Kelvin Temperature Scale

[FrankM]

The kelvin temperature scale is based upon the heat magnitude of water at its triple-point. Heat is an infrared (IR) electromagnetic (EM) emission that has a specific frequency range. What is the IR frequency at the triple-point of water?

 

Do kelvin measurement instruments measure heat magnitude at the same frequency of the triple-point IR emission across the whole kelvin scale?

[CraigD]

The kelvin temperature scale is based upon the heat magnitude of water at its triple-point. Heat is an infrared (IR) electromagnetic (EM) emission that has a specific frequency range. What is the IR frequency at the triple-point of water?

There are some complications involved in answering this question, because bodies don’t emit a single frequency of EM radiation, but a spectrum of different frequencies that depends in a complicated way on the temperature and composition of the bodies. However, treating a body at the triple-point temperature of water (273.16 K) as an ideal black body, we can easily calculate (or just look up the results of the calculation of) its peak emission wavelength (the wavelength that carries the most power). It’s 10,608.3 nm (1.06083 x 10^-5 m), which is in the long infrared range. (sources: wikipedia articles “temperature” and “electromagnetic radiation”)

 

Do kelvin measurement instruments measure heat magnitude at the same frequency of the triple-point IR emission across the whole kelvin scale?

I don’t understand this question well. Given my previous answer, does this question still make sense to you, Frank?

[FrankM]

Craig, my two questions were directed at the same material, water.

 

It makes no sense to me at all to treat the IR emission at the triple-point of water as an ideal black body if it is not known if the EM spectrum emitted truly represents the spectral characteristics of an ideal black body. Since the specific spectral characteristics at the triple-point of water is the basis for the kelvin scale, it seems reasonable to expect that a measurement instrument that displays a kelvin temperature should be measuring that same spectral characteristic of water at different magnitudes. Do kelvin measurement instruments do this?

 

I would expect, to be consistent, the kelvin measurement instrument would be filtered to detect only those IR emissions that match the spectral characteristics at the triple-point, otherwise the spectral signature would be different.

 

It has to be realized that the establishment of absolute zero and the creation of the kelvin scale, 1848, was done before the scientists of that era knew about the propagation of electromagnetic (EM) waves, nor anything about where heat fit into the EM spectrum. I do not know when it was determined that the EM emission signature from a black body shifted the peak power point to a shorter wavelength with increasing temperature or the materials used to obtain these EM signatures. Kelvin would have been unaware of the black body spectral shift. Would Kelvin have come to the same conclusions had he known about the black body spectral shift with increasing temperature?

 

The term heat is based upon a human sensual determination. The heat we feel is the result of some type of energy transfer structure (ETR) that produces EM emissions in a range humans can detect, that is, within what we define as the IR range. Are all humans equally sensitive to heat across the IR spectral range? It seems illogical to develop a measurement scale, to be used to measure the temperature of any material, that is based upon the spectral characteristics of a one particular material at its triple-point.

 

If the IR signature at the triple-point of water is unique to water only, how can a kelvin measurement instrument reading be valid for a material other than water, which brings us to your statement below.

 

There are some complications involved in answering this question, because bodies don’t emit a single frequency of EM radiation, but a spectrum of different frequencies that depends in a complicated way on the temperature and composition of the bodies.

Since we know that heat is an IR emission, with a specific spectral range, why is the kelvin an SI orphan with no link to any of the other SI base units? The kelvin is allegedly defining an individual increment, a magnitude, of energy. One would think that the kelvin should be linked to the SI derived unit, the Joule (Energy, Work, Quantity of Heat). Or should it be just the opposite, the Joule defined as a base unit of energy, and the kelvin a derived unit? We know that SI does not provide for a base unit the defines a base unit of energy.

 

SI Base Units

SI Diagram

 

Aren't all EM emissions a type of energy? How are the SI folks at the BIPM going to fix their base unit definitions?

 

New SI Definitions

 

The kelvin will remain an SI orphan, and the BIPM has excised from their website the recommendations of the Consultative Committee on Units 2005 report, "the consensus that now exists on the desirability of finding ways of defining all of the base units of the SI in terms of fundamental physical constants so that they are universal, permanent and invariant in time." I had saved the report and its original URL, and will attach the report to a subsequent post if someone wants to read it.

