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Blood, Butter, and Deep Cellars

(last edited on 22nd. February 2011)

This page arises out of my talk to the Leicester U3A Science group on 27th January 2011

My title lists three of the many suggested fixed points for a temperature scale.

The favoured cellars were those of the Paris observatory.

Other suggested fixed points were: candle flame, ice/salt freezing mixture, the most severe Winter temperature, the greatest Summer heat, boiling spirit (alcohol), ‘water hottest to be endured by a hand held still’, Hooke favoured freezing distilled water, Boyle suggested congealing oil of aniseed, Newton used melting snow and blood heat. As late as 1771 the first edition of the Encyclopaedia Britannica proposed floating wax (I guess that candle wax was intended) on water and heating the water till the wax melted.

I shall talk about the early history of temperature scales, so I’m describing took place when there was no science of thermodynamics, when no one knew about the mechanical equivalent of heat and when knowledge of electricity was confined to an anecdotal account of electrostatics.

Since the first thermometers were constructed towards the very end of the sixteenth century, people have used many different scales. In the early days every thermometer had its own scale. I shan’t confuse you with such details, and whenever I mention the temperature of anything, without mentioning the scale, I shall use the Celcius scale, even when I’m describing work done by people using other scales.

The development of science is sometimes presented as a steady progress towards greater enlightenment. Perhaps it is sometimes like that, but I’m going to tell a story of a very different kind, of 250 years of snags, confusion and accidents, not all of them happy accidents. This is going to be less the relation of a simple theme, and more the relation of a string of anecdotes, loosely related by their connection to temperature. If the story is less inspiring that those we are often told, it is also more interesting.

There is surprisingly little about temperature in popular accounts of science, and very little about heat, apart from occasional references to entropy that sometimes suggest it as a companion for the four horsemen of the apocalypse and never mention integral dQ/T along a eversible path.

I checked the indices of two works of popular science that aim to be comprehensive: Roger Penrose The Road to Reality and Isaac Asimov A New Guide to Science. Neither contained either ‘temperature’ or ‘Thermometer. Nor did the index of Jenny Uglow’s The Lunar men, even though several of the Lunar Men made important contributions to Thermometry. Penrose did mention temperature in passing, treating it as the mean kinetic energy of the molecules of a gas, quite overlooking the fact that the only practicable way to determine the mean kinetic energy of those molecules is to take the temperature. Stephen Inwood The man Who Knew Too Much, says nothing about Hooke’s work on Thermometry

Almost all my information about early thermometry comes from a single book:

Hasok Chang,

Inventing temperature: Measurement and Scientific Progress

Many well known scientists were involved in developing thermometry, though popular histories usually concentrate on other aspects of their work. Galileo seems to have produced on of the earliest thermometers, Mersenne (of Mersenne numbers), Boyle, Halley, Newton, Josiah Wedgwood, Cavendish, and Lavoisier were also involved.

It would take too long to distinguish the contributions of each individual, so apart from a little name dropping I shall most of the time speak impersonally about a gradual but rather haphazard accumulation of information and refinement of standards.

Temperature is something we tend to take for granted in the same way that we do length, treating it as a measurement that is just accessible to us, yet temperature is much trickier than length, hence the inadequacy of what I’ll call the optimistic account of temperature which I remember from my schooldays as something like this:

As children we hear people talking about the ambient temperature and hear weather forecasts long before we come across anything like a definition, and so we are not surprised that, when it comes, the definition makes things sound very simple. So far as I can recall it, when we were introduced to heat in the grammar school it was a matter of: call melting ice zero (or 32, we still sometimes used funny temperatures in those days), call boiling water 100 (or 212), and divide the interval equally into 100 intervals (or 180) and there’s your temperature scale. Later we thought we were being very sophisticated when we replaced boiling water by steam over boiling water, and specified the atmospheric pressure.

That makes it sound very easy. On the other hand a pessimist could make thermometry seem impossible.

A temperature scale needs fixed points, or at least one fixed point, and it needs some physical property that varies with temperature.

Yet how can we know that something always happens at the same temperature, unless we already have a temperature scale to measure it ?

Even if we have fixed points, how can we justify fitting a scale between them? Early thermometers usually depended on measuring the expansion of some fluid, and their graduation assumed that equal changes in temperature produced equal expansions. How could that be justified without referring to some temperature scale?

