## 6.14.2007

### Worst Death Scene Ever Goes To..... The Universe!!!!

So a general warning, this post is going to have a somewhat nerdy and engineering bent.

Entropy is kind of funny. I have used it alot in my thermodynamics classes. It is one of the state variables that can be used to describe a system and so it combined with the word "Isentropic" is problem solving gold. I first heard about it in chemistry where we learned that the gibbs free energy change is equal to the change in enthalpy minus the change in entropy times temperature. This occured way back in high school and sadly, I think I am only now recovering from it.

What is entropy? I can tell you what it isn't... it isn't a physical thing. You cant touch it, you can't smell it, you cant even measure it but indirectly. In this sense there is no way that entropy can cause anything. Its like saying that the slope of a hill caused the ball to roll down it. Gravity moved the ball, the slope just tells you how fast and how far.

None the less, there is the persistant impression that changes in entropy can cause something to happen and I believe this is a direct result of gibbs equation. And yet, most people ignore the fact that for anything to happen requires energy of some kind. That energy can be in the form of potential energy, kinetic, or whatever. So what then is the entropy term in gibbs energy equation?

Energy! Specifically entropy measures the amount of energy in a system that is unavailiable for work. Sweet. This is a definition we can work with! So in gibbs equation if a change in temperature, or more generally a change of state, frees up some energy to do work. And if there is energy availiable to do work then things can change which is the whole point of gibbs equation.

What are the different ways that we can have energy present but not availiable for work? Well, we know from intro thermodynamics ( and physics I think, but that was probably 8 or 9 years ago at this point so I am not sure if it was in it) that the efficiency of any heat engine has to be lower then that of the Carnot heat engine which relates the max efficiency to the highest and lowest temperatures of the system (kind of). So right there we have the fact that based on temperatures (a state variable) we can vary the amount of usable energy we have. Voila, I give you entropy.

What else? Well, in chemistry we have many different forces and interactions taking place that are irrelevent for power cycles. Namely, inter and intramolecular forces. In both cases we now have a positional potential energy. This energy is kind of like the energy stored in a bunch of magnets that you tacked to a table. Based on the arrangement you can have positive or negative potential energy (to many north poles facing north poles or conversely to many north poles facing south poles). In anycase the arrangement of molecules in a liquid gas or solid can be thought of in much the same way. If there is lots of order in a system then essentually all your north poles are facing other north poles and you can use the fact that the system wants to force itself apart to do work. If, however, there is alot of dissorder then for every north pole facing a north pole there is likely a north pole facing a south pole that cancels it out.

How does this relate to the heat death of the universe? Well there must be a reason that the universe tends to disorder and I like to think that it is the fact that nature abhores an energy gradient. As we have stated, any time we have something that is well ordered it is almost the equivilent of saying that we have energy we can use all nice and localized in one area. So the tendency towards disorder is the tendency to spread out this energy.

But why does energy spread? Why do energy gradients tend towards zero? Thermal fluctuations helped along by a tiny dose of quantum uncertainty mean that any barrior to energy movement is likely to be crossed as time goes to infinity. So any barrier that is put into place to localize energy or equivently to create order is going to be crossed and that energy will spread into the surroundings. Since the probability of that crossing is proportional to the amount of energy present it is more likely for energy to leave then to enter. Maybe only slightly so, but it is inevitably the case.

There are alot of details missing but basically it makes sense to me and I supose that is what counts :-)