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Johann Mahne

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How was Absolute Zero discovered?
« on: 28/07/2011 15:12:06 »
I've always wondered how the value of -273 deg c was discovered as the coldest possible temperature.
Was it through experiment or from astronomical measurements (spectrometers) or calculated theoretically?


 

Offline JP

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How was Absolute Zero discovered?
« Reply #1 on: 28/07/2011 16:23:52 »
It's a theoretical idea.

Temperature is defined as the average kinetic energy of particles making up matter.  Kinetic energy is energy of motion, so it's a measurement of the average motion of a lot of particles.  It makes sense that the lowest possible temperature is when that motion stops.  This was the original idea of absolute zero.

More recently, scientists have learned that small particles can never stop moving because of the rules of quantum mechanics.  Absolute zero can still defined as the temperature where they're moving the least amount possible.
 

Offline Phractality

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How was Absolute Zero discovered?
« Reply #2 on: 28/07/2011 17:28:49 »
It was discovered by graphing the relationship among temperature, pressure and volume of gasses. For a constant volume of most gases, the pressure to temperature graph follows a straight line which reaches zero pressure at -273.15C.
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #3 on: 28/07/2011 17:55:28 »
It's a theoretical idea.

Temperature is defined as the average kinetic energy of particles making up matter.  Kinetic energy is energy of motion, so it's a measurement of the average motion of a lot of particles.  It makes sense that the lowest possible temperature is when that motion stops.  This was the original idea of absolute zero.

More recently, scientists have learned that small particles can never stop moving because of the rules of quantum mechanics.  Absolute zero can still defined as the temperature where they're moving the least amount possible.

It was first proposed by Einstein, it has a value of 1/2 \hbar ω. It not a theoretical idea, it's a proven limit on temperatures of systems, free and bound.
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #4 on: 28/07/2011 18:00:39 »
I've always wondered how the value of -273 deg c was discovered as the coldest possible temperature.
Was it through experiment or from astronomical measurements (spectrometers) or calculated theoretically?


It was proposed in 1913 using a formula that was develeoped by Max Planck. Einstein used it to describe vibrational energy, and was given as

ε = (hv/ehv/kT-1) + hv/2

hv/2 can be thought of an existing kinetic energy for a system, which means that -273 can never be accomplished. This also means the zero point energy does not actually exist! I've even proposed that Fermi energy equations propose a faulty premise as it requires the idea that the ZP-energy is a real value.
« Last Edit: 28/07/2011 18:02:25 by Mr. Data »
 

Offline imatfaal

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How was Absolute Zero discovered?
« Reply #5 on: 28/07/2011 18:11:46 »
from wikipedia
http://en.wikipedia.org/wiki/Absolute_zero
Quote
Limit to the 'degree of cold'

The question whether there is a limit to the degree of cold possible, and, if so, where the zero must be placed, was first attacked by the French physicist Guillaume Amontons in 1702, in connection with his improvements in the air thermometer. In his instrument, temperatures were indicated by the height at which a column of mercury was sustained by a certain mass of air, the volume or "spring" which varied with the heat to which it was exposed. Amontons therefore argued that the zero of his thermometer would be that temperature at which the spring of the air in it was reduced to nothing. On the scale he used, the boiling-point of water was marked at +73 and the melting-point of ice at 51, so that the zero of his scale was equivalent to about −240 on the Celsius scale.

and from the 1911 (ie before the the planck formula you mention)  encyclopedia britannica
http://www.1911encyclopedia.org/Cold
Quote
After J. P. Joule had determined the mechanical equivalent of heat, Lord Kelvin approached the question from an entirely different point of view, and in 1848 devised a scale of absolute temperature which was independent of the properties of any particular substance and was based solely on the fundamental laws of thermodynamics (see Heat and Thermodynamics). It followed from the principles on which this scale was constructed that its zero was placed at - 273, at almost precisely the same point as the zero of the air-thermometer.
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #6 on: 28/07/2011 18:16:40 »
There is no question that the equation and experimental evidence implies the zero point energy limit is not attainable. The reason why is because of:

E = ∫ (Th/Tc - 1) C dT

If the integral here is taken to the Th to Tc, (hot and cold temperatures) then if C is a constant and as Th approaches Tc, E tends to infinity.

This means that it will take an infinite amount of energy to reach T=0. This is along the same idea's as a system requiring an infinite amount of energy to reach speeds equalling c.
 

Offline imatfaal

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« Reply #7 on: 28/07/2011 18:32:41 »
Mr Data could you also explain your variables and notation a bit as well so that those not versed in quantum mechanics can attempt to follow the equations and thus your argument.

As an example
ε = (hv/ehv/kT-1) + hv/2

This looks similar to the average value of a planck oscilator - but it should normally be in terms of Ehat rather than epsilon.  And if we are using greek script then the nu should be a nu

 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #8 on: 28/07/2011 18:39:15 »
Mr Data could you also explain your variables and notation a bit as well so that those not versed in quantum mechanics can attempt to follow the equations and thus your argument.