It starts to sound as if it’s impossible to get started, because defining a temperature scale makes assumptions that cannot be justified without a pre-existing temperature scale.

As the process took about 250 years, there’s to be something to be said for the pessimistic story.

Our modern concept of temperature is embedded in the theory of thermodynamics, which connects it to our theories about energy and the nature of heat. Yet there were working temperature scales before those theories were developed, and it is arguable that there had to be some sort of temperature scale before anyone could develop thermodynamics.

Today heat is usually measured in the same units we use for mechanical energy, but the mechanical equivalent of heat was an important scientific discovery which only made sense if heat could already be reliably measured in units that were not mechanical,

After all:

I Joule = 1 Joule

is unexciting and there must be more than that in an important scientific discovery.

I’ll be talking about the 250 years from 1600 to 1850 during which people managed to construct a rough and ready but still usable ad hoc temperature scale, that made it possible to establish the mechanical equivalent of heat and develop the science of thermodynamics. Those in their turn made it possible to establish temperature on a sounder theoretical basis.

Fixed points

A temperature scale needs fixed points. Note that the number two is not sacrosanct, one fixed point may suffice, and it is possible to use more than two.

The original Réaumur scale was defined with a single fixed point, the melting point of ice, which Réaumur set at 0. Using alcohol as thermometric fluid Réaumur defined a temperature as (increase in volume)*1000/(volume at the fixed point).

Fahrenheit used three fixed points: ice/salt freezing mixture, ice/water mixture and blood heat.

Of the two temperature scales in use today, the Thermodynamic Scale uses a single fixed point - the triple point of water, and the International Temperature Scale has 17 fixed points, including the triple point of neon, the melting point of gallium and the freezing point of gold. There is a list of all 17 at the end of this document.

Notice that melting point is not the same as freezing point. Both are measured for systems where both liquid and solid are present, but melting point is measured when heat is flowing into a system, and freezing point when heat is flowing out of the system.

Things aren’t quite as bad as the pessimistic story suggests, because checking that a fixed point is fixed doesn’t require a temperature scale. It is enough to be able to tell whether one thing is hotter than another; we don’t need to measure the size of the difference.

Chang suggested using thermoscope for an instrument that tells us which of two bodies is the hotter, and reserving thermometer for an instrument that assigns a numerical value to a difference in temperature.

The boiling and freezing of water gradually emerged as more reliable and convenient than other fixed points, so those processes were studied in considerable detail.

Boiling water seemed to work reasonably well, so long as one didn’t try to define it precisely, however a fixed point must be defined precisely so that anyone can reproduce it, so we have to answer the questions:

What is water ? and

What is boiling?

Boiling

Once people sought precision, boiling started to seem elusive. There appeared to be degrees of boiling. As the temperature of water rises first a few bubbles appear, then more until eventually the entire body of the water irrupts energetically. What stage in the process was to be used to define a fixed point?

There were several ways in which the prevailing conditions appeared to affect the boiling of water.

Most easily dealt with was atmospheric pressure. By the end of the seventeenth century interested parties knew that atmospheric pressure affected boiling point.

It would have been possible to specify that readings should be taken when the barometer stood at a certain value, but once there was a rough temperature scale, it was possible to record the variation of boiling point with pressure and hence construct a more precise scale.

Note that there is an element of circularity. Boiling point is needed to calibrate a thermometer, but a calibrated thermometer is needed to record the variations in boiling point. However it is possible to proceed by a series of approximations. A rough scale can be constructed without bothering about atmospheric pressure. That rough scale can be used to find roughly how boiling point varies with pressure, and those rough estimates can in turn be used to correct the temperature scale, and the corrected scale can be used to obtain improved figures for the variation of boiling point with pressure.

A column of liquid exerts a pressure, so if the boiling point of water depends in pressure, it should vary with depth. Investigations showed the variation to be only half what would be expected, so it was decided to measure the temperature near to the top of the boiling water.

Water

Boiling point is also affected by dissolved impurities, which raise the boiling point.. People therefore tried to use water free from impurities, boiled in clean containers. That means using distilled water that had been heated to remove dissolved air. Glass containers were favoured, I suppose partly because its easy to see what is going on inside them, but also because glass withstands all the acids known in the eighteenth century, so that they could be cleaned with concentrated sulphuric acid.

