# Theory of Heat (Maxwell, 4th edition)/Chapter 2

CHAPTER II.
ON THERMOMETRY, OR THE THEORY OF TEMPERATURE.
Definition of Temperature.—The temperature of a body is its thermal state considered with reference to its power of communicating heat to other bodies.
Definition of Higher and Lower Temperature.—If when two bodies are placed in thermal communication, one of the bodies loses heat, and the other gains heat, that body which gives out heat is said to have a higher temperature than that which receives heat from it.
Cor. If when two bodies are placed in thermal communication neither of them loses or gains heat, the two bodies are said to have equal temperatures or the same temperature. The. two bodies are then said to be in thermal equilibrium. We have here a means of comparing the temperature of any two bodies, so as to determine which has the higher temperature, and a test of the equality of temperature which is independent of the nature of the bodies tested. But we have no means of estimating numerically the difference between two temperatures, so as to be able to assert that a certain temperature is exactly halfway between two other temperatures.
Law of Equal Temperatures.—Bodies whose temperatures are equal to that of the same body have themselves equal temperatures. This law is not a truism, but expresses the fact that if a piece of iron when plunged into a vessel of water is in thermal equilibrium with the water, and if the same piece of iron, without altering its temperature, is transferred to a vessel of oil, and is found to be also in thermal equilibrium with the oil, then if the oil and water were put into the same vessel they would themselves be in thermal ​equilibrium, and the same would be true of any other three substances.
This law, therefore, expresses much more than Euclid's axiom that 'Things which are equal to the same thing are equal to one another,' and is the foundation of the whole science of thermometry. For if we take a thermometer, such as we have already described, and bring it into intimate contact with different bodies, by plunging it into liquids, or inserting it into holes made in solid bodies, we find that the mercury in the tube rises or falls till it has reached a certain point at which it remains stationary. We then know that the thermometer is neither becoming hotter nor colder, but is in thermal equilibrium with the surrounding body. It follows from this, by the law of equal temperatures, that the temperature of the body is the same as that of the thermometer, and the temperature of the thermometer itself is known from the height at which the mercury stands in the tube.
Hence the reading, as it is called, of the thermometer—that is, the number of degrees indicated on the scale by the top of the mercury in the tube—informs us of the temperature of the surrounding substance, as well as of that of the mercury in the thermometer. In this way the thermometer may be used to compare the temperature of any two bodies at the same time or at different times, so as to ascertain whether the temperature of one of them is higher or lower than that of the other. We may compare in this way the temperatures of the air on different days; we may ascertain that water boils at a lower temperature at the top of a mountain than it does at the sea-shore, and that ice melts at the same temperature in all parts of the world.
For this purpose it would be necessary to carry the same thermometer to different places, and to preserve it with great care, for if it were destroyed and a new one made, we should have no certainty that the same temperature is indicated by the same reading in the two thermometers.
​Thus the observations of temperature recorded during sixteen years by Rinieri at Florence lost their scientific value after the suppression of the Accademia del Cimento, and the supposed destruction of the thermometers with which the observations were made. But when Antinori in 1829 discovered a number of the very thermometers used in the ancient observations, Libri was able to compare them with Réaumur's scale, and thus to show that the climate of Florence has not been rendered sensibly colder in winter by the clearing of the woods of the Apennines.
In the construction of artificial standards for the measurement of quantities of any kind it is desirable to have the means of comparing the standards together, either directly, or by means of some natural object or phenomenon which is easily accessible and not liable to change. Both methods. are used in the preparation of thermometers.
We have already noticed two natural phenomena which take place at definite temperatures—the melting of ice and the boiling of water. The advantage of employing these temperatures to determine two points on the scale of the thermometer was pointed out by Sir Isaac Newton ('Scala Graduum Caloris,' Phil. Trans. 1701).
