Solving the Mystery of Entropy

[martix]

I've always found entropy a hard concept to grasp. Some time I read something that seems to make it more clear, then another time I read something else which completely disturbs my understanding of the idea.

My current problem with entropy is the violation of the the conservation laws. And the fact that there exist actually irreversible processes.
I read this wiki article that states that "During [state] transformation, there will be a certain amount of heat energy loss or dissipation due to intermolecular friction and collisions; energy that will not be recoverable if the process is reversed."
But that would mean energy loss and if taken on scale of the whole universe it means that energy is destroyed...
Explain please.

 

[f95toli]

That statement does not mean that energy is "destroyed"; it merely says that some of the energy after the transformation is in the form of heat (which is just "useless" energy).

The total energy of a closed system is always conserved; but whenever we use some of energy to do something useful some of that energy -regardless if it is electrical, chemical etc- will always be converted to heat.

 

[SW VandeCarr]

My current problem with entropy is the violation of the the conservation laws. And the fact that there exist actually irreversible processes.

The concept of entropy is consistent with local reversible processes.

=[PLAIN]http://en.wikipedia.org/wiki/Irreversibility]this[/URL] wiki article that states that "During [state] transformation, there will be a certain amount of heat energy loss or dissipation due to intermolecular friction and collisions; energy that will not be recoverable if the process is reversed."
But that would mean energy loss and if taken on scale of the whole universe it means that energy is destroyed...
Explain please.

Entropy is based on the probability that a given state of a system can exist out of n possibilities. So if each state is equally probable, the probability of a given (observed) state is 1/n. This is usually expressed as the logarithmic function of p: S= -k ln(p) where k is a constant. In the thermodynamic case k is usually the Boltzmann constant. (In information theory the constant is usually 1 and the log base is 2). Entropy only has meaning (in the opinion of many) locally. Afaik modern physical theory doesn't attempt to describe the entropy of the whole universe.

In any case, energy is not destroyed. It's simply dissipated as heat. It may not be recoverable, but it is not destroyed.

 

[Monocles]

SW VandeCarr did a good job of explaining it - I just wanted to add that if taking the logarithm of the number of accessible states seems mysterious, it is only done because it makes a lot of other math work out nicely. If you wanted to, you could define entropy as the number of accessible states (instead of the logarithm of it), but your math would end up being a lot uglier. Physically, though, the results would be identical.