Thermodynamics Example 19: Increase in Entropy

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Thanks for doing a good example on entropy generation for an isolated system.
Question.
When we sum up positive & negative entropies in the ice melting & melting to a higher temperature example or throwing a red hot iron in a lake example or for some heat engine cycle between the source & sink example, are those net change in entropy we get not for an isolated system.
Those changes in entropies & this entropy generation are different?
The method used to calculate entropies in both cases is the same.
Could us please explain how come the two are not the same thing.
Thank you so much.

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