[CraigD]

Craig, my two questions were directed at the same material, water.

 

It makes no sense to me at all to treat the IR emission at the triple-point of water as an ideal black body if it is not known if the EM spectrum emitted truly represents the spectral characteristics of an ideal black body.

The electromagnetic emissions of fairly pure water in solid, liquid, or gas state (AKA phase) is certainly NOT close to black body, because water is not nearly opaque.

 

It’s difficult to measure the characteristics of water at its triple point temperature (0.01 C, 273.16 K) because at that temperature and common surface-of-the-Earth conditions, water of different purities and gas pressure may be in a solid, liquid, or gas state. Under standard atmospheric temperature, it will usually be liquid, though phase transition complications can result in it being solid (ice). State affects the emission spectra of materials fairly dramatically.

 

Water ice and liquid are partially transparent and reflective, so measuring their emission spectrum is complicated, because it is easily “drown out” by that of other radiation sources transmitted or reflected by them. To do it, you’d have to put an ice sample and a spectrometer in a vacuum in a container with walls cooled to as near 0 K as possible. I’ve never personally done, or read about, such an experiment, but wouldn’t be surprised if one wasn’t described in the literature, as it might give valuable data about the characteristics of water, which is a subject of much research.

 

Since the specific spectral characteristics at the triple-point of water is the basis for the kelvin scale ...

This statement isn’t completely accurate.

 

The basis for the Kelvin scale is two part:

• the Celsius (AKA centigrade) scale, which defines the difference between the freezing/melting (solid-liquid phase transition) temperature and boiling temperature (liquid-gas transition) of pure water at 1 atmosphere pressure as 100 units,
  
• and the empirical behavior of gases described by the gas laws.
  

From the latter, it’s possible to directly relate the temperature to the average kinetic energy of a material. From the former, a standard unit size, already well-known at the time of its publication (Celsius wrote about the C scale in 1742, Kelvin about the K scale in 1848, though the concept was fairly well-known in for a decade or so before then), was borrowed.

 

It’s noteworthy that Kelvin’s 1848 measurement and calculation of 0 K = -273 C was very close to the present day value of 0 K = -273.15

 

The definition of the C and K temperature scales in terms of absolute zero and the triple point of water is a more modern (1954) redefinition, intended to be more precise, as the high-pressure phase transition temperatures used in the 1700 and 1800s are too “noisy” for very precise measurements.

 

The key feature of the K, or any zero-at-absolute-zero temperature scale, however, is independent of its attendant conventions and history: it permits a simple conversion between average kinetic energy of the particles [imath]E[/imath] in a material and the temperature [imath]T[/imath] of the material, of the form [imath]E = k T[/imath], where [imath]k[/imath] is a Boltzmann’s constant, in SI units, about 1.3806488 x 10^-23 J/K.

 

... it seems reasonable to expect that a measurement instrument that displays a kelvin temperature should be measuring that same spectral characteristic of water at different magnitudes. Do kelvin measurement instruments do this?

What units a given instrument displays and how it works are independent. For example, consider a ordinary mercury-in-glass thermometer. I can make it display a temperature reading in Fahrenheit, Celsius, Kelvin, or any other units I want, simply by changing the paper scale I affix to it

 

The kind of thermometer you’re describing, Frank, is know as “radiometric”. Because such thermometers produce complicated data – spectra – which must be combined with various assumptions – such as that the emitting body is nearly a black body – they’re useful mostly for measuring the temperature of bodies that are too far away or otherwise difficult or impossible to measure the temperature of in the more reliable way of just sticking a more common thermometer, such as a bimetal or thermistor (electronic) –based one – in them, such as stars and distant moons and planets.

 

No matter what or how measured, it’s conventional to state temperatures in K. However, this is just a convention, valuable only in that everyone uses the same convention, and common temperatures are easy to remember and use in common measurements and calculations.

 

I would expect, to be consistent, the kelvin measurement instrument would be filtered to detect only those IR emissions that match the spectral characteristics at the triple-point, otherwise the spectral signature would be different.

