09 August 2012

Second Law of Thermodynamics with Goofy Dives and Pole Vaults

I love thinking about and writing about the physics of the sports world.  Dozens of Olympic events are almost too much stimuli for the nerdy brain in my head that can't stop searching for the physics behind nuances in motions, trajectories, strategies, and so forth.  Sometimes it's fun just to think about what's not there and what's not seen, even in the context of physics.  Allow me to illustrate that idea with a great physics law.

The second law of thermodynamics is one of my favorite topics in physics to teach.  It is not some stale equation or lifeless group of words.  Mathematics may be the language of the universe, but physics is the poetry.  Consider the following quote from C P Snow's famous book, The Two Cultures:

A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists.  Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics.  The response was cold:  it was also negative.  Yet I was asking something which is the scientific equivalent of:  Have you read a work of Shakespeare's?

In other words, know something about the second law of thermodynamics if you wish to consider yourself an educated person possessing scientific literacy.  Why?  Well, for starters, that law drove the industrial revolution, as well as technological developments today.  Imagine holding a lump of coal in the palm of your hand.  That lump of coal contains a certain amount of chemical energy, but we can only extract about a third of that energy for the task of performing work.  Two thirds of that energy is wasted in the process of getting that needed work, often as heat pollution in the sky or in a river.  Energy conservation, which is actually the first law of thermodynamics, doesn't help us understand why so much energy must be wasted, but the second law does.  The second law tells us about the direction in time certain things happen, and that going back to the starting point is impossible.  Once we extract useful work from a lump of coal and lose twice as much heat energy in the process, we can't "fix" the wasted energy and make it useful.

Okay, time for a couple of sports examples to make the second law of thermodynamics a little clearer.  Think back to this past weekend when Wu Minxia of China won gold in the women's 3-m springboard diving event.  She would jump from the diving board, execute a bunch of twists and rolls, and then enter the water with little splash.  Now, what if after entering the pool, you saw Wu Minxia emerge back from the water, do all the twists and rolls in reverse order and backwards, and then land back on the diving board.  Would you believe your eyes?  Or would you think someone hit "rewind" on your television?  The movie doesn't run backwards in real life, right?!?  Of course not!  But, and here's the great thing about it, the law of conservation of energy would not be violated if you saw the dive undo itself!  No energy would be created or destroyed if the energy from the sound wave you heard from the splash, the heat energy of the pool and diver, and the energy of the undulating waves, all recombined back into kinetic energy for the diver and sent her flying back up out of the water.

So why don't we see divers pop back up out of the water and onto the diving board?  The second law of thermodynamics is what provides us with an "arrow of time," as it's often called.  Seeing the "movie" run backwards is so statistically improbable that we say it can't happen.  Disorder is created out of order during a normal dive.  Simply put, there are so many zillions of ways to distribute energy in the disordered post-dive environment that a diver will never return to her more ordered pre-dive environment.  Of course, she can get out of the pool and climb back up to the diving board so that everything "looks" the same, but it's not.  She burned chemical energy and did work to get back to the diving board.  Doing "work" is the key to getting back to the starting point, and that means that some energy is wasted.

Want an even simpler example?  How many possible ways are there for your bedroom to get messy?  How many possible ways are for it to be neat and orderly?  There are many, many more ways for the former to happen than the latter.  Over time, if you don't "work" on it, your bedroom gets messy, not orderly.  That's the second law of thermodynamics in action -- in your very own bedroom!

If the idea is starting to sink in, you'll won't be able to stop thinking of examples.  Did you watch Jennifer Suhr of the US win the women's pole vault event this past Monday?  Her gold-medal-winning vault took her 4.75 m (15.6 feet) over the bar.  Her mass is 64 kg (corresponding to a weight of 141 pounds) and at 1.83 m (6' 0") tall, her center of mass had to raise about 3.75 m (12.3 feet) to clear the bar.  Her gravitational potential energy increase was about 2.35 kJ, but she also needed some kinetic energy to keep moving horizontally over the ball.  That might have accounted for another 5% - 10% more energy.  Where did all that energy come from?

First, Suhr needed to converted stored chemical energy in her body to kinetic energy as she ran faster and faster leading up to her vault.  She lost a little energy along the way to air resistance and track friction.  When she planted her pole on ground and it began to bend, while at the same time elevating her upward, energy was transferred into potential energy in the pole, much like a compressing spring, and gravitational potential energy.  As the pole began to straighten out, like a spring uncoiling, potential energy in the pole got transferred into more gravitational potential energy as she continued to move upwards.  After clearing the bar, gravitational potential energy was converted into kinetic energy as she fell, and that energy was converted into potential energy in the compressed mat, the sound wave you heard when she smacked into the mat, and heat in both her and the mat.

None of the aforementioned energy transfers are 100% efficient, meaning energy is wasted along the way.  She would have needed more than 2.35 kJ just before vaulting.  By the time she jumped off the mat, the kinetic energy Shur had just before her vault was no longer with her.  It was wasted, at least in the physics sense of "waste," meaning it wasn't doing useful work.

So, what if all that wasted energy were to recombine into kinetic energy for Jennifer Suhr and propel her back over the bar?  Energy conservation won't tell us why that can't happen, but the second law of thermodynamics can.

These diving and pole vaulting examples may seem goofy, and they are, but I've always found that the goofier something is, the better it is to remember.  Do you think you'll have trouble remembering something about the second law of thermodynamics after reading my silly examples?!?

1 comment:

  1. Very useful blog on thermodynamics and the equation of motion.These equations are base of the classical mechanics.
    Examples of Kinetic Energy