The first of these points of reference is commonly called the Freezing Point. To determine it, the thermometer is placed in a vessel filled with pounded ice or snow thoroughly moistened with water. If the atmospheric temperature be above the freezing point, the melting of the ice will ensure the presence of water in the vessel. As long as every part of the vessel contains a mixture of water and ice its temperature remains uniform, for if heat enters the vessel it can only melt some of the ice, and if heat escapes from the vessel some of the water will freeze, but the mixture can be made neither hotter nor colder till all the ice is melted or all the water frozen.
The other point of reference is called the Boiling Point. The temperature at which water boils depends on the pressure of the atmosphere. The greater the pressure of the air on the surface of the water, the higher is the temperature to which the water must be raised before it begins to boil.
To determine the Boiling Point, the stem of the thermometer is passed through a hole in the lid of a tall vessel, in the lower part of which water is made to boil briskly, so that the whole of the upper part, where the thermometer is placed, is filled with steam. When the thermometer has acquired the temperature of the current of steam the stem is drawn up through the hole in the lid of the vessel till the top of the column of mercury becomes visible. A scratch is then made on the tube to indicate the boiling point.
For instance, if we take any tall narrow vessel, as a coffee-pot, and cover its mouth and part of its sides with a wider vessel turned upside down, taking care that there shall be plenty of room for the steam to escape, then if we boil a small quantity of water in the coffee-pot, a thermometer placed in the steam above will be raised to the exact temperature of the boiling point of water corresponding to the state of the barometer at the time.
To mark the level of the mercury on the tube of the thermometer without cooling it, we must draw it up through a cork or a plug of india-rubber in the steam-jacket through which the steam passes till we can just see the top of the column of mercury. A mark must then be scratched on the glass to register the boiling point. This experiment of exposing a thermometer to the steam of boiling water is an important one, for it not only supplies a means of graduating thermometers, and testing them when they have been graduated, but, since the temperature at which water boils ​depends on the pressure of the air, we may determine the pressure of the air by boiling water when we are not able to measure it by means of the appropriate instrument, the barometer.
We have now obtained two points of reference marked by scratches on the tube of the thermometer-the freezing point and the boiling point. We shall suppose for the present that when the boiling point was marked the barometer happened to indicate the standard pressure of 29.905 inches of mercury at 0° C. at the level of the sea in the latitude of London. In this case the boiling point is the standard boiling point. In any other case it must be corrected.
Our thermometer will now agree with any other properly constructed thermometer at these two temperatures.
In order to indicate other temperatures, we must construct a scale—that is, a series of marks—either on the tube itself or on a convenient part of the apparatus close to the tube and well fastened to it.
For this purpose, having settled what values we are to give to the freezing and the boiling points, we divide the space between those points into as many equal parts as there are degrees between them, and continue the series of equal divisions up and down the scale as far as the tube of the thermometer extends.
Three different ways of doing this are still in use, and, as we often find temperatures stated according to a different scale from that which we adopt ourselves, it is necessary to know the principles on which these scales are formed.
The Centigrade scale was introduced by Celsius. In it the freezing point is marked 0° and called zero, and the boiling point is marked 100°.
The obvious simplicity of this mode of dividing the space between the points of reference into 100 equal parts and ​calling each of these a degree, and reckoning all temperatures in degrees from the freezing point, caused it to be very generally adopted, along with the French decimal system of measurement, by scientific men, especially on the Continent of Europe. It is true that the advantage of the decimal system is not so great in the measurement of temperatures as in other cases, as it merely makes it easier to remember the freezing and boiling temperatures, but the graduation is not too fine for the roughest purposes, while for accurate measurements the degrees may be subdivided into tenths and hundredths.
The other two scales are called by the names of those who introduced them.
Fahrenheit, of Dantzig, about 1714, first constructed thermometers comparable with each other. In Fahrenheit's scale the freezing point is marked 32°, and the boiling point 212°, the space between being divided into 180 equal parts, and the graduation extended above and below the points of reference. A point 32 degrees below the freezing point is called zero, or 0°, and temperatures below this are indicated by the number of degrees below zero.
