[Il Divo]

I'm having a bit of trouble understanding the Second Law of Thermodynamics, which seems to be far less intuitive than the First. From what I've read on it, the best way to describe it is that energy tends to disperse from being more "concentrated" to spread out/diluted. This makes sense from the perspective of a gas expanding into a vacuum or energy distributing from hot to cold, but feels more difficult in applying to the theoretical perpetual motion machine.

1) The Second Law tells us that we can't have any mechanism where all heat is completely converted into work, there is always some "waste heat". Heat and Work are both quantities which tell us the change in internal energy/kinetic energy of a system. When a system does work on its surroundings, while there is a reduction in heat, shouldn't an increase in the volume of the container increase the entropy, since you're increasing the number of positions which the gas can now occupy? Also, with expansion work, couldn't this result in a temperature increase of the surroundings, thereby increasing the overall entropy? I think my problem is that I'm not clear on the role which work plays in determining entropy, beyond representing ordered motion.

2) Also, because Entropy is considered a state function, how does this relate to the fact that the entropy of the universe is always increasing? Shouldn't it be possible to restore the state of the original system if it's considered an inherent property?

[Jorriss]

Starting with two, can you clarify why you think that it should be possible to change a state back to a lower entropy state because it is a state function?

[Il Divo]

Starting with two, can you clarify why you think that it should be possible to change a state back to a lower entropy state because it is a state function?

Hmm, I'll give it a shot:

a state function is a property inherent in the system. We can speak of Temperature, which indicates how fast a molecule/atom is moving, or pressure which is the amount of force exerted over an area of space. But because these are state functions, they are path independent, unlike heat or work.

If we were to plot pressure and volume against each other, between any two points there would be a number of different paths we could take, but at a single point, all of the state variables would remain the same. This is why entropy's constant increasing is giving me trouble, since if entropy is increasing for an irreversible process, we can't attain the original state of the system.

[curiouscat]

"entropy's constant increasing" just means you cannot bring back the universe to the same state ever again.

Doesn't mean you cannot bring back your system.