I hope my explanations above show that there’s the term “kelvin measurement instrument” isn’t very useful, that spectra are not the first choice for measuring temperatures when other alternatives are available, and that water and other materials at 273.16 K and 611.73 Pa (the triple point of water) don’t have especially significant emission spectra around which an engineer might build a very useful instrument.

 

Since we know that heat is an IR emission, with a specific spectral range ...

This is untrue in an important way.

 

A critical concept here is that heat – the average kinetic energy of a material – is not directly related to EM radiation of a specific collection of frequencies (or inversely, wavelenghs). Any body, real or abstract, that consists of more than one part (or is associated with other bodies) has a temperature, and can be said to contain heat (though possible zero). 2 bodies with the same temperature, however, don’t necessarily emit the same distribution of photons of various frequencies – that is, have the same spectra.

 

More importantly, even for 2 bodies of similar size and composition, both of which are nearly ideal black bodies, but of different temperatures, the cooler body emits many photons of greater frequency than many emitted by the hotter body. The average frequency, of the photons from the hotter body collected over a long enough time are of greater frequency than of those from the cooler body, but photons from neither body are confined to a particular band of the EM spectrum. Most are in a band around the body’s peak emittance frequency, which is higher for the hot body, but other than the upper limit imposed by possible quantum mechanical mechanisms that can produce the photons (ie: no know naturally occurring mechanism can produce photons with frequencies greater than 10²⁴ hz), the frequency distribution for both bodies is spread out over the entire EM spectrum

 

In short, bodies or compositions and temperatures that we intuitively consider “warm”, such as people, have their EM emission peaks in the infrared range. Cold stuff has its peak in the sub-infrared and below. Hot stuff, such as the Sun and heated tungsten fillaments, peaks in the visible range – we commonly say they glows – while really hot stuff peaks in the ultraviolet and above (eg: neutron stars and really hot tungsten filaments, which emit lots in the X-ray spectrum). But a cup of coffee emits some UV photons, while a neutron star emits some infrared – neither is confined to a specific range.

 

It has to be realized that the establishment of absolute zero and the creation of the kelvin scale, 1848, was done before the scientists of that era knew about the propagation of electromagnetic (EM) waves, nor anything about where heat fit into the EM spectrum.

 

Kelvin and his contemporaries were familiar with the idea of the wave nature of light, which Newton wrote about and was widely read ca. 1775, and knew that hot things glowed in shorter wavelengths of visible light, cooler things in longer. That EM radiation extended beyond the range of wavelengths visible to the human eye was known by about 1800, and that it was related to electricity and magnetism (and thus “electromagnetic”) by about 1845. Kelvin and his fellows were well educated and informed, so I expect knew about this, too.

 

I think you’re a bit off in your understanding of science history here, Frank.

 

I do not know when it was determined that the EM emission signature from a black body shifted the peak power point to a shorter wavelength with increasing temperature or the materials used to obtain these EM signatures. Kelvin would have been unaware of the black body spectral shift.

Would Kelvin have come to the same conclusions had he known about the black body spectral shift with increasing temperature?

I’m only a dabbler in biographical science history, but given that Kelvin live until 1907 (age 82), and was lecturing ‘til at least 1900, I imagine he was aware of early research into black body radiation, which commenced around 1860, and the 1890s work of Wien and later Plank, which by 1900 produced essentially the same laws that we use now. All that work build on Kelvin’s earlier work in a non-contradictory way, and resulted in no great public revisions from Kelvin, so I think it’s safe to say he would have reached the same conclusion if he’d know about black body radiation 30-40 years earlier than he likely did.

 

 

The term heat is based upon a human sensual determination.

Since the late 1700s, when Rumford’s work essentially retired a previous popular theory of heat, caloric theory, the equivalence of heat and mechanical work (energy) has been accepted science. Kelvin and later scientists didn’t invent this new paradigm, only refined it. So I don’t believe the claim “the term head is based upon a human sensual determination” has been accurate for at least 300 years.

 

How are the SI folks at the BIPM going to fix their base unit definitions?

I don’t believe any standard unit definitions involving heat or energy need fixing. The equivalence between them is well understood each has a scientific context in which it’s useful. Fundamentally, heat is average energy, so is arguably redundant and unneeded, but like many scientific concepts that can be explained in terms of more fundamental ones, temperature remains so useful I doubt it will ever disappear.

