Blame it on Entropy (Science)

Entropy gets a bad rap. It's honestly a fairly straight-forward kind of thing... not too difficult to understand, and examples of it can be observed all around us in our every day life. But it's kind of got a bad reputation, and always seems to be at the center of discussions of uncertainty and chaos. It even seems to have it's hand in the whole global warming issue, for goodness sake!

I was first introduced to entropy in my junior year at Cal Poly, in my aerothermodynamics class. (Five days a week, 7 a.m. -- not a fun year.) Despite the early hour, I actually learned a lot from that course. Granted, that was in large part because I was scared to death of my professor, and didn't want to have to repeat this torture again in a "junior year redux". But regardless, the stuff stuck with me, including today's topic: entropy.

In simplest terms, entropy has to do with the tendency of the pressure, temperature, and density differences within a defined environment to equalize over time. The entropy of the defined environment, or "thermodynamic system", is a measure of how far the equalization has progressed.

Doesn't sound so simple? That's okay, I've come armed with an example.

Let's say, that on a hot summer day, you pour yourself a big glass of ice water. Now, being a mom, you'll never actually have a chance to take a sip of this water before some chaos will erupt in another room and you will have to go investigate. In the process of settling whatever dispute required your attention, you will remember that you have a wet load of laundry sitting in the washer that needs to be attended to. When you go to move the wet items into the dryer, you will discover that there is still a load of towels in there which now need to be folded and put away. While putting the clean towels away in the bathroom, you will notice that there is no longer any toilet paper on the roll and no spares under the sink. So you will go to the closet to get some more, and realize that you are almost out. Before this key point is forgotten, you will run to your desk to start a list of things you need from the store. But on the desk you will see the telephone bill that needs to get out in the mail today. After writing the check however, you will be dismayed to discover you are out of stamps. So before it gets any later, you gather the kids, outfit them in the necessary sneakers and sweaters, and take the whole brood to the post office.

By the time you get back from all of this, or whatever version of "If You Give a Mouse a Cookie" that your life resembles, you discover that your refreshing glass of ice water has now warmed to an unappealing room temperature.

So where does entropy fit in?

Well, while you were busy attending to the never-ending demands of the career we call motherhood... the heat energy that exists in the closed environment of your house, began spreading to the newly-introduced element inside of it, the ice water. When left alone long enough, the temperature of both equalized. Entropy is simply the yardstick that is used to measure this change that took place between the time when you poured the water, and when you returned back from the post office.

To make this official and scientific-like, the equation used to calculate entropy is dS=dQ/T.
Where for this situation:
dS is the change in entropy during the defined time period,
dQ is the heat exchanged between the warm house and cold ice water during this same period,
and T is the starting temperature (in degrees Kelvin) when you first poured the water.
For this case, the controlled enviornment that we are going to determine the entropy of will be the inside of your house, which contains the ice water and the air that surrounds it.

In our above ice water example, there are actually two elements in which we would need to measure: the ice water, and the air in your house surrounding the ice water. We would then add the changes that occured in both together to get the "total" entropy. Because, in addition to the water warming up, the air in the surrounding house actually cooled after the ice water was introduced... even if it was an imperceptable amount.

If you look at the two elements separately; in the case of the ice water, dQ would be the heat required to melt the ice and warm the water to room temperature, and T would be the starting temperature of the water which is 32 degrees F, or 273 degrees Kelvin (K).

In the surrounding house, dQ would be the amount the house cooled after you poured the ice water (which let's all agree, would be significantly less than a smidge), and T would be the starting temperature of the house, which let's assume would be 77 degrees F, or 298 K.

When you add the two together, the positive increase in heat energy used to warm up the water, far outweighs the negative heat lost with the slight cooling of the air, so the overall entropy for the controlled environment, or "thermodynamic system" of your house is positive -- or in other words, the entropy increased.

The interesting thing about entropy as a matter of fact, and the reason I still remember it from school, is that entropy always increases. In fact, that is such an absolute truth, that it is actually the Second Law of Thermodynamics: "The entropy of an isolated system not at equilibrium will tend to increase over time, approaching a maximum value."

(Some consider our entire universe to be an "isolated system" of it's own. As such, it may be subject to the Second Law of Thermodynamics, so that its total entropy is constantly increasing. Some even warn that the universe is fated to eventually reach a "heat death", in which all of the available energy ends up being distributed equally throughout the universe as thermal energy, so that no more work can be extracted from any source. But as I understand it, Al Gore is looking into all of this, so we should be okay.)

It is this "ever increasing" characteristic of entropy that has begun to give it a bit of a bad reputation. Because beyond this strictly thermodynamic definition, the word "entropy" has been used to describe the general tendency of all "systems" to mix it up a bit. In fact, the statistical interpretation of entropy is explained as the amount of uncertainty of a system -- or in terms a mom can understand, how many potential ways the elements of the system can spread out all over the place and make a big mess. And because entropy can only increase, things can only get messier.

For example, a jar of marbles would have a greater entropy than let's say a chair. As many ways as a child can knock a chair about, it's nothing compared to what he or she could do with a jar of marbles. And by the same token, the entropy of a jar of marbles would be small compared to that of a 5 pound bag of sugar. So based on this perspective, entropy is often viewed as the probablity of chaos.

This is something that all mothers have been instictively been measuring since the beginning of time... we just didn't know there was a special name for it.