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 Subject: conservation of mass+energy Category: Science > Physics Asked by: placain-ga List Price: \$6.00 Posted: 14 Oct 2002 16:50 PDT Expires: 13 Nov 2002 15:50 PST Question ID: 76608
 ```http://www.appliedthought.com/InsightPress/ThinkSample.html gives a sample question from the book 'Thinking Physics': Which of the following statements is correct? (a) E=mc^2 tells us how much mass loss, m, must be suffered by a flashlight battery when the flashlight puts out a given amount of energy, E. (b) E=mc^2 applies to nuclear energy in a reactor, but not to chemical energy in a battery The answer is given ( http://www.appliedthought.com/InsightPress/EmcAnswer.html ) as (a). This seems wrong to me. I thought that nuclear reactions actually convert mass to energy, whereas chemical reactions merely rearrange mass into higher or lower entropy (potential chemical energy) forms. It seems to me that their example violates conservation - the mass lost doesn't "go" anywhere, it is *converted* to energy! The total mass+energy of the system remains constant. Please provide a detailed explanation of either why I'm wrong or right.```
 Subject: Re: conservation of mass+energy Answered By: mvguy-ga on 14 Oct 2002 18:14 PDT Rated:
 ```Wow. I like to think I learn something everyday, and I usually do. But it rare that I learn something so contrary to everything I had learned earlier. My answer to the question would have been the same as yours. It makes perfect sense -- and besides, that's always what I had been told. But now that I think about it, answer B does make sense. The key is that the amount of mass loss is so incredibly tiny that for all practical purposes there is no mass loss -- certainly nothing you nor I could measure. Nowadays, as a matter of fact, the law of conservation of mass is worded to say that there is no detectable (note that word) loss or gain of mass in a chemical reaction. Here's another way it's described: Conservation of Mass in Chemical Reactions "In chemical processes, the most important property to be conserved is the number of atoms of each kind that are present. Unlike nuclear processes, chemical reactions do not create or destroy atoms, or change one kind of atom into another. They only reshuffle the atoms that were originally present into different molecular combinations. What we would like to be able to do is to count each kind of atom before and after a reaction and make sure that none has been gained or lost. "Counting atoms directly is not practical, but because mass-energy conversion is NEGLIGIBLE in chemical reactions, conservation of the number of atoms effectively means the conservation of mass." [emphasis added] http://www.chem.ox.ac.uk/vrchemistry/Conservation/page07.htm One theoretical explanation is on that page you provided a link to. Similarly, imagine a flashlight in outer space emitting light (or a satellite emitting electromagnetic energy) while powered by a battery. The device is receiving no energy (we'll assume it's in complete shade), yet it's emitting energy. Where's that energy coming from? It can't be getting energy from nothing. The answer is that Einstein's formula (E=mc^2) applies. A tiny amount of mass is being converted to energy in order to balance that formula. In other words, if a closed system is producing energy, it must be coming from mass for Einstein's formula to hold true. How tiny is the loss of mass? The following page has the answer: Conservation of Mass, Charge, and Energy "In principle, if a reaction gives off energy, the products formed must have lower energy and be lighter than the reactants. But a release of 100 kcal mole^-1 by a typical chemical reaction corresponds (via the Einstein relationship) to a mass loss of only 5 x 10^-9 amu per molecule, or one hundred thousandth the mass of an electron. This amounts to only 5 x 10^-9 gram per mole, which is far less than we can measure. This is why we can say that, for chemical reactions, mass and energy are conserved independently." http://www.chem.ox.ac.uk/vrchemistry/Conservation/page05.htm Similar figures are included on this page: The Conservation of Mass-Energy "The Law of Conservation of Mass is still a useful idea in chemistry. This is because the energy changes in a chemical reaction are so tiny that they did not affect any measurements. 