This scale is very generally used in English-speaking countries for purposes of ordinary life, and also for those of science, though the Centigrade scale is coming into use among those who wish their results to be readily followed by foreigners.
The only advantages which can be ascribed to Fahrenheit's scale, besides its early introduction, its general diffusion, and its actual employment by so many of our countrymen, are that mercury expands almost exactly one ten-thousandth of its volume at 142° F. for every degree of Fahrenheit's scale, and that the coldest temperature which we can get by mixing snow and salt is near the zero of Fahrenheit's scale.
To compare temperatures given in Fahrenheit's scale with temperatures given in the Centigrade scale we have only to ​remember that 0° Centigrade is 32° Fahrenheit, and that five degrees Centigrade are equal to nine of Fahrenheit.
The third thermometric scale is that of Réaumur. In this scale the freezing point is marked 0° and the boiling point 80°. I am not aware of any advantage of this scale. It is used to some extent on the Continent of Europe for medical and domestic purposes. Four degrees of Réaumur correspond to five Centigrade and to nine of Fahrenheit.
The existence of these three thermometric scales furnishes an example of the inconvenience of the want of uniformity in systems of measurement. The whole of what we have said about the comparison of the different scales might have been omitted if any one of these scales had been adopted by all who use thermometers. Instead of spending our time in describing the arbitrary proposals of different men, we should have gone on to investigate the laws of heat and the properties of bodies.
We shall afterwards have occasion to use a scale differing in its zero-point from any of those we have considered, but when we do so we shall bring forward reasons for its adoption depending on the nature of things and not on the predilections of men.
If two thermometers are constructed of the same kind of glass, with tubes of uniform bore, and are filled with the same liquid and then graduated in the same way, they may be considered for ordinary purposes as comparable instruments; so that though they may never have been actually compared together, yet in ascertaining the temperature of anything there will be very little difference whether we use the one thermometer or the other.
But if we desire great accuracy in the measurement of temperature, so that the observations made by different observers with different instruments may be strictly comparable, the only satisfactory method is by agreeing to choose one thermometer as a standard and comparing all the others with it.
​All thermometers ought to be made with tubes of as uniform bore as can be found; but for a standard thermometer the bore should be calibrated—that is to say, its size should be measured at short intervals all along its length.
For this purpose, before the bulb is blown, a small quantity of mercury is introduced into the tube and moved along the tube by forcing air into the tube behind it. This is done by squeezing the air out of a small india-rubber ball which is fastened to the end of the tube.
If the length of the column of mercury remains exactly the same as it passes along the tube, the bore of the tube must be uniform; but even in the best tubes there is always some want of uniformity.
But if we introduce a short column of mercury into the tube, then mark both ends of the column, and move it on its own length, till one end comes exactly to the mark where the other end was originally, then mark the other end, and move it on again, we shall have a series of marks on the tube such that the capacity of the tube between any two consecutive marks will be the same, being equal to that of the column of mercury.
By this method, which was invented by Gay-Lussac, a number of divisions may be marked on the tube, each of which contains the same volume, and though they will probably not correspond to degrees when the tube is made up into a thermometer, it will be easy to convert the reading of this instrument into degrees by multiplying it by a proper factor, and in the use of a standard instrument this trouble is readily undertaken for the sake of accuracy.
The tube having been prepared in this way, one end is. heated till it is melted, and it is blown into a bulb by forcing air in at the other end of the tube. In order to avoid introducing moisture into the tube, this is done, not by the mouth, but by means of a hollow india-rubber ball, which is fastened to the end of the tube.
​The tube of a thermometer is generally so narrow that mercury will not enter it, for a reason which we shall explain when we come to the properties of liquids. Hence the following method is adopted to fill the thermometer. By rolling paper round the open end of the tube, and making the tube thus formed project a little beyond the glass tube, a cavity is formed, into which a little mercury is poured. The mercury, however, will not run down the tube of the thermometer, partly because the bulb and tube are already full of air, and partly because the mercury requires a certain pressure from without to enter so narrow a tube. The bulb is therefore gently heated so as to cause the air to expand, and some of the air escapes through the mercury. When the bulb cools, the pressure of the air in the bulb becomes less than the pressure of the air outside, and the difference of these pressures is sufficient to make the mercury enter the tube, when it runs down and partially fills the bulb.
