Talk:Scale of temperature

0-th law

The concept of a "quotient set" beyond two systems being in thermal equilibrium is tautological, in more scientific terms, redundant. Thus any failure by E. Fermi to mention the 'zeroth law' in his book really does not amount to a deficiency. To be more precise, in thermal terms, systems in thermal equilibrium are thermally indistinguishable, it is only when the distribution of energy is disturbed that they become (thermally) distinguishable. This is reinforced by the fact that the manner in which the disturbance takes place is crucial to the future state of what will become two (or more) systems not in equilibrium. To explain, should the original equilibrium be disturbed by work then there will be consequent changes, perhaps of volume; if the change is caused by friction then temperature will change; radiation will also produce characteristic changes. Much the same can be said about how the various systems came into equilibrium in the first place.

This whole article is misconceived. Reading here [of temperature#Empirical scales] it says "Empirical scales are scales based on thermal properties of a particular substance." which is completely untrue. The essential characteristic of the measure "temperature", be it Kelvins, Celsius, Fahrenheit or any other scale, is that it is completely independent of the "thermal properties of a particular substance". --Damorbel (talk) 07:49, 28 October 2010 (UTC)

I completely don't understand what the whole paragraph starting with "The concept of a "quotient set" beyond..." means. As for the empirical scales, I have stated clearly in the article that only the old Celsius and Fahrenheit and contemporary ITS-90 are empirical scales; Modern definition of Celsius and Fahrenheit are based solely on the concept of thermodynamic temperature.--Netheril96 (talk) 09:14, 28 October 2010 (UTC)

Besides, I suggest all of you to read the references in section Formal description, for they will expound the opinion better than me. I guess your knowledge is mainly from coursebooks; as one of my physics teacher, an American from U.C. Berkely, said, American coursebooks focuses more on physical intuition than the rigorous logic underlying, though his original meaning was praise rather than criticism. I believe that also accounts for why I hadn't found content like equivalence of Kelvin and Clausius statements of second law or the well-definition of thermodynamic entropy in Wikipedia before I made my edits.--Netheril96 (talk) 10:17, 28 October 2010 (UTC)

I have come to better understand and partially agree with Netheril96's concept of temperature scale, having found references to "empirical scales" in the literature. An empirical scale is one which IS based on the thermal properties of a physical substance. For example, a mercury scale is one in which you take a tube of mercury, dip it in freezing water, make a mark, dip it in boiling water, make a mark, divide the mark into 100 equal distances. The readings bear a one-to-one relationship with thermodynamic temperature, but are not equal to it nor are they linearly related. For this reason it is not a very useful or helpful scale. I prefer to think of them as inaccurate attempts to measure thermodynamic temperature.

Thermodynamic temperature is a pure concept to within a scale factor. The second law defines thermodynamic temperature only to within a scale factor. The scale factor must be defined experimentally. The minute you define that scale factor, your temperature scale becomes dependent on the behavior of a physical substance. The Kelvin scale is dependent upon the behavior of water at the triple point, and upon our ability to measure its behavior at that point. I know Netheril96 does not like this analogy, but a straight line is a pure concept, distance on the line is a pure concept. But once you decide to measure distance in feet, or meters, you must depend on the behavior of a physical object or phenomenon, and your ability to measure that object or phenomenon. A meter used to be the distance between two scratches on a platinum bar in Paris. Now its so many wavelenths of some spectral line of Krypton, or something like that. All of which are not perfectly defined and cannot be measured without some experimental error. The same is true of the temperature of the triple point of water. It is not perfectly defined and cannot be measured without some experimental error.

In that sense, all temperature scales are dependent on the behavior of the thermal properties of a physical substance, even though the concept of thermodynamic temperature is not. All distance scales are dependent upon the physical properties of some object or phenomenon, even though the concept of distance is not. PAR (talk) 12:24, 28 October 2010 (UTC)

PAR you have to distinguish between a scale and the calibration of a thermometer in Celsius or Fahrenheit or Kelvins etc. These are scales and thermometers are calibrated calibrated according to, let us say mm per ^oF, mm per^oC or mm per K; or in the case of thermocouples, perhaps mV per ^oF, mV per^oC or mV per K, this is how temperature measurement becomes dependent on "the behavior of the thermal properties of a physical substance"