 

Sources: wikipedia articles Thermometer, Isaac Newton, Electromagnetic spectrum, Black-body radiation, Planck's_law, Caloric theory

Edited April 29, 2013 by CraigD
Fixed link-breaking spelling error

[FrankM]

Ignoring the issue that the triple-point of water does not represent an ideal black body, all the kelvin scale represents is how much any material's temperature is relative to the idealized zero level on the scale. The numeric values on the scale do not represent a fundamental basic unit of measure, it is an artificial scale based upon the triple-point of a particular molecular material, water. Basically, Kelvin selected a material where they could, at that time, determine the triple-point. Is a fundamental physical law being demonstrated by the triple point of water? If all materials, molecules and elements, had the same triple-point, one might conclude a physical law is being revealed.

 

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

 

Additionally, the triple-point of all materials presented in the above URL is relative to an average atmospheric pressure, which is an earth-centric value.

 

In 1848, how much did Kelvin know about the electromagnetic nature of heat?

 

Wiki Electromagnetic_radiation - In 1862-4 James Clerk Maxwell developed equations for the electromagnetic field which suggested that waves in the field would travel with a speed that was very close to the known speed of light. Maxwell therefore suggested that visible light (as well as invisible infrared and ultraviolet rays by inference) all consisted of propagating disturbances (or radiation) in the electromagnetic field.

Kelvin was making conclusions and developing a temperature scale based upon what he knew in 1848. Keep in mind scientists can be stubborn and refuse to acknowledge something that becomes generally accepted. Linus Pauling refused to recognize the existence of quasi-crystals to the day he died.

 

Kelvin knew nothing about the energy states of atoms.

 

Absolute Zero not Absolute

 

Sciencemag - Absolute temperature is usually bound to be positive. Under special conditions, however, negative temperatures—in which high-energy states are more occupied than low-energy states—are also possible. Such states have been demonstrated in localized systems with finite, discrete spectra. Here, we prepared a negative temperature state for motional degrees of freedom. By tailoring the Bose-Hubbard Hamiltonian, we created an attractively interacting ensemble of ultracold bosons at negative temperature that is stable against collapse for arbitrary atom numbers. The quasimomentum distribution develops sharp peaks at the upper band edge, revealing thermal equilibrium and bosonic coherence over several lattice sites. Negative temperatures imply negative pressures and open up new parameter regimes for cold atoms, enabling fundamentally new many-body states.

It is no wonder that the SI basic unit, temperature, is an orphan, it has no connection to any fundamental physical law.

[CraigD]

... all the kelvin scale represents is how much any material's temperature is relative to the idealized zero level on the scale.

Correct. The Kelvin scale represents thermodynamic (AKA absolute) temperature. Because absolute temperature is essential in gas laws and radiation laws (such as Plank’s law), the K scale is useful in calculations involving them.

 

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

 

Additionally, the triple-point of all materials presented in the above URL is relative to an average atmospheric pressure, which is an earth-centric value.

This is incorrect, Frank. You appear to have misread the wikipedia article you cite, which states:

The single combination of pressure and temperature at which liquid water, solid ice, and water vapour can coexist in a stable equilibrium occurs at exactly 273.16 K (0.01 °C) and a partial vapour pressure of 611.73 pascals (ca. 6.1173 millibars, 0.0060373 atm).

Standard atmospheric pressure is 101325 pascals (1013.25 millibars, 1 atm), about 166 times the pressure of the gas-liquid-solid triple point of water.

 

The triple points of water, or of any other substance, are not dependent on what, if any planet, they are measured. They aren’t Earth-centric.

 

In 1848, how much did Kelvin know about the electromagnetic nature of heat?

An important point I was trying to make in my previous post is that there is no “electromagnetic nature of heat”. The heat of a substance is its average kinetic energy. Kinetic can be transmitted by EM radiation. However, the two concepts are not innately linked. Heat and EM radiation are not the same thing, nor is one necessarily the cause of the other. EM adiation can result from and cause heat in bodies, but is not the only phenomenon that can do so, and is not the same thing as heat.

