[lightarrow]

Generally hotter water is less dense than cooler water , but it's the other way round between 0°C to 4°C  ...

From that picture it seems that what you say happens not only between 0°C to 4°C but also between -40°C to 4°C...

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[jeffreyH]

Point conceded, I think.

Now the question revolves around the definition of "heavier" and "proof". And then we have to consider the range of validity of that proof. Whilst it is obviously true that  a single molecule gains mass as it gains velocity (but relative to what, in the case of an isolated molecule in space?), "hotter" is not defined for a single molecule - temperature is an ensemble property, but we'll return to that in a moment.

Consider two isolated molecules, with different velocity vectors. How do we measure their mass? In principle (I'll grant you this bit is well outside the realm of experimental physics) the only way is to measure the gravitational force exerted on a test mass that is stationary with respect to each molecule. And to our (theorietical) astonishment, they both have the same mass.

Back to the ensemble. Even if the said boss is indeed conversant with relativistic physics, he will still need an exceptional grasp of the Gibbs energy of dynamic Voronoi polyhedra if he is going to accept a theoretical proof, and despite advances in chaos theory since I last worked on shortrange order in water, the numbers remain very vague and entirely experimental.

So we have to subtract the calculated relativistic contribution to the ensemble mass from the currently-incalculable density variation.

Once again, I have to ask you to do the calculation, on the assumption that the said boss will understand it. I'll be generous here and let you use RD's (experimental) graph, just this once, to check your answer.  And perhaps you will let us know, as an aside, how many angels can sit on the head of a pin!

Frankly, I think putting a wine bottle in a freezer is a lot easier. But then I'm an experimentalist.

PS - belated good Thanksgiving wishes. Thanks to the Pilgrim Fathers I now have plenty of wine bottles and an empty freezer!

I don't see why you would concede at all. Weight is simply a measure of gravitational force. Does mass really increase with velocity? If you weigh something on a mountain top there will be a very small difference to the weight at sea level. On a different planet things would be much different. 1KG would no longer make sense. I doubt if we can say the mass has increased or decreased in those circumstances. The same could be said for relativistic velocities. It is just harder to move a massive object like a particle at those velocities so it appears to gain mass. Photons have no such problem. I will always side with an experimentalist over a theorist.

[lightarrow]

Except that the water is  hotter. This means that the molecules have more kinetic energy, not that they have gained in mass - you can't have your cake and eat it!

In Newtonian mechanics this is true. In relativistic mechanics its not true. However in the later case the increase is very very small. Too small in fact to be measured in a typical lab. One needs a mass spectrometer to measure such a small increase.

I haven't understood what you say here. Are you talking of a mass increase of a particle with speed or what? And what are you saying about a mass spectrometer? That you could measure a particle's mass increase with speed using that device? If you are saying this, it's incorrect, and not because it would be too small, but because you can't.

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lightarrow.

[PmbPhy]

I haven't understood what you say here. Are you talking of a mass increase of a particle with speed or what?

Yes. I'll restate it to make it clearer. In what follows what I mean by the use of the term mass I mean inertial mass in the Newtonian case and relativistic mass in the relativistic case.

In Newtonian mechanics mass does not increase with speed.
In relativistic mechanics mass does increase with speed.

Simple, yes?

And what are you saying about a mass spectrometer?

That's one way to measure the relativistic mass of a charged particle.

That you could measure a particle's mass increase with speed using that device? If you are saying this, it's incorrect, and not because it would be too small, but because you can't.

That's  incorrect. In fact Wikipedia states that in 1901 Walter Kaufmann used a mass spectrometer to measure the relativistic mass increase of electrons. See http://en.wikipedia.org/wiki/History_of_mass_spectrometry

See also the article in American Journal of Physics about this particular point at
http://gabrielse.physics.harvard.edu/gabrielse/papers/1995/RelativisticMassAJP.pdf

However a mass spectrometer is in essence a cyclotron which can measure a mass increase due to relativistic mass.

The physics principles are the same as they are in a cyclotron. The particle is charged and that makes it move on a circle in a magnetic field. The radius of the circle it moves in. The physics for a cyclotron and a mass spectrometer is in the following webpage in my website: http://home.comcast.net/~peter.m.brown/sr/cyclotron.htm

If you are saying this, it's incorrect, and not because it would be too small, but because you can't.

