Entropy Explained

[N]o one really knows what entropy really is, so in a debate you will always have the advantage.

– John von Neumann

So here’s a quick take on entropy.  It’s usually defined as dH/T – that is, change in heat energy (dH) divided by temperature (T).  Keep in mind a couple of things.  First, the temperature is absolute temperature, i.e., starting from absolute zero.  This means that in some sense, the temperature we’re discussing here is total average energy per unit of mass/stuff/whatever.  The second thing to keep in mind is dH is the amount of “energy in play” for a given heat transfer.  

OK, so the usual way to set up an entropy equation goes like this.  We have two “heat reservoirs” – think of them as big tanks full of hot water.  One is hotter than the other.  We're somehow going to let some small amount of heat energy (dH) flow between them.  In this simple example, it’s not enough to affect the temperature of either heat reservoir, because they’re that big.  (You can do the problem where they aren’t that big, but it takes calculus.  Not going there now.)  So we can write down the total change in entropy as:

dS = dH/T1 + (-dH)/T2

where: dS is the change in entropy, dH is the amount of energy transferred, and T1 and T2 are the temperatures of the two reservoirs.  The negative sign is on the last term because Reservoir 2 is losing dH of energy, while Reservoir 1 is gaining dH of energy.

Everyday experience tells us that heat will flow from the hotter reservoir to the colder reservoir.  So if T2 is the one losing heat here (remember that negative), it must be the hot one.  So let’s do some hand-waving math: if T2 > T1 (i.e., Reservoir 2 is hotter), then dH/T1 > dH/T2, and so the total change in entropy, dS, is always going to be greater than zero.  Another way of saying this is: entropy always Increases in a closed system.  (Closed?  Huh?  Whazzat mean?  It means in this simple example, heat can only flow between 1 and 2, it’s all insulated from the outside world, and there is no Resivoir 3.)

Here’s another way to get your mind around the concept: think of heat as money, and temperature as how rich someone is.  A $100 bill isn’t going to make much difference to Warren Buffett, but it will make a whale of a lot of difference to a starving undergrad.  So if there’s any mooching going on, who’s more likely do the mooching?  Which way will money tend to flow?

dS$ = $100/T1 - $100/T2

That’s right, T2 is “hotter” or richer, so it must be Warren Buffett’s wallet.  And once again, the entropy increases as the $100 bill changes hands.

But what IS entropy?  How can we think of it?  Statistical mechanics mathematically re-defines it as a measure of disorder.  In other words, in a closed system (here, two tanks full of hot water, insulated from the rest of the world) disorder always increases.

More on this as it relates to housework tomorrow.

Gojira

Finally saw Gojira, which was pretty good in a pulp-monster-noir kind of way.  Much, much better than the Hollywoodized version, Godzilla, King of the Monsters!, which is best described as silly.  Why in the world someone would re-cut a movie like Gojira and insert Raymond Burr is beyond me.
Ah well, time for my morning stroll.

Chopping the U.S.'s Only Current Spacecraft Development Program

Neil Armstrong says don't cut it.  We'll lose vital expertise and infrastructure for the long-shot hope that commercial launch services will eventually fill the gap, and in the meantime will be wholly dependent on the Russians for manned access to space.  Trashing a 10 billion dollar investment doesn't sit well with him either.
Buzz Aldrin says chop away and good riddance.  His thinking is that this move will free up money for other NASA priorities (good ones too: ISS operating funds, planetary science, and Mars mission planning), and spur private manned access to space.


My take: the both make valid points, but why isn't the damned thing flying already?  Yeah, I know: money.  But it's not like we had to – expensively – invent everything completely from scratch either.  Ten billion wasn't enough?  In constant 2005 dollars that's about 10% of what we spent on all of Apollo.  Most damming though is that it's been SEVEN YEARS since since Columbia crashed and the decision was made to go with Constellation.  That's longer than the initial "go" for Mercury to fully operational Gemini spacecraft.  The whole Constellation program reeks of development hell.


Here, go read up on it a Wikipedia (and keep going from there) and make up your own mind.

How to Work a Physics Problem in Four Easy Steps

Here’s the first class lecture from my former teaching days in a nutshell.  I’d grade on four things (hold up fingers) roughly equally, be they homework or test problems, and I’d tell the students to break the work down the same way.

1. Identify the equations from the text that seem relevant to the question.  What we were just talking about in class should give a big hint.
2. Start setting up the problem.  Identify what in the equations from Step 1 are given, what is being asked for, what the missing pieces may be.  Maybe sketch out the physical situation, but at least set up a coordinate system.  Go get more or different equations if there are loose ends, spare pieces, or missing parts.  Underlining the symbols in the equations for given information in green, the target unknown in red, and stuff to be gotten from other equations in blue can really help with this step.
3. Do the math.  Not with a calculator, solve for the answer analytically, pencil-and-paper style, keeping everything in symbols.  You want to end up with the variable you’re solving for neatly isolated so that you can plug in numbers and have an answer pop out.
4. Plug in the numbers and check your answer.  Is the value reasonable?  Or are you predicting that it will take 3600 seconds for a coyote to to fall off a 20 meter high cliff?  Take a moment to explain your cross-checking on the answer.

1-2-3-4, easy for the students to lay out, easy for me to grade.  I’d give an example here, but I’m too tired to sort out math symbols on blogspot right now.  “Left as an exercise for the student” as the saying goes.  Naturally, this is 1-2-3-4 is only a beginner’s technique.  Too frequently in the course of research, just coming up with the equations for Step 1 is the real problem.

Rancho Costa Nada

In short, the author of this literary masterpiece moved out to a patch of nearly free (well, $300) uninhabitable desert, built a shack, and started doing as he damned well pleased.  Model rocket launching in front, .22 & .303 ranges out back, extended morning walks anytime the mood strikes him.  Apart from the broiling heat, freezing cold, utilities powered by his Geo Metro's 12V battery, and his chief social interaction consisting of rambling chats with "The Demented Vet" down the road, it sounds pretty sweet.


Well, it's an option.  Needs a mountain bike though.  Not quite ready to make the jump, personally.

Klunkerz, the movie

Just a straight-up documentary about the origins of mountain biking.  Highly recommended.  You can find more about it here.

Machine Soul

The machine soul of a mountain bike is defined in this old essay by John Gurklis in Dirt Rag: "Machine soul is acquired as the rider's mental energy becomes infused into the frame members of the bike."


After almost ten long years of riding, my Trek STP (picture here, scroll down) has a respectable helping of machine soul.  And now after swapping out the stem, the cranks are the only original component left on the bike.  Currently on the third back wheel, second fork, fourth rear deraileur, second set of brakes, umpteenth chain (I'd estimate somewhere in the neighborhood of seventeen), the carbon frame is going strong.  We'll see how much longer this soul machine keeps going. This bike always fit well, but now after replacing the stem (due to long-term stress, didn't want to keep taking chances on the old hunk of aluminum) with a slightly shorter one, it fits even better.


ps: The coyote mojo is on its fourth bike.  But that's a separate matter.