The triple point represents a convenient temperature which has different numbers assigned to it in the various scales but the actual temperature is the same whatever scale you are using, ^oF ^oC or K. The triple point is convenient because the temperature remains constant (to within acceptable limits) during unavoidable fluctuations in the total energy of the ice/water/vapour system, the energy fluctuations being absorbed by phase changes (vapour/water and water/ice) which take place with little or no apparent change in temperature, you could say the temperature of the triple point is buffered by the phase changes at the triple point. --Damorbel (talk) 20:27, 28 October 2010 (UTC)

Yes, the triple point is quite stable, which is why it was chosen over the freezing point which used to be stable to within acceptable limits. But new technology made those limits unacceptable. In the future, new technology will make the triple point unacceptable.

I do not distinguish between a scale and the calibration of a thermometer in e.g. Celsius. You cannot define a practical scale which does not imply a calibration procedure, by definition. That calibration procedure will always involve a physical substance or phenomenon, which means instability and experimental error. Always. PAR (talk) 00:11, 29 October 2010 (UTC)

I got lost. In what way do you want this article to be modified? You want to overhaul the definition of temperature scales, or just want to add a sentence saying that the practical purpose of empirical scales is to simulate thermodynamic scale?--Netheril96 (talk) 01:26, 30 October 2010 (UTC)

I was objecting to the idea that the zeroth law defines temperature and/or a temperature scale. It only accomplishes part of the job. The second law is needed to define thermodynamic temperature or any other temperature scale. If I have a thing with a dial on it, that does not make it a thermometer. If I have a thing with a dial on it that reads the same for any two objects in thermal equilibrium, (i.e. obeys the zeroth law), I still do not have a thermometer. Only with the second law, can I prove that my thing with a dial on it is a thermometer. PAR (talk) 02:18, 30 October 2010 (UTC)

Then our opinions are irreconcilable. I'm getting busy now and seeing no end of our dispute, and we're in fact contravening Wikipedia's policy since Wiki is not a place for what we think but what reliable sources say. So go find sources backing you up and append your definition of temperature and temperature scales with references to those sources, per WP:Neutrality. Or find substantial evidence that my references are holding just minority opinions so as to rule mine out.--Netheril96 (talk) 10:00, 30 October 2010 (UTC)

If we disagree on what is true or false, our opinions are not irreconcilable. One of us is simply wrong. But I think we have a semantic disagreement. You say the second law contribution to the definition of temperature is not fundamental to its definition, I say it is. We both agree that the second law is used to help specify a real number which is called thermodynamic temperature. Our definition of "fundamental" is irreconcilable, perhaps. At any rate, there is an article I am trying to understand called "An Axiomatic Approach to Classical Thermodynamics", Boyling, J.B. PRoc. R. Soc. Lond. A 1972 329,35-70 (Availiable HERE).

On page 45 it states:

The zeroth law as it stands is not strong enough to guarantee the existence of an empirical temperature scale, i.e. of a (1-1) correspondence between isothermals and real numbers. It has to be supplemented by auxiliary assumptions involving a special kind of simple system called a "thermometer".

I will look for others. In the thermodynamic temperature article and the Fermi book, there is a derivation of the definition of temperature which makes no reference to the zeroth law. Until I understand clearly why this is so, I mean, where the zeroth law implicitly enters into that definition, I hesitate to edit any definition of temperature. PAR (talk) 11:54, 30 October 2010 (UTC)

I skimmed your reference and don't quite catch the logic of "The zeroth law as it stands is not strong enough to guarantee the existence of an empirical temperature scale" as the illustration below that statement involves the concept of manifolds, which is beyond my current knowledge of mathematics. And it seems to me not to have mentioned the role of second law.

Besides, I disagree on "If we disagree on what is true or false, our opinions are not irreconcilable". If that is true, what is the point of maintaining neutrality on Wikipedia by addressing different views appropriately? What we are arguing about may be deemed as the axioms of thermodynamics, which is hardly able to be resolved by logic and reasoning since we don't have a common axiom system to base our reasoning on.--Netheril96 (talk) 10:18, 31 October 2010 (UTC) --Netheril96 (talk) 10:18, 31 October 2010 (UTC)

I think of neutrality as applying to politics/religion articles and semantic arguments. I see no "truth" in politics or religion, only agendas and points of view. Semantic arguments revolve around the use of language to describe a subject, not the subject itself. I thought we had a semantic disagreement.

