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Assessment of such topics as global warming requires a grasp of the thermodynamic meaning of temperature.
Introduction
A few years ago I had a conversation with a thermal sciences expert of international repute who has tended to view some of the current ideas on global warming with considerable reserve. He made the point that we hear a great deal about changes in the temperature of the earth over a period of centuries or even millennia, yet temperature itself was not defined in thermodynamic terms until the mid 19th Century. He is undoubtedly correct in saying that. This article is not concerned with global warming but with temperature per se and the statement quoted is by way of introduction to the topic of temperature as a thermodynamic quantity.
The earliest thermometric devices and temperature scales
One can only measure temperature indirectly as its effect on an observable characteristic of a substance. For example, in a simple mercury-in-glass thermometer it is the volume of the mercury which is the property which is correlated with temperature. No user of the mercury-in-glass thermometer is interested in the temperature of the mercury. It is intended that the temperature of the mercury will be representative of that of the air in which the thermometer is standing.
This relates to thermal equilibrium between the thermometer and the air and a full understanding of this actually belongs to a later stage in the development of thermodynamics.
In circa 1600, Galileo constructed a device in which rise and fall of a column of water in response to temperature changes could be observed. It lacked any sort of calibration and is sometimes referred to as a thermoscope rather than a thermometer 1. Gabriel Fahrenheit constructed the first reliable liquid-in-glass thermometers, initially with alcohol as the liquid and then with mercury. He reported his findings in Philosophical Transactions of the Royal Society in 1724.
There were two sides to them: the thermometer itself and the temperature scale bearing Fahrenheit’s name which resulted from its initial usage. He anticipated much later work in thermodynamics by observing that the boiling point of water depends on the pressure. An understanding of this had to wait until Gibbs’ publication of the phase rule in the 1870s.
Fahrenheit observed that salt water has a lower freezing point than pure water and that whereas the value for the latter was reproducible that for the former depended on the amount of salt present. Here of course he was observing colligative properties. He set 0oF as the temperature of ‘the most intense cold obtainable artificially’, meaning the salt water solution of lowest freezing point in his experimental tests.
A value of 32oF was assigned to the freezing point of water and a value of 212oF to its boiling point at a pressure of 1 bar, that is, what we’d now call the normal boiling point. Thermometers using air as fluid also came into use and these will be more fully discussed below when Kelvin’s work is described.
“we hear a great deal about changes in the temperature of the earth over a period of centuries or even millennia, yet temperature itself was not defined in thermodynamic terms until the mid 19th Century”
Kelvin’s seminal paper
In 1848 Lord Kelvin published an article entitled ‘On an absolute thermometric scale’ 2. This provided the vital link in placing temperature on a fundamental basis with a true zero, not an arbitrary one. The ideal gas laws were known by the time of the work by Kelvin under review, and the volume of a gas was used thermometrically, that is, the volume was taken to be a measure of the temperature. If, as was usual, the gas was air the device constituted an ‘air thermometer’. The Celsius temperature scale had been in use for about a century by this time, and it was known that the boiling point of water was 100oC and its freezing point 0oC. It was also known, from experimental measurements, that other things being equal a gas declines in volume by a factor of 0.366 over the temperature range 100oC to 0oC. Kelvin reasoned along the following lines. He first stated 2:
‘….infinite cold must correspond to a finite number of degrees of the air thermometer below zero.’
and went on to perform the very appealing calculation summarised in the shaded area below.
If a temperature change from 100oC to 0oC causes a drop in volume by a factor 0.366, a drop in volume by a factor of 1.000, corresponding to true zero of temperature and to the ‘infinite cold’ referred to above, occurs over a further temperature interval:
(-100/0.366) oC = -273oC
That absolute zero of temperature corresponds to -273oC is known to the student of physics even at the most elementary level. Kelvin derived that figure from extrapolating results from an air thermometer to a hypothetical zero volume of enclosed air. Returning to the comment quoted at the beginning of the article that the thermodynamic basis of temperature did not come until well after many of the temperature records now being invoked in the global warming timeline, it is difficult to see perceive a difficulty with retrospective amendments of such temperatures using the factor determined by Kelvin.