Thus people tried to calibrate thermometers by boiling distilled water free from dissolved air, in glass vessels that had been scrupulously cleaned.

Those precautions had the opposite effect to that intended. Instead of insuring a constant boiling point, they created the conditions for superheating, so water would reach a temperature several degrees above what we should now consider its proper boiling point, and then the sudden irruption of lots of steam would be accompanied by a fall in temperature. The process would be repeated so the temperature would fluctuate by several degrees.

The discovery of superheating inspired a sort of sideshow, a competition to see how hot one could get water without it evaporating. The most impressive results were obtained by suspending droplets of water in hot oil, presumably oil with the same density as water. I imagine that the significance of those conditions was that the water was not in contact with any water vapour, though I don’t think the significance of that was realised at the time. Claims have been made for temperatures getting to 170 degrees without boiling. I think someone once claimed 200 degrees.

A big contributor to thermometry was someone we don’t usually hear much about.

Jean André De Luc (1727-1817) was a Swiss scientist whose father was a clock maker. He was interested in geology and meteorology and designed meteorological instruments. He was a mountaineer who pioneered the calculation of the heights of mountains from atmospheric pressure. He eventually settled in England and became a Fellow of the Royal Society.

De Luc devoted a lot of time to studying the boiling of water, and concluded that the boiling point is not clearly defined.

Cavendish and De Luc were both members of a Royal Society committee set up to investigate the boiling point of water. The committee reported in 1777, describing the variations, and various ways of reducing superheating. It also reported that the temperature of steam over boiling water appeared less variable than the temperature of the water itself. Cavendish in particular strongly advocated the use of the temperature of steam as the fixed point, and that was generally adopted.

Fortunately for the development of thermometry people did not at the time look too closely at the behaviour of steam. Had they taken care to exclude dust particles from the surrounding air, they might have discovered supersaturated water vapour, and thus created more problems for thermometry.

The freezing point of water gave less trouble. Although it is possible to have super cooled water, seeding with ice makes some of the water freeze until the temperature rises to the equilibrium value

Thermometric Medium

Temperature has to be measured by observing some physical quantity that changes as things get hotter or colder. There are many such physical properties, but in the early days people used lengths or volumes, nearly always volumes of fluids, and the favourite fluid was mercury, which remains in the liquid state for most of the temperature range we encounter in day to day life. Alcohol was also sometimes used.

Mercury: MP -38.9C, BP 356.6C

Ethanol: MP -117C, BP 78.5C

Different thermometric fluids give appreciably different temperature scales. The first of the following graphs compares the expansions of alcohol with that of mercury. The second graph compares the expansions of alcohol, (top curve) water (bottom curve) and various mixtures of the two.

Notice that just above its freezing point water contracts with increasing temperature, making it uniquely unsuitable for use in a thermometer.

Mercury probably became the favourite fluid because of the wide range of a mercury thermometer, but that may not have been the only consideration. Some thought mercury rather special, there was even a theory that mercury was ‘intrinsically fluid’ and could never freeze, so when the mercury in a thermometer did freeze, a process accompanied by contraction, people thought the temperature was much lower than it actually was.

Undetected freezing of mercury may explain some remarkably low temperatures claimed to have been observed by explorers in a party led by Johann Geog Gmelin that spent 10 years exploring Siberia. They set out in 1733 and in their second Winter recorded a temperature of -120 Fahrenheit (-84 Celsius). As mercury is now known to freeze at -39 degrees C , even allowing for the possibility of some super cooling, it would unlikely to remain liquid at so low a temperature. The explorers must have been misled by frozen mercury

Is the choice of thermometric fluid just arbitrary, or at most a matter of convenience? Once people have a number, they are inclined to calculate with it. Calculation with the numbers that appear in science involves incorporating them in some sort of theory. The first theory used to suggest calculations with temperature was the Caloric theory, that heat was a sort of fluid.

There were two schools of thought among Calorists. The Irvinists followed William Irvine Irvine in thinking caloric was just mixed with the matter of hot objects, and the chemical Calorists, like Lavoisier who invented the word ‘caloric. The chemical Calorists believed that caloric was an element that formed chemical compounds.