Please provide a proof of this. A derivation whose results show what you assert would be fine. Thanks.

[alancalverd]

Consider two isolated molecules, with different velocity vectors. How do we measure their mass?

Their relativistic mass does not depend on its direction so we only need to measure its mass as a function of speed.

That's why I asked you to consider two particles with different velocity vectors. To make it closer to a practical experiment, think of two identical rocks hurtling at constant speed through space on nonintersecting courses. Their speed relative to each other (a) is variable and different from their fixed speeds (b and c) relative to a third-party frame of reference, which are also different. But their masses, as determined by the gravitational force on a test particle travelling with each (the only way you can determine the mass of a free asteroid), must be constant and identical because there is no universal frame of reference and neither rock is moving with respect to its test mass. Or variable with a. Or fixed but different according to b and c. Please choose, and show your reasoning.   

To do that one can measure the mass of a moving particle such as a molecule by ionizing it and using a cyclotron to measure its mass by determining it's deflection by a magnetic field and measuring its radius of orbit.

You're an experimental physicist aren't you? If so they why didn't you know this?

I not only knew it, but recently used it in another thread as an example of the experimental proof of relativity!

Once again, I have to ask you to do the calculation, ...

I don't see the point. I'm going to assume that "michael clark" is satisfied.
[/quote]

He asked for a proof that would convince his boss. I gave him a simple experiment that showed water in the range below 4°C was lighter than water at 4°C and this was unique, but you showed that thanks to the relativistic effect it always got heavier as you increased the temperature without bound, whilst RD presented a graph that contradicted that statement, so it seems that some calculation is in order if Mr Clark is not to go away completely confused! 

[PmbPhy]

That's why I asked you to consider two particles with different velocity vectors.

I don't understand what you mean. What do you mean by "That's why I asked...." I don't understand. Exactly why did you ask?

But their masses, as determined by the gravitational force on a test particle travelling with each (the only way you can determine the mass of a free asteroid), must be constant and identical because there is no universal frame of reference and neither rock is moving with respect to its test mass. Or variable with a. Or fixed but different according to b and c. Please choose, and show your reasoning.   

I don't understand at all what you're leading to or asking me. Please be more clear. Also I don't understand what you mean by "Please choose" What am I choosing?

Also since we're talking about relativistic mass why are you ignoring it in the case of the case of a particle moving through a gravitational field? E.g. see equation 16 in my web page -  http://home.comcast.net/~peter.m.brown/gr/weight_moving_body.htm

The m_p in that equation is the passive gravitational mass of the object and it depends on both the field and the gravitational potential and as such the position of the particle in the gravitational field.

I not only knew it, but recently used it in another thread as an example of the experimental proof of relativity!

Then why were you asking me how to measure it rather than posting it yourself? Unless it didn't come to your mind?

He asked for a proof that would convince his boss. I gave him a simple experiment that showed water in the range below 4°C was lighter than water at 4°C ....

If this

Fill a cup close to the brim with water, put  it in the freezer, and stir it with a thermometer. When it reaches about 5°C, top it up to the brim, then watch what happens as it cools further. It will spill over the edge just before it freezes because cold water takes up more space (i.e. is less dense) than warm.

is true then its not because there's a change in mass but a change in density. It's simply not possible to measure changes in mass that small in situations like this. In fact today there is no experiment of any kind which can show the mass increase for a macroscopic body due to an input/output of heat.

If you have the text Spacetime Physics - Second Edition by Taylor and Wheeler, then turn to page 223 and you'd see that they communicated with Vladimir Braginsky at the University of Moscow about a device to measure the increase in the weight of a tiny heated quartz pellet. They concluded that the technology does not exist to detect it yet. That it surpasses the present limit of technology

He asked for a proof that would convince his boss. I gave him a simple experiment that showed water in the range below 4°C was lighter than water at 4°C and this was unique, but you showed that thanks to the relativistic effect it always got heavier as you increased the temperature without bound, whilst RD presented a graph that contradicted that statement, so it seems that some calculation is in order if Mr Clark is not to go away completely confused! 

