Re: entropy in a closed area?

Patrick,

Okay bear with me for a little while, because first I'm going to give brief
explanations of what heat and entropy are. I think that by the time I get
done with those explanations you will probably be able to answer your
question yourself. 

Heat is just another name for thermal energy; that is, energy that is
associated with the motion of particles. There are many other forms of
energy out there though, and even the definition I just gave is a bit
misleading since most thermodynamicists you talk to will also group
infrared radiation (which is technically electromagnetic energy) in with
"heat" since it is a well-known way for heat to be transferred through
space (even empty space). Why does it matter if infrared radiation is
considered heat? In your question, you imagine a large cube that prevents
the transmission of heat, and what I think you really wanted to say was
that it prevents the transmission of *all* energy (and mass, naturally). If
you limit the cube to just being able to block heat, there is still the
possibility that electromagnetic energy would flow in or out and that would
mess things up.

The concept of entropy is a difficult one to grasp. You hear people talk
about entropy as a measure of the "disorder" of a system or a relation of
the number of possible states of a system, but neither of those
descriptions is particularly helpful to most people. I typically think of
entropy as it relates to "usable" energy in a system. Specifically,
whenever entropy is created, some energy is "lost" and cannot be used to do
work. The normal explanation given for this "lost" energy is that it is
turned into heat, and that is true, but it's not really the whole story.
Some of that heat could be collected and transformed into other kinds of
energy (for example, it could heat air that is then run through a turbine
to generate electrical power). But because of the entropy rise that
occurred, you could never reclaim all of the energy that was initially
present. The larger the entropy rise, the less energy you could reclaim. Is
there a simple explanation for why this is true? Unfortunately, there
isn't, but there are parallels that can help you understand the
consequences of entropy generation. 

For example, say you have an aquarium that is divided in half, and you fill
one half with water. Let's say we let it sit long enough for the
temperature to be even and all motion to stop. We now have a system with a
certain amount of potential energy, and if we removed the separator, some
of that potential energy would be transformed to kinetic energy and cause
the water to move. As soon as the water starts to move, friction begins
turning the kinetic energy to heat, and eventually all the motion stops
again after the water settles out at its new level. At this point, we have
absolutely no way of restoring the original state (with all the water on
one side of the aquarium) unless we add more energy. This example
illustrates what nature is all about: it tries to even things out (or if
you want to be technical, it tries to eliminate gradients). The only way to
restore a gradient once it is gone is to add more energy. Eventually, if
you have no energy added to the system, all of the gradients will
disappear. All of the energy would still be accounted for, but it would be
evenly spread out and there would be no way to group the energy together or
use it to do work. 

So let's go back to your question. If you put the earth in a box that did
not let mass or energy flow in or out, and that box didn't also contain the
sun, we could not get light from the sun. Even if you make the box big
enough to contain the sun (or perhaps the whole solar system), eventually
the earth would not be able to support life. Eventually the entropy would
increase so much that none of the energy in the box could be used to do any
kind of work. Everything in the box would be inert and energy would be
spread evenly throughout the box. There would probably be quite a bit of
heat in the box, but the energy could take other forms as well (radiation
comes to mind). The part that would be the real killer is that no chemical
reactions would be taking place, and that's obviously a requirement for
life as we know it. So I think the answer to your question is definitely
"yes," although I should probably point out that it would take so long to
generate this much entropy that it's more likely the sun would run out of
fuel, turn into a red giant, and engulf the inner planets (including earth)
before we had to worry about entropy. 

Well there it is, and I think I got a little carried away, but I hope this
is more helpful than a simple "yes."

David Coit