Boyle's statement about the zeroth law is simply realizing that although the zeroth law can define an equivalence class of systems in equilibrium, it cannot be used to order those classes, to decide which system is hotter or colder. I think we agree on this, its just obvious. We disagree on whether this set of equivalence classes may be called a temperature scale, and that is a semantic argument. By my way of thinking, temperature is not fully defined until you can use it to decide which system is hotter, which is colder. As I understand it, you do not. So now we go to the literature to justify our use of the language.

There are a number of ways to provide the ordering, I think. Fermi says the second law and reversible engines, Boyle introduces the concept of a thermometer and "empirical temperature scales" to give the ordering, without the second law. Check out [1] as a possible support to your point of view. He calls the unordered function an "empirical temperature". But he then goes on to use Pfaffian equations (rather than the second law) to provide ordering. This is also Caratheodory's approach, I think. So here are three ways to provide the order that the zeroth law does not give. PAR (talk) 16:12, 31 October 2010 (UTC)

Most time neutrality is not a problem in sci-tech articles because ratiocination will always yield same conclusion with same presumptions, if logic is correct. But here our discrepancy is the presumptions ,i.e., what constitutes temperature. Basically I think, as many sources do, that ordering is some structure constructed upon temperature rather than what makes temperature temperature. This is insoluble by reasoning.--Netheril96 (talk) 14:08, 2 November 2010 (UTC)

I fully agree with that - its a semantic disagreement, of little fundamental importance. Lets work on the fundamentals. PAR (talk) 20:11, 2 November 2010 (UTC)

There is no problem or lack of 'ordering' as put here. The 0-th law exists for one reason only, namely it was recognized that the 2nd law provides no logistical justification of temperature measurement, while the previously known definitions of thermal equilibrium do, when they formalize the representative coordinate spaces of thermodynamic system in diathermic contact, using measurable thermometric parameters as state coordinates. Thus the gas thermometer is clearly a device covered by the 0th law. If this didn't suffice, the 0th law would have never been raised to the status of a fundamental law. It's only utility is the definition of empirical temperature scales, and the justification why a thermometer may be used to measure temperature. The 0th law permits the construction of many scales in fact, with the common mapping through the isotherm in each. It does not however, define the thermodynamic temperature, this is indeed the achievement of the 2nd law, it selects a preferred, absolute scale, based on energy and entropy considerations. Kbrose (talk) 16:59, 2 November 2010 (UTC)

Additional Temperature Scales

There are additional temperature scales beyond those mentioned directly in the article. For example, plasma physicists typically measure temperature in electron-Volts (eV), with 1 eV=11604 K. Since an eV is a unit of energy (1 elementary charge times one volt), this is the same as multiplying T in Kelvin by Boltzmann's constant (in eV/K). Typical SI prefixes are used - keV and MeV come up in specific contexts. An eV is a typical temperature where thermal energies are enough to cause ionization. MeV temperatures see pair-production. See the NRL Plasma Formularyp. 15, 17, 40-41 for a formal reference. Should this be added to the article? Are there other specialized temperature scales?SMesser (talk) 19:13, 24 November 2011 (UTC)

The development of any scale to measure any phenomena is a skill that ought to be part of basic science education, if only to use different numeric bases such as representing the Kelvin Scale in Hexadecimal to enter the data directly into binary storage(??).

Take the proposal to amend how time is presented, although I suspect that there may be an element of academic satire here....[2]

Even the way that a scale is presented - with a digital display, rotary dial or vertical scalar needs some thought with changing cultures?[3]

I added some posts in the Wiki- Temperature:Talk page to illustrate this point, expanding on the fact that Fahrenheit (and other less known contemporaries) originally proposed that the scale would range from a cold European day 0F to body temperature 96F with freezing water at 1/3 scale 32F. The scale subdivided by prime numbers 2 and 3 - almost base 12 ??

They were eventually archived by the page editors.... here is the text of the last post if any readers/contributers are curious?

