## If entropy is a state function, how can it keep on increasing?

I just have this confusion which is completely eating me up. They say entropy of a system is a state property. Then they say that for a completely isolated system, entropy either increases or remains zero depending on the process being irreversible or reversible.

So, let's say for an isolated system I go from A to B thru a reversible path then entropy is zero. And if I go thru an irreversible path, it's something else. But if entropy is a state property, how can it be different for the two paths between same points? This completely makes no sense to me.

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 Recognitions: Science Advisor [QUOTE=champu123;4224876 So, let's say for an isolated system I go from A to B thru a reversible path then entropy is zero. And if I go thru an irreversible path, it's something else. But if entropy is a state property, how can it be different for the two paths between same points? This completely makes no sense to me.[/QUOTE] If entropy increases, the two paths will not link the same points. There is a set of points B which can be reached on reversible paths starting from A and there are other distinct states B' which can only be reached in irreversible processes.
 Plot the state of the system using Entropy and Temperature as coordinates.

## If entropy is a state function, how can it keep on increasing?

 Quote by DrDu If entropy increases, the two paths will not link the same points. There is a set of points B which can be reached on reversible paths starting from A and there are other distinct states B' which can only be reached in irreversible processes.
Thanks for the reply. That cleared up some confusion. I also found some long discussion here: http://www.physicsforums.com/showthread.php?t=313396. This thread poses the same question as my confusion.

Hence, I'd like to quote the above mentioned thread and answer the question posted in above thread based on my understanding. In the above thread, the user say:

 If we consider an isolated system in which a process occurs, then according to the clausius inequality : dS≥dQ/T Since dQ = 0 , it follows that if the process occurs reversibly dS = 0 and irreversibly dS > 0. But entropy is a state function , how could this possibly be ?
My answer: The point here is that if the process occurs irreversibly it takes the system to a different state then when it'd have been reversible.
Now, if I say that the system is at state A, and perfectly isolated. Now, if there is a reversible process which takes it to state B. So, are you saying that it's impossible to design an irreversible process that can take the system to state B? By using an irreversible process, you could take it another state B' or B'' but not B. I think the answer should be yes (i.e. it'd be impossible). And in that case it's a very interesting conclusion.

So now tell me is the conclusion indeed true??

 Recognitions: Science Advisor If you mean with perfectly isolated that the system is thermally isolated but can also not do any work (or that no work can be done on the system) then you are right, the state cannot change at all. However, usually with isolated one understands only thermally isolated, so that work can still be done.

 DrDu However, usually with isolated one understands only thermally isolated, so that work can still be done.
This is not a standard definition.

Look at line 3 of this recent handout from the University of Oxford (a reasonabale authority)

http://www-thphys.physics.ox.ac.uk/p...1/handout1.pdf

 Tags entropy