WILLIAM TUCKER: If You Want To Understand Nuclear, Learn Algebra

By William Tucker

If you want to see how fast the United States is deteriorating on the world stage, just take a look at last Sunday’s New York Times, where Queens College political science professor Andrew Hacker comes up with a brilliant idea for improving education in America.  He wants us to stop teaching algebra!

“The toll mathematics takes begins early,” writes Hacker. 

To our nation’s shame, one in four ninth graders fails to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason. . . . Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course.

So what’s the solution?  Give up, says Hacker.   The subject is too hard.  It doesn’t relate to anything.  It has nothing to do with real life.  Give everybody a bye and let them get on to more important things such as the impact of disco on late 20th century American sartorial styles or influence of the Mario Brothers on early computer games.  

Now consider this for a moment.  Korea is a country that consistently ranks at the top in international mathematics tests.  (The US ranks in the low middle, although American students usually think they’re doing better – the “self-esteem” effect.)  The highest concentration of Ph.D.’s in the world is in Seoul.  Korea has also embracing nuclear technology like no other country.  After only ten years of making their own reactors, the Koreans landed a $20 billion contract to build four reactors in the United Arab Emirates.  A year ago they held a “National Nuclear Day” to introduce the next generation to the excitement of the new technology.

What does this have to do with algebra?  Well, just as an example, the easiest way to understand the almost other-worldly capacity of nuclear reactions to produce energy lies in a simple algebraic equation.  It’s written: 

E = mc2

Ever hear of it?  Most people have.  But few understand its true significance.

The equation describes the interchangeability of matter and energy at the subatomic level.  E equals energy, m equals mass and c is the speed of light.  That   c-squared factor is a very, very larger number, something on the order to 10 quadrillion.  What that means is that you can take a very, very small amount of matter and turn it into a very, very large amount of energy.

Perhaps the best way to illustrate the uniqueness of nuclear energy transformations is to compare it to the almost identical algebraic expression for kinetic energy, the energy we can get from a body in motion.  This equation reads:

      E = ½ mv2

Here again, E stands for energy, m is the mass of the moving object and v is the velocity of the moving object.  The energy of a thrown baseball, for instance, is the mass of the object (about 5 ¼ ounces) times the velocity at which it is thrown (somewhere between 50 and 90 miles an hour).  

When we talk about getting “renewable energy” from harnessing the wind or falling water, we are tapping flows of kinetic energy in nature.  The velocity of these moving masses is usually between 10 and 60 miles per hour.  Water falling off an 800-foot dam can reach 60 mph.  A strong wind will blow at 40 mph.  (It is blows much faster, a windmill will have to be shut down because it can’t take the stress.)

Now by our everyday experience, 60 mph is pretty fast.  A car going at 60 mph can travel the length of a football field in three seconds.  When we deal with nuclear energy, however – the E = mc2 equation – we’re talking about 186,000 miles per second or eight-and-a-half-times around the world in the blink of an eyeAnd that number has to be squared!  As you can see, there’s an almost unfathomable difference between the two, something on the order of 10 quadrillion.  

Now a quadrillion hasn’t really entered our understanding yet.  We know what a trillion is these days.  It’s the size of the federal budget deficit.  You’ve probably heard all these analogies of a trillion dollars making a stack of bills that would reach almost to the moon.  Well a quadrillion is what comes after that – a thousand trillion.  And that’s the number we’re dealing with when we talk of nuclear energy.  

If you know any algebra, you’ll also see in both formulas that mass and velocity are inversely related.  As one gets bigger, the other can get smaller in order to produce the same amount of energy.  What that means is that when we’re stuck with relatively low velocities – say 60 mph – the only way to increase the energy output is to increase the mass.  That’s why a 1000 MW hydroelectric dam must back up a 250-square-mile reservoir in order to generate a steady flow of electricity.  It’s why we have to cover about 400 square miles of windmills to produce that same 1000 MW.  And it’s the reason why there is no theoretical possibility of changing the scale of any of these technologies.  You’re never going to be able to increase the energy density, as it’s called, of renewable resources.  The only way to expand them is to build more windmills or bigger dams.  

When we’re dealing with an almost unimaginable number like the speed of light squared, however, the amount of mass required becomes almost unimaginably small.  A 1000-MW coal plant is fed by a “unit train” of 100 coal cars arriving at the plant every 30 hours or 300 times a year.  A nuclear reactor is refueled when a fleet of six trucks arrives carrying a new load of fuel rods once every 18 months.  That fuel will remain in the reactor for five years.  When it is removed, a total of six ounces of its mass will have been completely transformed into energy.  Yet because E = mc2, that transformation of six ounces of matter will be enough to power a city the size of San Francisco for five years.  And as the French like to remind us, the amount of “nuclear waste” produced in the process will be equally small.  A person living in a contemporary industrial society can use nuclear energy to meet their energy needs over the course of a lifetime and the amount of “nuclear waste” produced will fit into an empty soda can.  

So algebra does have some applications in everyday life.  It’s one way of understanding the enormous potential of nuclear energy.  In a country where math is taught and understood, people are likely to appreciate its enormous possibilities.  In a country where many people don’t understand math and educators don’t even want to teach it, emotion and illogic are more likely to reign.  

*

  • Day Brown

    The Liquid Fluoride Thorium Reactor (LFTR aka “Lifter”) is a vastly better solution than the above standard Uranium units. For one, the Fluoride Thorium salt melts at 400 deg C, the Molten Salt Reactor (MSR) has been operated at 1000 deg C, far hotter than a Uranium unit, but it cant melt down. Its already molten, and it cant get hotter unless you add more fuel rods. Left utterly alone it will just sit there until the fuel rods are exhausted, then it’ll cool down all by itself; which could be in several millennia if the cauldron it is in is made of alloys that dont rust. Because of the higher temp, the LFTR cauldron could replace a coal furnace and power the very same steam turbines with no carbon emissions at all, and do so producing less than 1% of the conventional nuclear waste.

    It is most curious that “experts” in nuclear energy dont know about this. The dollar/watt venture capital needed is far lower than wind or solar so undeveloped economies could afford it.

    • stevek9

      No fuel rods, the fuel is part of the molten salt.