The reason I gave a relativistic description is because there is no classical mechanism that allows a water to become lighter. It just can't happen. It would mean that the law of the conservation of mass would be violated. It's only violated when relativistic effects are taken into account. You mistook the effects of the change in the density of water with a change in weight and therefore a change in mass.

See:
http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Conservation_of_mass.html
http://en.wikipedia.org/wiki/Conservation_of_mass

I'll post that section of Taylor and Wheeler's text after I scan it in and upload it to my website.

[CliffordK]

He asked for a proof that would convince his boss. I gave him a simple experiment that showed water in the range below 4°C was lighter than water at 4°C and this was unique,

The OP hasn't replied yet, so it is difficult to know the ultimate intentions. 

Yes, most materials have a positive expansion coefficient (decrease in density when heated), except for a few materials in specific circumstances, such as water that has a negative expansion coefficient between 0°C and 4°C.  Of course, that isn't a change in mass, but would be visible as a change in volume in a sealed container.

As far as Einstein E=mc², that would be more difficult to prove.  I derived some of the quantities on paper, but that is far from a rigorous empirical proof, and it would be difficult to weigh a cubic km of water or ice to an accuracy of a few grams.

I'm not sure a mass-spec has high enough of accuracy.  It also requires ions which may be problematic for a liquid water sample, but should still be representative.  Is, say, altering the temperature of a set of ions representative of the change in mass, or are there other confounding variables?

[PmbPhy]

Here is that page from the text Spacetime Physics 2nd Ed that I mentioned
http://home.comcast.net/~peter.m.brown/stp2_page_223.jpg

The OP hasn't replied yet, so it is difficult to know the ultimate intentions.

My impression is that the rarely do anyway.

Of course, that isn't a change in mass, but would be visible as a change in volume in a sealed container.

Yup. It happens every time I make ice cubes. I'm very surprised that one got by an experimental physicist like Alan.

As far as Einstein E=mc², that would be more difficult to prove.

As I indicated above, one does not "prove" things in physics other than those cases when it's a mathematical proof. One forms postulates, makes predictions from those postulates, designs experiments from those predictions and observes what happens in the experiments. If the experiment is consistent with the predicted results then one has more confidence in the theory. Otherwise one has to either abandon the theory or modify it. See

What is Science - http://home.comcast.net/~peter.m.brown/ref/what_is_science.pdf
The first paragraph reads

The following statement was originally drafted by the Panel on Public Affairs (POPA) of the American Physical Society, in an attempt to meet the perceived need for a very short statement that would differentiate science from pseudoscience. Am. J. Phys. 67 (,

I derived some of the quantities on paper, but that is far from a rigorous empirical proof, and it would be difficult to weigh a cubic km of water or ice to an accuracy of a few grams.

I'd enjoy reading what you derived. Can you post it here for me or send it to me in PM or e-mail? Thanks. Or please take a look at
http://home.comcast.net/~peter.m.brown/sr/mass_energy_equiv.htm and let me know if it's the same thing.

I'm not sure a mass-spec has high enough of accuracy.

It depends on the particular mass spectrometer. In any case, as I said above the physics is the same as a cyclotron so if the spectrometer doesn't work merely use a spectrometer.

It also requires ions which may be problematic for a liquid water sample, but should still be representative.

I'd say that a ion of H₂O would be just fine. However it'd be better to find out why he's so concerned with water as opposed to any other substance or element. If we find that out then it'd make things easier.

Is, say, altering the temperature of a set of ions representative of the change in mass, or are there other confounding variables?

At this point it's time to talk to the OP and his boss and get details. If he is still around that is. He might have forgotten all about this. After all he asked the question 4 days ago and we haven't heard even a whisper from either of them since.

[PmbPhy]

I'm not sure a mass-spec has high enough of accuracy.

Note: The reason I mentioned a mass-spectrometer is because it works like a cyclotron which can be used to measure the relativistic mass of a particle or ion. So tell you what we can do. Instead of using a mass-spectrometer, let's use a cyclotron instead. That way we don't have to worry about it working.

Of course Mike's boss can't get his hands on a cyclotron so that's the end of that.   Besides, the physics is too hard to work with when quantities are that small and increases that small too.

[alancalverd]

This is all fascinating stuff, but from the point if view of psychology and philology, not physics!