I imagine we’ve all heard of Lavoisier, but William Irvine was new to me, so I’ll say a bit about him. Born in in 1743, he was trained as a doctor. He worked with Black in Glasgow, and died in 1747.

The chemical theory was too complicated to inspire anything as definite as a calculation is it was the Irvinists who succeeded in making testable predictions.

They thought that the temperature of a body depended solely on the concentration of caloric in it. That provided them with a criterion for the accuracy of a temperature scale. An accurate scale would be one which accurately reflected the concentration of caloric. That was equivalent to making the specific heat of every material independent of temperature. From a Calorist point of view it would have been neater if every substance had the same specific heat, but differences in specific heat could be accommodated by saying that different substances had a different capacity for holding heat, provided that capacity was independent of temperature

Method of mixtures

The Calorists thought that if we mix two samples of the same fluid that are at different temperatures, it should be possible to calculate the final temperature of the mixture from the initial conditions.

Considering the simplest possibility, if we take equal quantities of a fluid, one sample at temperature T1, and the other at temperature T2, the final temperature of the mixture should be:

½(T1 + T2)

Had the Caloric theory been correct, the final temperature would be the same, whatever the fluid used, but that was found not to be so.

Estimation of the absolute zero.

In the 18th Century people had two reasons for suspecting there might be an absolute zero temperature.

First, if temperature somehow reflects the concentration of caloric, then if no caloric is present in a body, it must be as cold as any body can be.

Second, it had been observed that the volume of a gas at constant pressure decreases steadily with falling temperature, suggesting that if one extrapolated to the point where volume would be zero, one would reach a minimum possible temperature.

The Irwinists thought they might estimate the absolute zero by a calculation involving specific heats, and latent heat of fusion.

Using modern figures, the calculation for water would proceed as follows:

Near its freezing point liquid water has a specific heat of about 4.17 Joules/gram/oC, while ice has a specific heat around 2.03 Joules/gram/oC.

The latent heat of fusion of ice = about 325 Joules/gram

The difference in specific heats is about 2.14 Joules/gram/oC.

Irvinists attributed that difference in specific heats to ice having a lower capacity to absorb caloric than did water, and they believed that the same difference in capacity accounted for latent heat - liquid water has a greater capacity for holding heat than solid water, so that additional heat must be supplied to turn solid into liquid.

Hence, at 0oC (caloric in 1 g of water) = (4.17/2.03)*(caloric in 1 g ice)

= 2.05*(caloric in 1 g ice)

And (caloric in 1 g of water) - (caloric in 1 g ice) = 325 J

So 1.05*(caloric in 1 g ice) = 325 J

caloric in 1 g ice = 310 J

Hence melting ice is 310/2.03 degrees above the absolute zero,

so the absolute zero = -152 oC.

With the wisdom of hindsight we know that that value is quite wrong.

Contemporary physicists also knew it was wrong for a different reason.

If that calculation were correct, it would give the same answer if we used data for other fluids, but that was not the case. Using data for different fluids gave widely different values for the absolute zero.

The Irwinist version of the caloric theory was thus refuted. The alternative chemical theory of caloric lingered on for a while only because it was too complicated and confused to yield any testable conclusions.

Extending the scale

Mercury in glass thermometers are restricted to -39oC to 327 oC

Outside that range gas thermometers were often used, measuring temperature by finding the pressure of gas at constant volume.

Different gases gave slightly different results though air seemed quite popular, even though it was known to be a mixture of several gases.

However a gas needs a solid container, and the higher the temperature, the fewer substances remain solid - there is also the problem of dissociation.

The problem was not fully resolved until Kelvin developed a thermodynamic scale around 1850, and untidy loose ends continued to dangle for quite a while after that.

Josiah Wedgwood needed to measure very high temperatures in order to regulate the kilns in which he made his pots. The wrong temperature produced broken pots.

Nowadays such temperatures could be measured electrically, or by analysing radiation. Electrical methods were not available in Wedgwood’s day, and the nearest he could have come to analysing radiation would have been to note how brightly the oven glowed, and that didn’t give sufficient accuracy.