100 kJ is a typical value for the energy involved in a chemical reaction and it is only about 10¯9 gram. Only recently has such a small amount been able to be accurately measured. The mass loss or gain due to energy loss or gain in a chemical reaction may someday be something that is routinely measured." http://dbhs.wvusd.k12.ca.us/Thermochem/Law-Cons-Mass-Energy.html In other words, as far as a chemist is concerned the law of conservation of mass holds true. A chemist couldn't possibly measure any difference. It's a difference that only a subatomic scientist could love (or even care about). Here's another way of putting it: Conservation Principles "If we look at mass and energy closely enough, the principles that they individually are conserved turn out to be only approximately true. Mass and energy actually are interconvertible, and are different manifestations of the same thing. We can uncouple them in thinking about chemical reactions only because the quantities of energy involved in chemical processes correspond to infinitesimal amounts of mass." http://www.chem.ox.ac.uk/vrchemistry/Conservation/page04.htm As stated above, the amount of mass lost is so tiny that it can't be measured by normal means. Early in the last century there were numerous experiments to detect such mass loss, but the amount of measured loss was always less than the amount of possible measurement area. But more recently, mass loss has been measured in certain chemical reactions. The mass loss actually turned out to be higher than expected, leading to some new theories about various types of matter. You can find out more about those experiments in the following paper: Experimental Evidence of a New Type of Quantized Matter with Quanta as Integer Multiples of the Planck Mass http://redshift.vif.com/JournalFiles/Pre2001/V06NO1PDF/V06n1vol.pdf It's all very fascinating. Like I said, I suspected the same thing as you did. The key is that the amount of mass that is lost in a typical chemical reaction is so incredibly, incredibly small that it can be assumed not to exist for all practical purposes. But it is there nevertheless. I hope this helps. Sincerely, mvguy Google search terms: "conservation of mass in chemical reactions" ://www.google.com/search?q=%22conservation+of+mass+in+chemical+reactions%22&sourceid=opera&num=25&ie=utf-8&oe=utf-8 "conservation of mass in chemical reactions" relativity ://www.google.com/search?num=25&hl=es&ie=UTF-8&oe=utf-8&q=%22conservation+of+mass+in+chemical+reactions%22+relativity&btnG=B%C3%BAsqueda+en+Google``` Request for Answer Clarification by placain-ga on 14 Oct 2002 18:49 PDT ```imagine a flashlight in outer space emitting light (or a satellite emitting electromagnetic energy) while powered by a battery. The device is receiving no energy (we'll assume it's in complete shade), yet it's emitting energy. Where's that energy coming from? It can't be getting energy from nothing. The answer is that Einstein's formula (E=mc^2) applies. A tiny amount of mass is being converted to energy in order to balance that formula. This is precisely what I'm asking about. I was under the impression that a battery is storing chemical potential energy. As electrons flow from cathode to anode, potential energy is converted to electrical energy, which the filament converts to EM energy. In other words, I would think that the battery example is equivalent to the following example: A wind-up flashlight is wound and left to drift in outer space. As the winding unwinds, potential energy (stored in the spring) is converted to electrical energy, which is then converted to EM energy. Are you saying that as the spring unwinds, it's losing mass, and when the spring is wound up again, it's gaining mass?``` Clarification of Answer by mvguy-ga on 14 Oct 2002 21:44 PDT ```Yes, that's exactly what I'm saying. Go back to the page that you referred to in your question: http://www.appliedthought.com/InsightPress/EmcAnswer.html Just substitute "spring" for battery, and the principle is the same. I'm not sure that that page gives the best explanation, but I can also use my satellite-in-space analogy. The satellite, which is powered by a spring, while flying in space is taking in neither energy nor fuel, yet it's giving off energy (in the form of radio waves, for example). That energy has to be coming from somewhere -- so therefore according to Einstein's formula it must be losing mass. It doesn't really matter for this example whether the internal energy source is a battery or a spring or a tiny nuclear power plant. The device is still losing mass; that's where it's getting its energy from. What you need to ask yourself is, what is "potential energy"? It is mass! That's the key. What you're calling "potential energy" can also be thought of as the conversion of energy to some type of subatomic mass which is then released as energy when the mass is "destroyed." The "potential energy" in this case is in fact stored as an infinitestimal amount of mass. By "giving energy" to the spring you are actually increasing its mass. When it "gives off energy" it is in fact losing an infinitesimal amount of mass. Energy I "His [Einstein's] theory states that mass and energy are equivalent. When something gains energy, it gains mass. When something gains mass, it gains energy." http://www.geocities.com/j31645/15.html Here's another way of putting it: Mass and Energy "The fact that feeding energy into a body increases its mass suggests that the mass m0 of a body at rest, multiplied by c^2, can be considered as a quantity of energy." http://www.phys.virginia.edu/CLASSES/252/mass_and_energy.html