A benchtop mass spectrometer running at a few keV probably won't show the relativistic change of mass to a detectable level (it's calibrated with known ions - chemistry rather than physics - because it is very difficult to measure static magnetic fields to sufficient accuracy to make an absolute measurement of mass), but a hospital cyclotron certainly will, and we have to allow for it in designing the electronics.

But the real point of argument is the meaning of "heavier". Given that the original questioner didn't know how to demonstrate the effect, I think his enquiry was based on the common knowledge and observation of the anomalous expansion of water rather than the subtle timing corrections of a cyclotron driver - especially as you can't accelerate a water molecule in a cyclotron. Therefore he was talking about bulk density, not molecular mass.   

Is polystyrene heavier than gasoline? To the layman, the answer is clearly no because the "everyday" forms are foam and liquid respectively, but as a liquid or solid, the answer is yes, it is a lot denser. and if you want to be picky, it even has a higher molecular weight. But the molecular weight of gasoline is much greater than that of water, so surely water will float on gasoline? If only it did so, firefighting would be a lot easier!

[PmbPhy]

This is all fascinating stuff, but from the point if view of psychology and philology, not physics!

I can't see how that could possibly true at all. All I've done is to directly answer the OPs question and tried to do it in manner to answer what his boss is probably seeking the answer too rather than what he literally asked for proof of.

But the real point of argument is the meaning of "heavier".

I can't possibly see how that's a point of disagreement since most non-physicists confuse weight with mass. It's very clear to me that he wants to know which of two initially identical cups of water will have a greater mass will have a greater mass when one of them is heated, i.e. energy is added to the water. Most people I know are happy with thought experiments so I'd wager that Michael doesn't actually want to go out and do an experiment since he mentioned nothing about experiments. When he said "proof" it seemed to me that he wants to present a solid argument to present to him which will convince him that he's right.

Given that the original questioner didn't know how to demonstrate the effect, I think his enquiry was based on the common knowledge and observation of the anomalous expansion of water ...

I see absolutely no reason to assume that'd be the case. That is a major jump in my opinion.

..rather than the subtle timing corrections of a cyclotron driver - especially as you can't accelerate a water molecule in a cyclotron.

That's not true at all. And what's a "cyclotron driver" anyway and how is it related to this topic? There is absolutely no reason why a molecule of water, i.e. an H₂O ion couldn't be accelerated in a cyclotron. The following is close to what I'm referring to:
http://en.wikipedia.org/wiki/Ion_cyclotron_resonance

From my Google search I came up with this - ion cyclotron resonance mass spectrometry which appears to be what can be used in principle to measure the mass of water ion.

In any case, why are we so worried about experiments. Michael said nothing about experiments or that the answer had to be able to be done in practice. For all we know, and I know that if it were I then it's what I'd be looking for, I'd want to know what's going on in principle.


re - especially as you can't accelerate a water molecule in a cyclotron. - There is no basis for such an assumption. On what are you basing that assertion on?

Therefore he was talking about bulk density, not molecular mass.   

You don't know that at all. He specifically asked which was heavier, hot water or cold water. And as I said for most people, and nearly universally all layman, use weight synonymously for mass.


Sorry Alan but to me you're just grasping at straws now.

[lightarrow]

I haven't understood what you say here. Are you talking of a mass increase of a particle with speed or what?

Yes. I'll restate it to make it clearer. In what follows what I mean by the use of the term mass I mean inertial mass in the Newtonian case and relativistic mass in the relativistic case.
In Newtonian mechanics mass does not increase with speed.
In relativistic mechanics mass does increase with speed.
Simple, yes?

And what are you saying about a mass spectrometer?

That's one way to measure the relativistic mass of a charged particle.

That you could measure a particle's mass increase with speed using that device? If you are saying this, it's incorrect, and not because it would be too small, but because you can't.

That's  incorrect. In fact Wikipedia states that in 1901 Walter Kaufmann used a mass spectrometer to measure the relativistic mass increase of electrons. See http://en.wikipedia.org/wiki/History_of_mass_spectrometry

See also the article in American Journal of Physics about this particular point at
http://gabrielse.physics.harvard.edu/gabrielse/papers/1995/RelativisticMassAJP.pdf

However a mass spectrometer is in essence a cyclotron which can measure a mass increase due to relativistic mass.

