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Q: conservation of mass+energy ( Answered 5 out of 5 stars,   2 Comments )
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 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 ( ) 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
Subject: Re: conservation of mass+energy
Answered By: mvguy-ga on 14 Oct 2002 18:14 PDT
Rated:5 out of 5 stars
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

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

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
"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

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."

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
109 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

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

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

Experimental Evidence of a New Type of Quantized Matter with Quanta as
Integer Multiples of the Planck Mass

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

I hope this helps.



Google search terms:

"conservation of mass in chemical reactions"

"conservation of mass in chemical reactions" relativity

Request for Answer Clarification by placain-ga on 14 Oct 2002 18:49 PDT
<i>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:

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."

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."

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."

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."

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

I hope this helps.  If it doesn't, I'll see what else I can find.



Google search strategy: various combinations of terms such as
"conservation of energy," "loss of mass," "conversion of mass,"
"potential energy" and others
placain-ga rated this answer:5 out of 5 stars

Subject: Re: conservation of mass+energy
From: hedgie-ga on 14 Oct 2002 23:13 PDT
The answer b) is certainly flat wrong. The mass energy equivalence
to all kinds of energy equally.

The problem with a) and perhaps partly with the answer is that of
rather then of substance.  If we accept relativistic point of view, we
not talk about converting mass into energy. There is only one
mass-energy and that quantity is conserved. Meaning, when photon
leaves your
space flashlight, it carries away  h * frequency of energy and the
of the flashlight is h * frequency / c * c less after that. 

The semantic issue is agravated by the fact that in 'common life' the
non-relativistic terms are still useful and so we still talk about
released by a chemical reaction and say that mass is conserved in a
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.
Subject: Re: conservation of mass+energy
From: dannidin-ga on 17 Oct 2002 14:57 PDT
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, 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

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.)


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