Here's a much more technical explanation: Spacial Global Regularities "Material objects exert forces that can accelerate material objects, and our theory is that those forces are a form of matter that helps make up the material objects and whose quantity is counted in their rest masses. When potential energy has given the objects kinetic energy, for example, the objects have not only changed their relative positions, but the force field itself has changed. The change in the force field means that less matter is required to constitute it, and that is the source of the kinetic energy, which on our theory is also a form of matter. Thus, it is a conversion of some of the matter counted as rest mass into matter that is counted as kinetic energy. The opposite conversion occurs when kinetic energy becomes potential energy, and the same principle holds for conversions between potential energy and photons (and other forms of matter). Thus, the conversion between potential energy and kinetic energy does not violate the principle of the conservation of mass and energy." http://www.twow.net/ObjText/OtkCbGbS.htm Here is a simpler explanation of the concept I'm trying to get across: Chemical Energy "It is a good time to think about the how, what, and why of chemical energy. First we ought to discuss what energy is. Energy is a measurement of the quantity of matter. Depending on which measuring instrument is used, the quantity of matter in a sample will register as calories, watt hours, ergs, foot pounds, etc. The quantity of matter is also measured in units of mass, such as grams." http://philmintz.tripod.com/EssaysOnScience/page3.html Again, the key is that energy and mass are the same thing. What makes this so counterintuitive is that in chemical reactions and mechanical processes (such as the wound-up spring) the amount of mass converted to or from energy is so small as to not be noticed. But it does exist. I hope this helps. If it doesn't, I'll see what else I can find. Sincerely, mvguy Google search strategy: various combinations of terms such as "conservation of energy," "loss of mass," "conversion of mass," "potential energy" and others```
 ```The answer b) is certainly flat wrong. The mass energy equivalence applies to all kinds of energy equally. The problem with a) and perhaps partly with the answer is that of semantics, rather then of substance. If we accept relativistic point of view, we should not talk about converting mass into energy. There is only one quantity, mass-energy and that quantity is conserved. Meaning, when photon leaves your space flashlight, it carries away h * frequency of energy and the mass of the flashlight is h * frequency / c * c less after that. The semantic issue is agravated by the fact that in 'common life' the classical, non-relativistic terms are still useful and so we still talk about energy released by a chemical reaction and say that mass is conserved in a reaction. That is a (useful?) aproximation. We talk about converting one enrgy into another, potential into kinetic, chemical into light, etc. This is different from what Einstein meant, when in 1905 wrote: The law of conservation of mass is a special case of law of conservation of energy. [ Annalen der Physik, 18, 639, (1905) ] Going from E to E/c*c is more like going from Joules to ergs. It does not describe a physical process.```
 ```hedgie-ga is correct. the equation e=mc^2 is commonly misunderstood to mean that mass can be _converted_ into energy, where actually they are one and the same. this mistake is so common that it pervades many textbooks, and also, as careful reading of the quotes in mvguy-ga's answer shows, many science web-pages. the only source that he quotes that doesn't seem to fall into this trap is http://www.chem.ox.ac.uk/vrchemistry/Conservation/page04.htm, which correctly states: "Mass and energy actually are interconvertible, and are different manifestations of the same thing". (True, in some of the other web pages cited the mistake is more of a semantic nature than a misunderstanding) Chemists, for whom the whole mass-energy equivalence is mostly of curiosity value (as illustrated by the above quotes), seem especially prone to this sort of misunderstanding. Here's another thought experiment to illustrate mass-energy equivalence: An object weighing, say, 1 kilogram, is placed on a scale. Then a flame is applied from below and heats the object. What will happen to the scale measurement? (I assume of course that the scale is infinitely precise, and that the heating does not influence the scale directly but only the object...) Answer: The scale will now show that the object has grown in weight! Of course its mass will have grown since we are adding kinetic energy to its atoms, and now it will be attracted to the earth with a slightly greater force. (Of course, the increase in mass will be ridiculously small and is in practice not measurable in this setting.) Cheers, dannidin-ga```