In any case most modern thermometric devices including thermocouples and resistance temperature detectors (RTDs) are set up to give readings in Celsius not in Kelvin. Thermocouples and RTDs will be discussed later in the article.
We should note that had Kelvin worked not in Celsius but in Fahrenheit he’d have obtained the same result. The calculation is repeated using Fahrenheit in the shaded area below.
Boiling point of water = 212oF
Freezing point of water = 32oF
‘Infinite cold’ corresponds to: [(-180/0.366) + 32] oF = -460 oF
Now from one of the numerous web sites (e.g. reference 3) which enable degrees Fahrenheit to be converted to degrees centigrade, a reader can confirm that:
-460oF = -273oC
and each is equal to absolute zero. If one wishes to retain Fahrenheit whilst also using absolute zero, the Rankine scale (oR) can be used. The conversion is:
oR = oF + 460
and absolute zero corresponds both to 0 K and to 0 oR. The Rankine scale is far from obsolete, frequently being used in the analysis of such things as combined heat and power (CHP).
Some comments on absolute zero
This is a topic about which much has been written. It relates to what is frequently, perhaps a little vaguely, referred to as the ‘philosophical side’ to thermodynamics. Over very many years of teaching and writing in thermodynamics the present author has tended to emphasise the ‘nuts and bolts’ of the subject, concentrating on what quantities of scientific and engineering interest can be obtained by application of the Laws of Thermodynamics. What he has to say about ‘absolute zero’ in this section of his article will be in this spirit.
The First Law is concerned with work and heat and the quantity internal energy, usual symbol U, features in it. U has units joule or, if on a mass or molar basis, respectively J kg-1 or J mol-1. The relevance of absolute zero to this is that whenever U is expressed as a function of the temperature it is of the temperature on the Kelvin scale. A closely related quantity to U is specific heat at constant volume, symbol cv, defined as:
cv = (∂U/∂T)v
units J kg-1K-1. However, because a degree Kelvin and a degree Celsius are the same size, per degree Kelvin and per degree Celsius are the same so to express the units of cv as J kg-1oC-1 would not be incorrect. One frequently encounters cv in such units. The author has found not only in his teaching of thermodynamics itself but also in his MSc level teaching in hydrocarbon matters, which draws extensively on thermodynamic principles, that students sometimes have a difficulty with this. If one were working in oF and oR the units of cv would most likely also use British Thermal Units (BTU) for energy and pound (lb) for mass, giving as the units of cv:
BTU lb-1oR-1
and per degree Rankine and per degree Fahrenheit are also equivalent.
The Second Law is concerned with entropy, usual symbol S, units of which are the same as those of specific heat viz. J kg-1K-1. Heat produced in a process can be equated to TΔS, where ΔS is the entropy change and T the temperature. Here the temperature has to be in absolute units. The Third Law relates directly to absolute zero, stating that all substances in their pure crystalline state have the same entropy at absolute zero of temperature.
This value is not intrinsically zero but, as it is a value common to all substances, can be set at zero. For entropies then there is a true fundamental benchmark value applying to all substances. This is not true for internal energy U, the function if state which, as we have seen, features in the First Law. Substances do not have he same value of U at absolute zero so any benchmark value for that is arbitrary and has to be clearly defined and understood if internal energies are to be added or subtracted correctly.
“temperature is measured by its effect on the physical properties of some substance, for example the volume of a particular liquid in a liquid-inglass thermometer”
Modern temperature measurement devices
The point was made previously in this article that temperature is measured by its effect on the physical properties of some substance, for example the volume of a particular liquid in a liquid-in-glass thermometer. In the table below are three selected examples of modern thermometric devices and details of how they work. Comments follow the table.