"...Very good of you to contemplate this concept and take the time to reply. Methinks you must have a medical background, since the criticisms focus largely on clinical applications. It would, could, be an ambiguous situation when some students might assume that something other than 100 deg, (exactly) would be abnormal. However for lay persons observing any significant deviation from (about) 100 deg would be cause for concern and they would then check with their doctor. They would not have to try to remember if normal temp is 96.8 or 98.6. Celsius increments are too large - you have to focus on 1/10 degree changes to detect a developing complication such as an infection. [BTW the mean typical core temperature, for this scale, would be 98 2/3 F = 100 deg EXACTLY - more a numeric necessity than a medical one.] You make a good point though, body temperature is the business of doctors and biologists - what if this changes? Then the scale serves as at least an historical reference. Then again, if you have ever travelled to higher altitudes, the coffee is cooler. Water does not boil at 100C everywhere. The scale is still relevant, in fact it now reflects the change in barometric pressure. However, boiling water cannot be used to calibrate a transducer or an instrument. With the proposed scale, the scientist only has to place the probe in melting snow for the zero point and under his tongue for the 100 deg point to calibrate the equipment approximately. Then there is the application for environmental applications, specifically comfort temperatures. 54 deg would equal 68 exactly (numeric requirement).[BTW 54 X 0=0]. However the physiology of human and animal comfort is a science in itself. Actually "comfort" is a misnomer except at resorts, HVAC is more a matter of worker productivity in factories and offices. Referencing body core temperature to skin surface temperature to air temperature is a significant concept. However heat transfer and humidity complicates the equation.... think wind chill factors and humidex. The conversion factor of 1.5 X F is accurate (exactly) for Change in Temperature, i,e, "delta T", not the scale temperatures. However your conversion algorithm is correct - flattered by the use of the "P" symbol... thanks! This exchange of criticisms displays the other feature of the scale...... that of an academic teaching device. Asking the students to propose their own scale, or other system to measure paremeters is clever exercise in itself for the serious science students. Thnks, Peter (aka) Pete318 (talk) 20:18, 6 January 2010 (UTC) ...."

enjoy... Pete318 (talk) 23:34, 14 February 2013 (UTC)

Unphysical mathematics

There's a lot of unphysical mathematics in this article, starting with "Thus all thermal systems may be divided into a quotient set by this equivalence relation, denoted below as M. Assume the set M has the cardinality of c, then one can construct an injective function ƒ: M → R , by which every thermal system will have a number associated with it such that when and only when two thermal systems have same such value, they will be in thermal equilibrium."

If we are to assume that M is uncountable, what compels this assumption that its cardinality is exactly c, as opposed to some other uncountable cardinal, for example the least uncountable cardinal? Is thermodynamics founded on the continuum hypothesis? News to me. This all seems like completely unsourced original research.

In sharp contrast the section near the end comparing the various temperature scales is spot on.

Does anyone have any objection to getting rid of the "mathematics made difficult" portions of this article? If not I'll try to trim it down to something better reflective of conventional thermodynamic thinking. Vaughan Pratt (talk) 04:04, 3 April 2015 (UTC)

I dunno, there are a lot of books that describe thermal equilibrium as an equivalence relation in just this way. I tend to agree that talking about the cardinality of the set is going off topic, but I don't think it is wrong. Assuming the cardinality to be c is merely limiting consideration to only those sets that are continuums. It is hard to see how a scale of temperature can be constructed from anything else. SpinningSpark 08:48, 3 April 2015 (UTC)

I wasn't complaining about equivalence relations, which are fine here. As can be seen from the far longer article on the zeroth law of thermodynamics, there is no need to tie the concepts to any particular number system such as the reals. It suffices to refer to systems, surfaces (in the context of ideal gases), etc.

As to whether there's anything else besides the reals that temperature scales could be constructed from, conversions between temperature scales (the subject of this article) are done exclusively with rational functions. Hence rational numbers suffice, no need for π or e as a temperature.

But I'm not proposing to bring rationals into this article either, since temperatures could perfectly well be an integer number of, say, millikelvins, with the Kelvin and Celsius scales limited to a precision of 0.005 K and the Fahrenheit and Rankine scales therefore limited to a precision of 0.009 °F or 9 millirankine in order to keep the system closed under all well-defined conversions listed in the article. That is, a temperature given on the Kelvin scale would be required to be an integer multiple of 5, e.g. 273150 mK as the melting point of ice, which on the Rankine scale would be an integer multiple of 9, namely 491670 millirankine. Or pico in place of milli throughout (nine more digits) if more precision is needed; in either case the system would be discrete, unlike the rationals which are dense, or the continuum which is complete. Vaughan Pratt (talk) 19:16, 3 April 2015 (UTC)