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While taking thermodynamics our chemistry teacher told us that entropy is increasing in day by day (as per second law of thermodynamics), and when it reaches its maximum the end of the world will occur. I didn't see such an argument in any of the science books, is there any probablity for this to be true?

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What your describing is the theory of the Heat death of the universe which is speculated about since 1850s. However, as explained here, object at astronomical scale are often self-gravitating and that gives them have unintuitive thermodynamical properties like a negative heat capacity. This usually gives more structured systems as entropy increases, and negates the idea of heat-death.

Furthermore, given the fact that the universe is currently thought to be forever expanding and that the majority of the entropy is/will be in black-holes, the estimated time-scale for such thermal equilibrium to occur is huge (of the order of 10100 years), which gives us vastly enough time to change our cosmological theories about the end of the universe...

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The heat death is just when everything is absorbed either into a black hole at the center, or into the cosmological horizon due to inflating universe. The real heat death is when the two horizons equilibrate by exchanging Hawking radiation. It still ends with an empty deSitter universe (assuming the deSitter phase is stable, which is unlikely). –  Ron Maimon Jun 14 '12 at 0:42
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