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Question

For an isolated system U=0 what will be S?

Solution
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For an isolated system, ∆U = 0 and for a spontaneous process, total entropy change must be positive.

For example, consider the diffusion of two gases A and B into each other in a closed container which is isolated from the surroundings.
The two gases A and B are separated by a movable partition. When partition is removed, the gases begin to diffuse into each other and the system becomes more disordered. It shows that ∆S > 0 and ∆U = 0 for this process.
Morever, ∆S=qrev/T = ∆H / T

= ∆U + p∆V /T = p∆V /T

i.e. T ∆S or ∆S > 0

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