MadSci Network: Physics |
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
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