# Why does the entropy of the Universe always increase?

Est120
i don't really understand why S of the universe must be always positive,i know that only reversible process have constant entropy but why real proceses always increase S in the universe?
sorry for bad english I am not from USA or UK

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davenn
Mentor
i don't really understand why S of the universe must be always positive,i know that only reversible process have constant entropy but why real proceses always increase S in the universe?
sorry for bad english I am not from USA or UK
Can you think of any spontaneous process on any scale whatsoever for which the entropy of an isolated system does not increase? Just identify one such process.

davenn
Staff Emeritus
There are several different ways to look at it. One definition of "entropy" is the thermodynamic definition:

##\Delta S = \dfrac{\Delta Q_{rev}}{T}##

where ##\Delta S## is the change in entropy and ##\Delta Q_{rev}## is the heat added to the system (or removed, if ##\Delta Q## is negative) and where ##T## is the temperature (in Kelvin). (The subscript "rev" means "reversible"; basically, it's the heat that would be added if you had made the change slowly and reversibly.)

So if you transfer heat from a hot object (one with a large value of ##T##) to a cold object (one with a small value of T), then the entropy change of the hot object is negative, because it's losing heat, so ##\Delta Q## is negative. The entropy change of the cold object is positive (because ##\Delta Q## is positive, since it's gaining heat). But since entropy is inversely proportional to temperature, the amount of entropy lost to the hot system is smaller than the amount of energy gained by the cold system.

So saying that entropy always increases boils down to saying that if you put a hot object into contact with a cold object, the hot object gets cooler and the cold object gets warmer. If you want to know why THAT always happens, you've got to go a little deeper.