A reader is encouraged not to dismiss the mercury-in-glass thermometer simply because it is very much a ‘classical’ device. There has however been a move away from them partly because of the toxicity of mercury. A mercury-in-glass thermometer is a delicate device and when large numbers of them are used by inexperienced persons, for example in a teaching laboratory, breakages are inevitably frequent and mercury vapour enters the atmosphere.
The thermocouple has, over the last century, proved its worth in temperature measurement. A thermocouple consists of wires of two dissimilar metals in contact at a welded or soldered tip. Each metal is taken to a recording device in order that a measurement circuit is set up, and at points along the metal wires where the temperature Temperature Measurement changes an e.m.f. develops. This is the basis of the measurement, and such e.m.f.’s are of the order of millivolts.
There are, in 2009, still only eight ‘letter-designated’ types of thermocouples. One of the most common is Type K, one metal in which is a nickel-chromium alloy and the other a nickel-aluminium alloy. This is also known as the chromelalumel thermocouple.
A point concerning which the present author has already written a significant amount (perhaps too much!) is that for very many years in thermocouple usage the right practices were being followed for the wrong reasons. The 19th Century ‘Laws of Thermoelectric Thermometry’ were being used for guidance, and these are correct having been experimentally deduced. The difficulty is that they were misinterpreted because of the prevalent yet quite incorrect view that in a thermocouple the e.m.f. develops at the tip. It does not. It develops at places in the measuring circuit where the temperature changes, as noted in the previous paragraph.
In 2003 a reinterpretation of the Laws of Thermoelectric Thermometry according to the correct distributed e.m.f. idea was published in an ASTM (American Society for Testing and Materials) monograph4.
In a thermocouple circuit using a modern high-impedance recorder the resistance of the circuit is irrelevant to the reading and need not be known. By contrast an RTD (third row of the table) works by measurement of the resistance of a platinum conductor by a Wheatstone Bridge. Sometimes if it is proposed to use an RTD instead of a thermocouple a case has to be made that an RTD is superior for the particular measurement application.
Such a case can sometimes be argued on the grounds of intrinsic accuracy, the RTD having an advantage over the thermocouple in these terms. More particularly, the RTD has the advantage both of higher accuracy and of greater operational ease at cryogenic temperatures. There seemed to be a swing away from thermocouples towards RTDs in chemical processing about 20 years ago which has since been reversed.
“sometimes if it is proposed to use an RTD instead of a thermocouple a case has to be made that an RTD is superior for the particular measurement application”
Concluding remarks
This article has been concerned with what temperature is. Surely informed assessment of such topics as global warming requires a grasp of the thermodynamic meaning of temperature. Occasionally scientific writers experiencing difficulty with defining a particular phenomenon have referred to the Dickensian character Thomas Gradgrind, a headmaster who sought from a pupil a definition of a horse. The response he got was5: ‘Quadruped. Graminivorous. Forty teeth, namely twenty-four grinders, four eye-teeth, and twelve incisive. Sheds coat in the spring; in marshy countries, sheds hoofs, too. Hoofs hard, but requiring to be shod with iron. Age known by marks in mouth.’ Was that a definition, or a brief description? It is intended that at least a descriptive account of the term ‘temperature’ has been provided by this piece and that that will stimulate readers into reflecting at greater depth and in a more critical spirit on the matter of global warming which, as everyone knows, is dominating world affairs at present.
References
1 http://www.brannan.co.uk/pages/thermometers/invention.html
2 Thomson W. (a.k.a. Lord Kelvin) Philosophical Magazine, October 1848, accessible on: http://zapatopi.net/kelvin/papers/on_an_absolute_ thermometric_scale.html
3 http://www.wbuf.noaa.gov/tempfc.htm
4 Jones J.C. ‘Suggestions towards improved reliability of thermocouple temperature measurements in combustion tests’ Symposium on Thermal Measurements: The Foundation of Fire Standards Special Technical Publication, ASTM, Philadelphia 16-31 (2003)
5 http://www.doceo.co.uk/background/gradgrind.htm
Published: 10th Dec 2009 in AWE International