The physics principles are the same as they are in a cyclotron. The particle is charged and that makes it move on a circle in a magnetic field. The radius of the circle it moves in. The physics for a cyclotron and a mass spectrometer is in the following webpage in my website: http://home.comcast.net/~peter.m.brown/sr/cyclotron.htm

If you are saying this, it's incorrect, and not because it would be too small, but because you can't.

Please provide a proof of this. A derivation whose results show what you assert would be fine. Thanks.

In order to analyze relativistic dynamic experiments, what we need is:

E² = (c*|p|)² + (m*c²)²     (1)
v = c²*p/E     (2)

(p and v are momentum and velocity vectors, "| |" means modulus of the vector).
From these two equations we can deduce other relativistic equations, for example:

E = mc²*γ
p = M*v*γ

Where γ = 1/sqrt{1 - (|v|/c)²}.

We also need the law:

F = dp/dt     (3)

which is the definition of force in relativistic dynamics.

Let’s analyze the motion of a charged particle in a magnetic field.
We know that (Lorentz force):

F = q*v x B     (4)

Where “x” means vectorial product.

So F is always orthogonal to v, and orthogonal to p too, according to eq. (2). It follows that the modulus of p is constant (and according to eq. (1) even E is constant):

d|p|²/dt = 2 p.(dp/dt) = 2 p.F = 0.

(the dot between two vectorial factors means scalar product).

Defining the angular speed as: ω = |v|/r, according to kinematics we have:

|dp/dt| =  ω*|p|

(This equation is valid in galileian as well as in relativistic kinematics).

For the sake of simplicity, let’s assume v and p both orthogonal to the magnetic field B.
Then the trajectory is a circle, traveled of uniform motion and which lays in a plane orthogonal to B.
So, using equations (2), (3), (4) and the expression of the (modulus of) Lorentz force on a charged particle:

|F| = q*|v|*|B|

we easily deduce :

ω*|p| = q*|v|*|B|     (5)

|p|/r = q*|B| → |p| = q*|B|*r    (6)

and it’s this last equation that we can use for a mass spectrometer, measuring r and knowing |B|, to compute |p| and so to find the mass m according to eq. (1), knowing the total energy E. The last can be found using also:

E = E_k + m*c²     (7)

where the kinetic energy E_k is set by the potential difference V applied to the charge q: E_k = q*V.

Substituting in eq. (7) and then in eq. (1):

(q*V + m*c²)² = (c*|p|)² + (m*c2)²     

from which you can find the  invariant mass m of the charged particle.

No need of relativistic mass.

N.B. (Most of what written up is not mine, it comes from another source, but it's rather simple to understand.
The source is an italian thread started from prof. Elio Fabri:
https://groups.google.com/d/msg/free.it.scienza.fisica/UyfGXka6rgQ/MiEiUTVexIsJ).

But if you intended that the mass spectrometer allows you to find the momentum |p| and so the total energy E and you identify the last with relativistic mass (multiplied c²), then we again come back to what I have said before several times in various threads, even answering to you, that is that relativistic mass is nothing else than another name for total energy E.

Edit: coloured in blue eq. (6) - 01/12/2014

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[jeffreyH]

I haven't understood what you say here. Are you talking of a mass increase of a particle with speed or what?

Yes. I'll restate it to make it clearer. In what follows what I mean by the use of the term mass I mean inertial mass in the Newtonian case and relativistic mass in the relativistic case.
In Newtonian mechanics mass does not increase with speed.
In relativistic mechanics mass does increase with speed.
Simple, yes?

And what are you saying about a mass spectrometer?

That's one way to measure the relativistic mass of a charged particle.

That you could measure a particle's mass increase with speed using that device? If you are saying this, it's incorrect, and not because it would be too small, but because you can't.

That's  incorrect. In fact Wikipedia states that in 1901 Walter Kaufmann used a mass spectrometer to measure the relativistic mass increase of electrons. See http://en.wikipedia.org/wiki/History_of_mass_spectrometry

See also the article in American Journal of Physics about this particular point at
http://gabrielse.physics.harvard.edu/gabrielse/papers/1995/RelativisticMassAJP.pdf

However a mass spectrometer is in essence a cyclotron which can measure a mass increase due to relativistic mass.