As an example
ε = (hv/ehv/kT-1) + hv/2

This looks similar to the average value of a planck oscilator - but it should normally be in terms of Ehat rather than epsilon.  And if we are using greek script then the nu should be a nu



You want me to describe this equation for you? Epsilon is a small number, and refers to a small energy contribution. So let ε=Ef where Ef is zero energy field. Let hv/2 = KE where KE is the kinetic energy wherre h is planks constant and v is the frequency. We have expression here (hv/ehv/kT-1) which just looks like a mess of things, including an ugly exponential that non-mathematicians cannot appreciate easily. Just let this equal an energy, but look at it as an energy that equals zero. However, whilst that is a general limit on the system, the system does not actually have a non-zero energy because hv/2 is not equal to zero. So all in all, the equation above really reads

E = KE = 1/2hv

For an existing energy, and will always exist. It cannot reach zero because it would, again, require an infinite amount of energy.
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #9 on: 28/07/2011 18:41:42 »
You can even set v = ω so that

hbar ω/2 = E for a ZP-field fluctuation.
 

Offline JP

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How was Absolute Zero discovered?
« Reply #10 on: 28/07/2011 18:53:41 »
It's a theoretical idea.

Temperature is defined as the average kinetic energy of particles making up matter.  Kinetic energy is energy of motion, so it's a measurement of the average motion of a lot of particles.  It makes sense that the lowest possible temperature is when that motion stops.  This was the original idea of absolute zero.

More recently, scientists have learned that small particles can never stop moving because of the rules of quantum mechanics.  Absolute zero can still defined as the temperature where they're moving the least amount possible.

It was first proposed by Einstein, it has a value of 1/2 \hbar ω. It not a theoretical idea, it's a proven limit on temperatures of systems, free and bound.

Maybe you misunderstood what I mean by theoretical.  Absolute zero is theoretical because no one has ever seen it, nor will they, so it's based on theory work, not on observation or experiment.  But it's on solid foundation, as we know exactly what it means in terms of measurable quantities (energy).

Phractality and Matthew's points are good ones.  The original definition of absolute zero was based on extrapolating from a thermometer.  Modern understanding of it is based on the idea of energy in a system.
« Last Edit: 28/07/2011 18:58:36 by JP »
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #11 on: 28/07/2011 18:54:57 »
It's funny you ask what you did though, because I think

ε = (hv/ehv/kT-1) + hv/2

Is an ugly equation anyway, and does not really explain why ε is small, or even should contribute hv/2 (the existing energy). This is why the limit

E = ∫ (Th/Tc - 1) C dT

Is much more appropriate, because it is devised under the impression that it is

E = W = ∫ (Th/Tc - 1) C dT

meaning it is the ''work'' of the system. The work required to reach the limit is unattainable. It would require more energy than in the observable universe!
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #12 on: 28/07/2011 18:56:05 »
It's a theoretical idea.

Temperature is defined as the average kinetic energy of particles making up matter.  Kinetic energy is energy of motion, so it's a measurement of the average motion of a lot of particles.  It makes sense that the lowest possible temperature is when that motion stops.  This was the original idea of absolute zero.

More recently, scientists have learned that small particles can never stop moving because of the rules of quantum mechanics.  Absolute zero can still defined as the temperature where they're moving the least amount possible.

It was first proposed by Einstein, it has a value of 1/2 \hbar ω. It not a theoretical idea, it's a proven limit on temperatures of systems, free and bound.

Maybe you misunderstood what I mean by theoretical.  Absolute zero is theoretical because no one has ever seen it, nor will they, so it's based on theory work, not on observation or experiment.  But it's on solid foundation, as we know exactly what it means in terms of measurable quantities (energy).

Oh right, well... Let zero point energy equal any definition that makes sense in this case. It is still an experimental fact of a temperature we cannot reach rather than a postulation, it is an axiom.
 

Offline imatfaal

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How was Absolute Zero discovered?
« Reply #13 on: 28/07/2011 23:53:09 »
Mr Data - your use of terms is confusing me and I would hazard a guess others as well. 
1. You say firmly that this is not a postulate - but it is an axiom.  In my dictionary they are the same thing - they are the unproven basis of the logical progression from which the argument moves forward.
2. An experimental fact that we cannot do something? 
3. Please spell out the variables/constants you are using - I know it is a pain but it really helps understanding
4. you say epsilon is a very small number -  which I agree is how it is normally used in this area as a dimensionless increment.  However in your equation it clearly must have the same units as energy through dimensional analysis.  And what is omega etc?  BTW we do have greek letters available (click preview to get full editor) and the nu is nice and distinct
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #14 on: 29/07/2011 01:41:51 »
Don't hazard a guess for anyone else, unless they speak up. If anyone says to me that the zero-point energy is attainable, I would almost certainly disagree with the lack of experimental evidence. No matter how cold we set our instruments to, one will see that T=0 is very unrealistic. Can you proove this wrong? If you can, I will take back what I said, until then I hope you can appreciate that whatever is confusing you on this, will not naturally imply anyone else.
 