In order to get rid of the remainder of the air, and of any moisture in the thermometer, the bulb is gradually heated till the mercury boils. The air and steam escape along with the vapour of mercury, and as the boiling continues the last remains of air are expelled through the mercury at the top of the tube. When the boiling ceases, the mercury runs back into the tube, which is thus perfectly filled with mercury.
While the thermometer is still hotter than any temperature at which it will afterwards be used, and while the mercury or ​its vapour completely fills it, a blowpipe flame is made to play on the top of the tube, so as to melt it and close the end of the tube. The tube, thus closed with its own substance, is said to be 'hermetically sealed.'
There is now nothing in the tube but mercury, and when the mercury contracts so as to leave a space above it, this space is either empty of all gross matter, or contains only the vapour of mercury. If, in spite of all our precautions, there is still some air in the tube, this can easily be ascertained by inverting the thermometer and letting some of the mercury glide towards the end of the tube. If the instrument is perfect, it will reach the end of the tube and completely fill it. If there is air in the tube the air will form an elastic cushion, which will prevent the mercury from reaching the end of the tube, and will be seen in the form of a small bubble. We have next to determine the freezing and boiling points, as has been already described, but certain precautions have still to be observed. In the first place, glass is a substance in which internal changes go on for some time after it has been strongly heated, or exposed to intense forces. In fact, glass is in some degree a plastic body. It is found that after a thermometer has been filled and sealed the capacity of the bulb diminishes slightly, and that this change is comparatively rapid at first, and only gradually becomes insensible as the bulb approaches its ultimate condition. It causes the freezing point to rise in the tube to 0°.3 or 0°.5, and if, after the displacement of the zero, the mercury be again boiled, the zero returns to its old place and gradually rises again.
This change of the zero-point was discovered by M. Flaugergues. It may be considered complete in from four to ​six months. In order to avoid the error which it would introduce into the scale, the instrument should, if possible, have its zero determined some months after it has been filled, and since even the determination of the boiling point of water produces a slight depression of the freezing point (that is, an expansion of the bulb), the freezing point should not be determined after the boiling point, but rather before it.
When the boiling point is determined, the barometer is probably not at the standard height. The mark made on the thermometer must, in graduating it, be considered to represent, not the standard boiling point, but the boiling point corresponding to the observed height of the barometer, which may be found from the tables.
To construct a thermometer in this elaborate way is by no means an easy task, and even when two thermometers have been constructed with the utmost care, their readings at points distant from the freezing and boiling points may not agree, on account of differences in the law of expansion of the glass of the two thermometers. These differences, however, are small, for all thermometers are made of the same description of glass.
But since the main object of thermometry is that all thermometers shall be strictly comparable, and since thermometers are easily carried from one place to another, the best method of obtaining this object is by comparing all thermometers either directly or indirectly with a single standard thermometer. For this purpose, the thermometers, after being properly graduated, are all placed along with the standard thermometer in a vessel, the temperature of which can be maintained uniform for a considerable time. Each thermometer is then compared with the standard thermometer. ​A table of corrections is made for each thermometer by entering the reading of that thermometer, along with the correction which must be applied to that reading to reduce it to the reading of the standard thermometer. This is called the proper correction for that reading. If it is positive it must be added to the reading, and if negative it must be subtracted from it.
By bringing the vessel to various temperatures, the corrections at these temperatures for each thermometer are ascertained, and the series of corrections belonging to each thermometer is made out and preserved along with that thermometer.
Any thermometer may be sent to the Observatory at Kew, and will be returned with a list of corrections, by the application of which, observations made with that thermometer become strictly comparable with those made by the standard thermometer at Kew, or with any other thermometer similarly corrected. The charge for making the comparison is very small compared with the expense of making an original standard thermometer, and the scientific value of observations made with a thermometer thus compared is greater than that of observations made with the most elaborately prepared thermometer which has not been compared with some existing and known standard instrument.