The physics principles are the same as they are in a cyclotron. The particle is charged and that makes it move on a circle in a magnetic field. The radius of the circle it moves in. The physics for a cyclotron and a mass spectrometer is in the following webpage in my website: http://home.comcast.net/~peter.m.brown/sr/cyclotron.htm

If you are saying this, it's incorrect, and not because it would be too small, but because you can't.

Please provide a proof of this. A derivation whose results show what you assert would be fine. Thanks.

In order to analyze relativistic dynamic experiments, what we need is:

E² = (c*|p|)² + (m*c²)²     (1)
v = c²*p/E     (2)

(p and v are momentum and velocity vectors, "| |" means modulus of the vector).
From these two equations we can deduce other relativistic equations, for example:

E = mc²*γ
p = M*v*γ

Where γ = 1/sqrt{1 - (|v|/c)²}.

We also need the law:

F = dp/dt     (3)

which is the definition of force in relativistic dynamics.

Let’s analyze the motion of a charged particle in a magnetic field.
We know that (Lorentz force):

F = q*v x B     (4)

Where “x” means vectorial product.

So F is always orthogonal to v, and orthogonal to p too, according to eq. (2). It follows that the modulus of p is constant (and according to eq. (1) even E is constant):

d|p|²/dt = 2 p.(dp/dt) = 2 p.F = 0.

(the dot between two vectorial factors means scalar product).

Defining the angular speed as: ω = |v|/r, according to kinematics we have:

|dp/dt| =  ω*|p|

(This equation is valid in galileian as well as in relativistic kinematics).

For the sake of simplicity, let’s assume v and p both orthogonal to the magnetic field B.
Then the trajectory is a circle, traveled of uniform motion and which lays in a plane orthogonal to B.
So, using equations (2), (3), (4) and the expression of the (modulus of) Lorentz force on a charged particle:

|F| = q*|v|*|B|

we easily deduce :

ω*|p| = q*|v|*|B|     (5)

|p|/r = q*|B| → |p| = q*|B|*r    (6)

and it’s this last equation that we can use for a mass spectrometer, measuring r and knowing |B|, to compute |p| and so to find the mass m according to eq. (1), knowing the total energy E. The last can be found using also:

E = E_k + m*c²     (7)

where the kinetic energy E_k is set by the potential difference V applied to the charge q: E_k = q*V.

Substituting in eq. (7) and then in eq. (1):

(q*V + m*c²)² = (c*|p|)² + (m*c2)²     

from which you can find the  invariant mass m of the charged particle.

No need of relativistic mass.

N.B. (Most of what written up is not mine, it comes from another source, but it's rather simple to understand.
The source is an italian thread started from prof. Elio Fabri:
https://groups.google.com/d/msg/free.it.scienza.fisica/UyfGXka6rgQ/MiEiUTVexIsJ).

But if you intended that the mass spectrometer allows you to find the momentum |p| and so the total energy E and you identify the last with relativistic mass (multiplied c²), then we again come back to what I have said before several times in various threads, even answering to you, that is that relativistic mass is nothing else than another name for total energy E.

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lightarrow

I am so glad that you posted this. I don't think many will appreciate the subtleties.

[alancalverd]

Yup. It happens every time I make ice cubes. I'm very surprised that one got by an experimental physicist like Alan.

The OP concerned water, not ice. Expansion on solidification is not unusual - printers' "hot type" and several other materials do it - but the expansion of liquid water over a significant range of cooling is remarkable and very important. 

And what's a "cyclotron driver" anyway and how is it related to this topic?

It's the electronic gubbins that turns the cyclotron from a drawing into a working machine. But don't worry your pretty head about that nasty engineering stuff - you'll get you hands dirty! 

There is absolutely no reason why a molecule of water, i.e. an H2O ion couldn't be accelerated in a cyclotron.

A molecule is not an ion. Which seems a good reason to me.

[jeffreyH]

Yup. It happens every time I make ice cubes. I'm very surprised that one got by an experimental physicist like Alan.

The OP concerned water, not ice. Expansion on solidification is not unusual - printers' "hot type" and several other materials do it - but the expansion of liquid water over a significant range of cooling is remarkable and very important. 

