1. Jul 30, 2010

### zeromodz

The 2nd law of thermodynamics states that entropy can only stay the same or increase given time. My question is, is there a max limit to how much entropy can increase? And when it reaches this limit, can energy do any work at all?

2. Jul 30, 2010

Kelvin came up with this idea of heat death of the universe. That is where entropy reaches its maximum state, all matter is maximally disorganized, and energy is no longer available for doing work. Kind of a grim thought.
en.wikipedia.org/wiki/Heat_death

In an isolated system there is what's known as thermodynamic equilibrium. Once an isolated system reaches this state, it will cease to change.
en.wikipedia.org/wiki/Thermodynamic_equilibrium

3. Jul 30, 2010

### Locrian

I think the heat death link is good.

You've reached maximum entropy whenever you can't get a different macroscopic reading from microscopic changes.

As a side note, most people are only familiar with the defenition of entropy from thermodynamics. Understanding it from a statistical mechanics point of view added a tremendous amount of meaning to the topic for me. YMMV.

4. Jul 31, 2010

### zeromodz

It says on wikipedia that the maximum entropy in the universe will rapidly increase far faster than entropy in general increasing, pushing us away from "heat death". Why is it that the maximum entropy increases so fast because of the expansion of the universe?

5. Jul 31, 2010

### miezasaleh

1)example for function A and B such that function f and composite functions of g o f are both injective but g is not injective

2)1)example for function A and B such that function f and composite functions of g o f are both surjective but f is not surjective?

6. Jul 31, 2010

I find it very difficult to understand how this could be the case since the first law seems to indicate that no more energy is being added to the universe. (My lack of understanding might be due to my ignorance of thermodynamics or the theories behind the expansion of the universe. Take you pick )

An increase in volume (without a change in pressure or temperature) is an increase in entropy. If the universe is expanding rapidly, it stands to reason that entropy is as well. Clearly there is something I'm missing.

I wanted to check the source for that statement, but Wikipedia doesn't cite one!