 

It is no wonder that the SI basic unit, temperature, is an orphan, it has no connection to any fundamental physical law.

It’s not true that the SI unit Kelvin is an orphan, in the sense of having no connection to other SI units, or fundamental physical constants. It is connected to the SI unit Joule by Boltzmann’s constant. 1 J = 1 kg m²/s². The meter and second are defined in terms of 2 fundamental physical constants, the transition between the two hyperfine levels of the ground state of caesium-133 and the speed of light.

 

Only the kilogram is still defined by the SI by an artifact (a physical piece of platinum-iridium alloy stored in a vault in the outskirts of Paris. Work has been underway for a long time (oficially, since 2005, but informally for much longer) to replace this definition with one based on fundamental physical constants. This may happen officially as early as the 25th CGPM, in 2014.

 

The definition I give above for the K is likewise unofficial in the SI, which still officially uses the “1/273.16 of the thermodynamic temperature of the triple point of water” definition. A proposal to officially define it as I have is also currently under consideration by the CGPM.

 

So all the units in the SI are semi-officially based on fundamental physical constant, and likely to be officially based on them in the near future.

 

The wikipedia article Proposed redefinition of SI base units has more details and links on this subject.

[FrankM]

Correct. The Kelvin scale represents thermodynamic (AKA absolute) temperature. Because absolute temperature is essential in gas laws and radiation laws (such as Plank’s law), the K scale is useful in calculations involving them.

That does not mean K is based upon a fundamental physical constant.

 

The triple points of water, or of any other substance, are not dependent on what, if any planet, they are measured. They aren’t Earth-centric.

If each of the triple-point pressure measurement values noted in the wiki article are not related to a specific reference they are meaningless.

 

An important point I was trying to make in my previous post is that there is no “electromagnetic nature of heat”. The heat of a substance is its average kinetic energy. Kinetic can be transmitted by EM radiation. However, the two concepts are not innately linked. Heat and EM radiation are not the same thing, nor is one necessarily the cause of the other. EM adiation can result from and cause heat in bodies, but is not the only phenomenon that can do so, and is not the same thing as heat.

Please identify where you obtained the definition for kinetic energy, "The heat of a substance is its average kinetic energy".

 

It’s not true that the SI unit Kelvin is an orphan, in the sense of having no connection to other SI units, or fundamental physical constants. It is connected to the SI unit Joule by Boltzmann’s constant. 1 J = 1 kg m²/s². The meter and second are defined in terms of 2 fundamental physical constants, the transition between the two hyperfine levels of the ground state of caesium-133 and the speed of light.

SI base units are used to define SI derived units. Boltzman's constant is not a derived SI unit. What you are stating is that the kelvin definition as a base unit is justified because it has an association to a derived SI unit that can be linked to a non-derived unit.

 

However, the folks at BIPM actually deliberately define a base unit in terms of an SI derived unit and another base unit. The ampere is defined in terms of the meter and the newton. See URL below:

 

ampere definition

 

The folks at BIPM didn't stop there, they derive two basic units in terms of each other, the meter and the second.

METAS - The metre definition assigns a fixed value to the speed of light c. This fundamental constant can therefore no longer be measured; it has been fixed by definition. From this can be concluded that the unit of length is dependent on the unit of time, the second.

Meter Definition

 

To be correct, the NIST SIDiagram should have a solid blue line from the meter to the second and a solid purple line from the second to the meter, and a solid blue line from the meter to the ampere and a dashed green line from the newton to the ampere.

SIDiagram

[FrankM]

I had stated in the #3 entry to this thread that the BIPM had excised from their website the recommendations of the Consultative Committee on Units 2005 report, which was a stand-alone report. I found the recommendations in a different report, below, on page 16. "the consensus that now exists on the desirability of finding ways of defining all of the base units of the SI in terms of fundamental physical constants so that they are universal, permanent and invariant in time;"

 

Consultative Committee for Units (CCU) Report of the 17th meeting

 

Section 5 of the above report deals with a redefinition of the Kelvin.

 

However, SI units are being readjusted because of the new methods of measuring the Planck constant.

 

History and progress on accurate measurements of the Planck constant