And what's a "cyclotron driver" anyway and how is it related to this topic?

It's the electronic gubbins that turns the cyclotron from a drawing into a working machine. But don't worry your pretty head about that nasty engineering stuff - you'll get you hands dirty! 

There is absolutely no reason why a molecule of water, i.e. an H2O ion couldn't be accelerated in a cyclotron.

A molecule is not an ion. Which seems a good reason to me.

A molecule yes but look at the hydrogen bonding.

http://www1.lsbu.ac.uk/water/water_hydrogen_bonding.html

[PmbPhy]

The OP concerned water, not ice.

I didn't say he was. It was merely a thought on expansion of cold water.

But don't worry your pretty head ...

So this is what you resort to when you loose an argument, huh?

I know a great deal about engineering since I worked in the field for years before becoming a physicist.

A molecule is not an ion. Which seems a good reason to me.

An ion is an atom or a molecule for which the number protons is not the same as the number of electrons. That's how atoms and molecules can be accelerated in a cyclotron. And you claim to be an experimental physicist and you didn't know this simple fact that all physicists and chemists know?

You should learn the basics of physics before insulting and being rude to others. Start with these:

http://en.wikipedia.org/wiki/Ion

An ion (/ˈaɪən, -ɒn/)[1] is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving the atom or molecule a net positive or negative electrical charge.

http://en.wikipedia.org/wiki/Ion_cyclotron_resonance

Ion cyclotron resonance is a phenomenon related to the movement of ions in a magnetic field. It is used for accelerating ions in a cyclotron, and for measuring the masses of an ionized analyte in mass spectrometry, particularly with Fourier transform ion cyclotron resonance mass spectrometers. It can also be used to follow the kinetics of chemical reactions in a dilute gas mixture, provided these involve charged species.

See also - http://scienceworld.wolfram.com/chemistry/Ion.html

: an atom or group of atoms that has a positive or negative electric charge from losing or gaining one or more electrons

See the list of molecules in that page that they use as examples of ions.

[PmbPhy]

No need of relativistic mass.

So what? Do you realized just how many concepts there are in physics that aren't "needed"? In fact Hertz wrote an entire mechanics text without using the concept of force. I could write an entire textbook on relativity without using the concept of energy either. Let me show you how easy it'd be to derive the cyclone formula by using relativistic mass. Let B = Bk where B is a constant. Let v start out in the xy-plane. Then

F = qvxB

means that the force is perpendicular to the velocity which means the charge moves in a circle and the force is perpendicular to the velocity. As such F = ma. If you're not aware that this is true then see
http://home.comcast.net/~peter.m.brown/sr/long_trans_mass.htm

F = ma = mv²/r = qvB

or

mv = qrB = p

which is the cyclotron relation, i.e.

mv = qrB

Which requires a great deal less work that what you did.

[PmbPhy]

A molecule yes but look at the hydrogen bonding.

You're wrong too, Jeff. A molecule which has a different amount of electrons than protons is an ion. Same holds true with atoms.

[CliffordK]

As far as heat and relativistic mass, if it could be demonstrated for any substance, water, hydrogen, helium, radon, lead, etc, then it could be considered valid for all substances. 

While H₂O is not an ion, water is always a mix of ions, H₂O, OH^–, H⁺, and H₃O⁺.  With acid/base chemistry, it is relatively easy to force one or another ion to be more prevalent, at last in liquid water form.  Gases may tend to be more neutral.  There is no reason why water couldn't be used as a source of ions for analysis.  However, there may be better choices of materials for analysis.

[alancalverd]

A molecule is by definition electrically neutral and thus cannot be accelerated by a cyclotron.

An ion may have the same nuclides, almost the same mass and even most of the shape of a molecule but it is distinguished by having a charge, and thus quite different behaviour in an electric or magnetic field.  Which is why it has a different name, and why we ionise molecules in a mass spectrometer.

It is worth reconsidering the Wikipedia definitions. If I have an ion with 6 protons and 7 electrons, is it carbon plus an electron or nitrogen minus a proton? If we incorporate the nuclide into a fairly simple compound, the difference is between an inert plastic and an explosive, so we need to be a bit careful with our definitions here.