## Entropy at Equilibrium

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

Xuan Kuang 2L
Posts: 31
Joined: Wed Nov 14, 2018 12:23 am

### Entropy at Equilibrium

Could someone re-explain for me why entropy is a maximum at equilibrium? More specifically, could someone explain why at equilibrium, all possible states have been reached?

aisteles1G
Posts: 117
Joined: Fri Sep 28, 2018 12:15 am

### Re: Entropy at Equilibrium

Entropy can never decrease, if it would then the 2nd law of thermodynamics would be violated, so when a system reaches equilibrium that means that entropy has maxed out, and it can't increase either because every state has been reached as you said, this is considering the whole "universe" though. When a system at equilibrium enters surroundings its entropy can now decrease or increase based off how it interacts with the surroundings so it is no longer in equilibrium, which does not mean that the 2nd law has been violated if entropy of the system decreases, it just means the 'universe' has expanded to now include more surrounding which have their own entropy that needs to be incorporated and the total entropy of the 'universe' is still increasing. On a real world bases, entropy in the universe is always increasing and is far from equilibrium though, max entropy/equilibrium for us will occur when all fuel will be expended and temperature will be uniform meaning no more heat flow or work can be done in the entire universe bc every possible state has occurred, hope this helps!

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