Wedgwood didn’t really need a numerical scale. I imagine it would have sufficed to distinguish five cases:

(5) Much too hot

(4) A bit too hot

(3) Just right

(2) A bit too cool

(1) Much too cool

At a guess I should think (1) and (5) could be identified by looking inside the furnace to see how brightly it was glowing, so an instrument would be needed only to distinguish (2), (3) and (4)

However Wedgwood wanted to be more thorough than that, and managed to construct a numerical scale by using the properties of a certain variety of clay.

He found that the clay in question contracted when heated in a kiln, and the degree of contraction depended on the highest temperature it encountered. The contraction was permanent, so it could be measured after pellets of the clay had been removed from the kiln and allowed to cool.

Wedgwood defined one degree on his scale as a contraction of one part in 600. He used small pellets of the clay and measured their contraction by fitting them in a channel in a piece of wood. See the diagram in which one pellet is inside the channel. The channel was slightly wider at one end than at the other, so that a clay pellet that had not shrunk at all would just fit in the wide end of the channel, and the more a pellet had shrunk the further along the channel it would go. There was a scale at the side of the channel graduated in degrees Wedgwood.

The system proved satisfactory for adjusting kiln temperature to avoid broken pots, but Wedgwood was inspired by scientific curiosity to try to link his scale to that already in use to measure lower temperatures with mercury or alcohol thermometers.

He tried to bridge the gap between the two scales by measuring the thermal expansion of a piece of silver.

The results were surprising, giving temperatures of the order 10000 oC for the melting point of iron, but it was only many years after Wedgwood’s work that it was possible to provide any reliable extension of the temperature scale to encompass the sorts of temperature Wedgwood had been trying to measure.

A Puzzle

In 1791 Marc-August Pictet constructed an apparatus to demonstrate the focusing of thermal radiation by concave metallic mirrors.

Marc-August Pictet 1752-1825

Physicist, Meteorologist, Astronomer (Geneva Observatory)

He brought a hot object to the focus of one mirror, and noted that when he did so there was an apparently immediate effect on the thermometer at the focus of the upper mirror even though that was 69 feet away.

It then occurred to Pictet to use the apparatus to test a theory, advanced by various people inclosing Rumford, that just as hot bodies radiate heat, so do cold bodies emit ‘refrigerant radiation’. Pictet therefore brought a flask of snow to the lower focus. The thermometer at the upper focus showed an immediate fall in temperature there.

The illustration shows a repetition of the experiment in 1880 by one John Tyndall. In this case the mirrors are closer together, one is above the other and there is an inflated balloon at the focus of the upper mirror. The focussed heat burst the balloon. This version of the experiment is inferior to Pictet's because it leaves open the possibility of convection currents affecting the result.

The experiment was repeated in 1985 with the same result, though a report in a paper published in The American Journal of Physics received little attention.

Supplementary Material

Thermodynamic Scale

Triple point of Vienna Mean Standard water = 273.16 K (note that there is no o sign)

Heat absorbed/heat rejected = T1/T2

for perfect heat engine with source at T1 k, sink at T2 k

Equivalent to ideal gas pressure thermometer

International Temperature Scale

Substance and its state Defining point in K (range) Defining point in C (range)

Vapour-pressure / temperature (0.65 to 3.2), (-272.50 to -269.95)

relation of helium-3 (by equation)

Vapour-pressure / temperature (1.25 to 2.1768), (-271.90 to -270.9732)

relation of helium-4 below its lambda point (by equation)

Vapour-pressure / temperature relation of helium-4 above its

lambda point (by equation) (2.1768 to 5.0), (-270.9732 to -268.15)

Vapour-pressure / temperature relation of helium (by equation) ( to 5), (-270.15 to -268.15)

Triple point of hydrogen 13.8033, -259.3467

Triple point of neon 24.5561, -248.5939

Triple point of oxygen 54.3584, -218.7916

Triple point of argon 83.8058, -189.3442

Triple point of mercury 234.3156, -38.8344

Triple point of water1 273.16, 0.01

Melting point of gallium 302.9146, 29.7646

Freezing point of indium 429.7485, 156.5985

Freezing point of tin 505.078, 231.928

Freezing point of zinc 692.677, 419.527

Freezing point of aluminium 933.473, 660.323

Freezing point of silver 1234.93, 961.78

Freezing point of gold 1337.33, 1064.18

Freezing point of copper 1357.77, 1084.62


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