Equilibrium = Point of Max entropy?

[browncomputer]

Why is equilibrium the point of greatest entropy?

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[DrknoSDN]

Some context might be useful, but basically maximum entropy is when everything is uniformly distributed or energy has reached the lowest levels (equilibrium).

I wouldn't say that is always true because if you have other factors like heat, chemical equilibrium is dependent on Gibbs free energy.
i.e. A reaction can decrease entropy spontaneously if the reaction is highly exothermic, reaching a final equilibrium where entropy is lower than where it started.
∆G = ∆H - T∆S

I'd be curious about the passage containing that generalization. It is probably true for whatever context it's in.

 

[DrknoSDN]

As a system approaches equilibrium it is becoming more disordered (increasing entropy).
Example:
1. Coffee becomes cool
2. Ice melts

If the system is already at its maximum entropy, the entropy will remain the same.

Again that is a big generalization, there are many reactions that occur where something spontaneously goes from disorder (liquid) to order (solid) at equilibrium.
I would caution any MCAT taker to say equilibrium is always the point of greatest entropy (at least with "local minima" of energies). Only time that would always be true is the heat death of the universe.

Quick reference to the wiki about it says
"Maximum Entropy thermodynamics has generally failed to be accepted by the majority of scientists, with mainstream thermodynamicists considering Jaynes' work as an unfounded mathematical contrivance. This is in part because of the relative paucity of published results from the MaxEnt school, especially with regard to new testable predictions far-from-equilibrium.[10]"
"The maximum entropy approach is applicable to physics only when there is a clear physical definition of entropy"
http://en.wikipedia.org/wiki/Entropy_maximization

I'm not a physicist (so sorry if I'm wrong) but equilibrium is about minimum energy while entropy is about maximum disorder. They don't always have to correlate.

 

[DrknoSDN]

When a system is left by itself and can be influenced from the surroundings (an open system) it will approach equilibrium. As it approaches equilibrium it will increase its disorder.
When something goes from disorder to order it is not under standard conditions.

If you have an open system that has a greater entropy than it's surroundings it will approach equilibrium but it will not always increase it's disorder.
Uniform charge distribution (maximum entropy) is often disrupted when influenced by an external environment (open system conditions), leading to a decrease in entropy as it approaches equilibrium with the surroundings.

...Sorry to contradict but when i originally responded I knew that such a broad statement would need some parameters to go with it.

Another wiki: http://en.wikipedia.org/wiki/Principle_of_minimum_energy

• The maximum entropy principle: For a closed system with fixed internal energy (i.e. an isolated system), the entropy is maximized at equilibrium.

• The minimum energy principle: For a closed system with fixed entropy, the total energy is minimized at equilibrium.

These parameters explain that if nothing can be exchanged with the system (it's isolated), then you don't use the Gibbs equation to determine equilibrium because delta(H) is zero. So yes, MaxEnt=Equilibrium under very extreme conditions that are not normally accurate depictions of any chemical or physical system that would be on the MCAT.

 

[DrknoSDN]

The equilibrium configuration is the situation of greatest disorder, or maximum entropy.

You're not wrong from a physics standpoint.
... if you are dealing with only thermodynamics (physics vs chem), and in a theoretical isolated system (no surroundings), yes.
The 2nd law is talking about the entropy of the whole universe because that is the only real isolated system.

In chemistry a reaction in a 'isolated' system can be in chemical and thermal equilibrium and not be at maximum entropy. At that point the maximum entropy is determined by phase, molecules, bonding etc.
Check out the Purdue chem page under 2nd law, has good examples.
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch21/entropy.php

 

[browncomputer]

this is so helpful! thank you so so much to all of you! this max entropy principle only applies to an isolated system, and i believe the mcat deals with equilibrium from an isolated system standpoint most of the times