Re: Does electric charge defeat entropy?

Hi Tom,

It’s good to see that you’re thinking about entropy in terms of real-world 
examples.  However, in this case entropy is important in understanding 
static electricity, which is at its heart an atomic (quantum mechanical) 
property of materials.  Entropy is at work, but in a very subtle way that 
becomes clear when consider entropy in the context of the universe.

Atoms are comprised of three stable particles: protons that carry a 
positive charge, neutrons that are electrically neutral, and electrons 
that carry a negative charge.  The nucleus of any atom is made up of a 
combination of protons and neutrons, while the comparatively light 
electrons orbit around the nucleus.  By analogy with our solar system, you 
can imagine the sun as the nucleus and the planets as orbiting electrons.  
Just like in the solar system, the nucleus is large compared to the 
electrons. The atom is mostly empty space. And the electrons are very far 
away from the nucleus. While this model is not completely accurate, we can 
use it to help us understand static electricity.

The protons and neutrons in the nucleus are held together very tightly by 
something called the nuclear strong force, one of the fundamental forces 
of the universe. Normally the nucleus does not change. But some of the 
outer electrons are held very loosely. They can move from one atom to 
another. An atom that looses electrons has more positive charges (protons) 
than negative charges (electrons). It is positively charged. An atom that 
gains electrons has more negative than positive particles. It has a 
negative charge. A charged atom is called an "ion."

Some materials hold their electrons very tightly. Electrons do not move 
through them very well. These things are called insulators. Plastic, 
cloth, glass and dry air are good insulators. Other materials have some 
loosely held electrons, which move through them very easily. These are 
called conductors. Most metals are good conductors.

How can we move electrons from one place to another? One very common way 
is to rub two objects together. If they are made of different materials, 
and are both insulators, electrons may be transferred (or moved) from one 
to the other. The more rubbing, the more electrons move, and the larger 
the charges built up. (Scientists believe that it is not the rubbing or 
friction that causes electrons to move. It is simply the contact between 
two different materials. Rubbing just increases the contact area between 
them.)

The heart of your question concerns the equilibrium state of the universe, 
and how the one of the laws of thermodynamics, that “entropy always 
increases”, seems to be defied by the buildup of a net charge difference 
between materials that shows up as static electricity.  I need to spend a 
little time on thermodynamics.  At its essence, the thermodynamics of a 
system really describes an energy balance; like balancing a checkbook, the 
energy going into a system or flowing out of a system is in balance with 
the rest of the world.  (Money is a VERY good analogy to energy in a 
thermodynamic sense).  Here is my favorite description of the laws of 
thermodynamics in a colloquial sense:

1) You can’t break even (i.e. entropy always increases).
2) You can break even, but only when hell freezes over (i.e. you can stop 
entropy from changing/increasing at absolute zero temperature).
3) Hell isn’t going to freeze over (i.e. though you can get close, you 
can’t get to absolute zero).

All changes of energy are in balance on the scale of the universe; locally 
we can change the balance of energy in apparent defiance of the first law 
of thermodynamics.  It takes substantial effort to roll a large rock up a 
hill; perched on the top of the hill, it retains potential energy that 
would be released if the boulder rolls back down the hill under the force 
of gravity.  Static electricity is a lot like the energetic state achieved 
when the builder is perched at the top of a hill but has not begun rolling 
down.

In describing how static charges build up, I was careful to say that we as 
experimenters had to add work to the system in the form of rubbing two 
materials together in order to achieve a transfer of electrons from one 
material to another.  One material is now electrically negative and the 
other positive, and there is a potential energy difference between them as 
a result.  However, we be performing work on the system we have spent 
energy through the force required to rub materials together; the work 
required to rub materials together is always larger than the potential 
energy remaining when the two materials are separated, one carrying off 
electrons from the other.  Locally, we are in apparent defiance of the 
rule that entropy increases when we neglect the energy we put into the 
system.

Static charge buildup between two materials is a pseudo-stable state, as 
you know from experience when you touch something (light switch or 
siblings ear) that is electrically higher or lower than your current 
state.  The strength of the resulting electric field depends on many 
things, including the amount of charge, distance involved, and shape of 
the objects. This can become very complicated. We can simplify things by 
working with "point sources" of charge. Point sources are charged objects 
that are much, much smaller than the distance between them.

Charles Coulomb first described electric field strengths in the 1780's. He 
found that for point charges, the electrical force varies directly with 
the product of the charges. In other words, the greater the charges, the 
stronger the field. And the field varies inversely with the square of the 
distance between the charges. This means that the greater the distance, 
the weaker the force becomes. This can be written as the formula:

F = k (q1 X q2) / d**2

where q is the charge, and d is the distance between the charges. K is the 
proportionality constant (the dielectric constant), and depends on the 
material separating the charges.  The dielectric constant between the two 
separated materials is a function of what kind of material exists between 
the charges and the volume of it (for point charges, we’re using a simple 
distance rather than the volume).  Both factors determine the energy 
barrier preventing the two materials from returning to an electrically 
neutral state.  If we return the two materials close to on another, at 
some distance the potential energy difference between negatively charged 
and positively charged materials (which is fixed) will exceed the 
potential energy barrier of the air that separates the two materials (the 
energy barrier getting smaller as the volume of air between materials gets 
smaller) and there will be an electric discharge that makes both materials 
electrically neutral as the electron-rich material returns its borrowed 
electrons.

If we neglect the amount of energy we put into our system in generating a 
static charge, we are in apparent violation of the laws of entropy (which 
is true in a local sense).  When we consider the experiment as a whole and 
balance all forces and sources of energy, it’s clear that we had to invest 
energy into the system in order to achieve a temporary imbalance of 
electrons that is destined to return to normal once either material comes 
in contact with another electrically neutral object.  In the end, entropy 
will have increased as a result of our having spent energy to achieve a 
state that in the end will return to its starting position.  We can’t win, 
because hell won’t freeze over.

Thanks for the interesting question.

Regards,
Dr. James Kranz