Offline imatfaal

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How was Absolute Zero discovered?
« Reply #15 on: 29/07/2011 11:22:53 »
Mr D - experiments failing to reach absolute zero do not show that it is unreachable - merely that we havent reached it yet - it is theory that determines that abs zero is unattainable. 

If anyone says to me that the zero-point energy is attainable, I would almost certainly disagree with the lack of experimental evidence.

You are using zero-point energy and abs zero as interchangeable terms - they are not.  zero-point energy is the prime candidate for the casimir effect, which can be demonstrated in a lab - so there is experimental evidence.  Abs zero was and can still be seen as a classical limit - zpe is a non-classical quantum effect; whilst there are significant links they are not the same thing at all.

you never did explain any of your equations or why you felt they were relevant to the discussion.



 

Offline Bored chemist

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How was Absolute Zero discovered?
« Reply #16 on: 29/07/2011 14:46:03 »
I agree that Mr Data's use of symbols is confusing, but it's hardly the point.
He claims that absolute zero is based on some complicated equation drawn up in 1913 but there is documentation to show that it was known about earlier than that. In addition, the equation it framed in terms of the thermodynamic temperature. You can't define that unless you already know about absolute zero.
In short, Mr Data is wrong.
 

Offline JP

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« Reply #17 on: 29/07/2011 16:47:35 »
To sum it up:

1) In 1702, absolute zero was defined as the lower limit of a thermometer that worked by the expansion or contraction of a volume of air.

2) In 1848, Lord Kelvin came up with a definition from theory based on the motion of molecules (thermodynamics).  Absolute zero would be the point where all motion stopped.

3) In 1913, Einstein and Otto Stern came up with the idea that particle motion can't stop entirely due to quantum mechanics.  This changed the definition of absolute zero slightly to be the point at which the energy of motion of the particles is at a minimum.
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #18 on: 29/07/2011 23:29:06 »
I agree that Mr Data's use of symbols is confusing, but it's hardly the point.
He claims that absolute zero is based on some complicated equation drawn up in 1913 but there is documentation to show that it was known about earlier than that. In addition, the equation it framed in terms of the thermodynamic temperature. You can't define that unless you already know about absolute zero.
In short, Mr Data is wrong.

That will be because I've never heard of the other sources.
 

Offline Bored chemist

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How was Absolute Zero discovered?
« Reply #19 on: 30/07/2011 15:33:50 »
Then "Don't hazard a guess ".
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #20 on: 30/07/2011 17:57:08 »
I was perfectly right in what I said though. Zero Point energy is not a theoretical idea. It's a scientific principle. You cannot reach zero momentum; that would directly violate the UP.
 

Offline Bored chemist

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« Reply #21 on: 30/07/2011 22:10:56 »
You were "perfectly right" in that you said "It was proposed in 1913", but it was documented nearly half a century earlier and follows from work done in the 1780s.
http://en.wikipedia.org/wiki/Charles's_law

and also from even earlier work going back at least to the work in 1702 by Amontons.

I agree that you can't reach absolute zero.
Nernst pointed that out.
http://en.wikipedia.org/wiki/Third_law_of_thermodynamics
Interestingly, he did so just before 1913.

Zero point energies do exist and, for some systems they are a requirement of the UP.
However, while that's true for a vibrating molecule, it's not true for a lot of particles.
If they are stationary then the uncertainty of the momentum is zero, but, provided that you don't know where they are (ie the uncertainty of the position is infinite), that's not a violation. It applies to the much loved "particle in a box" but not to a free particle.

(if the vibrating molecule stopped vibrating the position of one atom WRT the others would be fixed, and so would its momentum. That's forbidden.)


« Last Edit: 30/07/2011 22:15:49 by Bored chemist »
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #22 on: 31/07/2011 01:21:22 »
Stop, stop stop!

Who said zero-point energies where a fundamental principle? Anything which imposes zero momentum implies an exact spacial coordinate... This is ALWAYS forbidden... who you reading from, englighten me please.
 

Offline Mr. Data

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How was Absolute Zero discovered?
« Reply #23 on: 31/07/2011 01:30:57 »
The concept and workable mechanism behind the experimental evidence behind the zero-point field should be no more complicated than excepting that spacetime, and every planck unit which occupies it, is constantly fuelled with a smallest unit of energy. This energy will at it's lowest energy refer to the kinetic energy of a vibrating energy 1/2 hbar \omega. You cannot have a unit of spacetime reach T=0 as much as you cannot accelerate it to c. Notice that the lowest speed possible will not equal v=0, as much as it's maximum speed will never reach c... everything is always in motion.
 

Offline Bored chemist

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How was Absolute Zero discovered?
« Reply #24 on: 31/07/2011 11:02:48 »
"who you reading from, englighten me please."
My old University notes; probably Atkins or Richards. Anyway, whoever it was I think they had the advantage over you of not saying both
"Zero Point energy is not a theoretical idea. "
implying that it's real and
"This also means the zero point energy does not actually exist! "
saying that it's not.
Perhaps, when you have made up your mind,...
 

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How was Absolute Zero discovered?
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