states that the state of entropy of the entire universe, as an isolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative.

According to that, $\Delta S$ of the universe should always be positive for a spontaneous reaction to occur. But what is the reason for that?

In Advanced Chemistry, Philip Matthews states:

Pg-287 This result cannot be proved; rather it is a statement of experiment

While there is true reasons for every point in chemistry, I feel there should be a real reason for it rather than experimental statement. But I searched it on Google but can't to find an answer. So, can you help me to give the reason?

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    $\begingroup$ The author is right. Anything referred to as a law cannot be proven. All the other things we know are derived from what we call laws. The second law is an experimental observation. If you wish, however, you could say that we figured there was some property that increased during any process, and it turns out this is entropy. Similarly, we wanted there to be some property whose value was constant for all processes and this we call energy. $\endgroup$ – jheindel Dec 19 '17 at 19:26
  • $\begingroup$ I would say to look into the Fluctuation Theorem. $\endgroup$ – Tyberius Dec 19 '17 at 19:52
  • $\begingroup$ There is no such a law that the "the entropy of the universe" increases, (does the universe have an entropy?); but there is a law derived from experience that the "entropy of a closed thermodynamic system can only increase". There is no experience that the universe is a closed system in the thermodynamics sense, and in no sense, especially not a mathematical one, that the former can be derived from the latter. $\endgroup$ – hyportnex Dec 20 '17 at 23:15
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According to second law of Thermodynamics,

During spontaneous process:

$$ ∆S_{total} > 0 \ or ∆S_{total} = 0 $$

So total entropy is positive.

But $ ∆S_{system} \ or \ ∆S_{surroundings} $ may be less than 0.

Which $ \implies $ any one of $ ∆S_{system} \ *OR* \ ∆S_{surr} $ may be less than 0.


Now, according to Big Bang theory, the Universe, soon after existence , is expanding more and more and so - its entropy is increasing.


Why entropy should be positive to occur a spontaneous reaction?

An example first: • Heat flow is unidirectional. That is, from higher to lower temperature. Similar to it, all Physical or Chemical Process will tend to proceed spontaneously in one direction only(unless altered by some external agency). Hence, Spontaneity is the potential to proceed without assistance of external agency.

Now, Entropy means randomness or disordered behaviour. And there is always a tendency for the system's energy to become more disordered. An example would be diffusion. Where gases diffuse and become more chaotic. And during the expansion of our universe, its entropy increases.

So, we interpret that entropy for a spontaneous process increases, till it reaches maximum. And our universe having a positive $∆U$ and gaining entropy in the direction of spontaneity.

$∆S=0$ at equilibrium.

If $∆S$ is negative that would mean that reaction or process is going opposite to the spontaneous direction, and which is not possible in case of our universe.

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    $\begingroup$ From your answer I understood why it is expanding of the delta S universe more and more. But could you say the reason why do it always be positive to occur a spontaneous reaction? $\endgroup$ – Osal Thuduwage Dec 19 '17 at 10:21
  • $\begingroup$ @Osal read my further answer. $\endgroup$ – Ravi Prakash Dec 19 '17 at 19:59

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