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Question

If a system is isolated the heat transfer between the system and the surroundings is zero i.e DeltaU =0 then how can entropy be a +ve value?

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Solution

We can explain increase in entropy using Clausius inequality.
We know that δwδwrev0
where δwrev is the reversible work.
First law of thermodynamics states that
du=δq+δw=δqrev+δwrev
Now since internal energy u is a state function, all paths between two states (reversible or irreversible) results to same change in u.
Now in an isolated system du = 0.
So, δwδwrev=δqrevδq0
Hence, δqrevTδqT
again we know that entropy change is: ds=δqrevT
So, ds=δqrevTδqT
For an isolated system : δq=0ds0


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