I have described at considerable length the processes by which the thermometric scale is constructed, and those by which copies of it are multiplied, because the practical establishment of such a scale is an admirable instance of the method by which we must proceed in the scientific observation of a phenomenon such as temperature, which, for the present, we regard rather as a quality, capable of greater or less intensity, than as a quantity which may be added to or subtracted from other quantities of the same kind.
A temperature, so far as we have yet gone in the science of heat, is not considered as capable of being added to another temperature so as to form a temperature which is Digitized by Google ​the sum of its components. When we are able to attach a distinct meaning to such an operation, and determine its result, our conception of temperature will be raised to the rank of a quantity. For the present, however, we must be content to regard temperature as a quality of bodies, and be satisfied to know that the temperatures of all bodies can be referred to their proper places in the same scale.
For instance, we have a right to say that the temperatures of freezing and boiling differ by 180° Fahrenheit; but we have as yet no right to say that this difference is the same as that between the temperatures 300° and 480° on the same scale. Still less can we assert that a temperature of
is equal to the sum of the temperatures of freezing and boiling. In the same way, if we had nothing by which to measure time except the succession of our own thoughts, we might be able to refer each event within our own experience to its proper chronological place in a series, but we should have no means of comparing the interval of time between one pair of events with that between another pair, unless it happened that one of these pairs was included within the other pair, in which case the interval between the first pair must be the smallest. It is only by observation of the uniform or periodic motions of bodies, and by ascertaining the conditions under which certain motions are always accomplished in the same time, that we have been enabled to measure time, first by days and years, as indicated by the heavenly motions, and then by hours, minutes, and seconds, as indicated by the pendulums of our clocks, till we are now able, not only to calculate the time of vibration of different kinds of light, but to compare the time of vibration of a molecule of hydrogen set in motion by an electric discharge through a glass tube, with the time of vibration of another molecule of hydrogen in the sun, forming part of some great eruption of rosy clouds, and with the time of vibration of another molecule in Sirius which has not ​transmitted its vibrations to our earth, but has simply prevented vibrations arising in the body of that star from reaching us.
In a subsequent chapter we shall consider the further progress of our knowledge of Temperature as a Quantity.
ON THE AIR THERMOMETER.
The original thermometer invented by Galileo was an air thermometer. It consisted of a glass bulb with a long neck. The air in the bulb was heated, and then the neck was plunged into a coloured liquid. As the air in the bulb cooled, the liquid rose in the neck, and the higher the liquid the lower the temperature of the air in the bulb. By putting the bulb into the mouth of a patient, and noting the point to which the liquid was driven down in the tube, a physician might estimate whether the ailment was of the nature of a fever or not. Such a thermometer has several obvious merits. It is easily constructed, and gives larger indications for the same change of temperature than a thermometer containing any liquid as the thermometric substance. Besides this, the air requires less heat to warm it than an equal bulk of any liquid, so that the air thermometer is very rapid in its indications. The great inconvenience of the instrument as a means of measuring temperature is, that the height of the liquid in the tube depends on the pressure of the atmosphere as well as on the temperature of the air in the bulb. The air thermometer cannot therefore of itself tell us anything about temperature. We must consult the barometer at the same time, in order to correct the reading of the air thermometer. Hence the air thermometer, to be of any scientific value, must be used along with the barometer, and its readings are of no use till after a process of calculation has been gone through. This puts it at a great disadvantage compared with the mercurial thermometer as a means of ascertaining tempera​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/63 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/64 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/65 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/66 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/67 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/68 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/69 ​proportional to the temperature and may be attributed to the expansion of the substance. The third term is constant.
* ↑ Pupil of Galileo; died 1647.
* ↑ Annales de Chimie et de Physique, xlv. (1830).
* ↑ Professor of Astronomy in the University of Upsala.
* ↑ 'From Hermes or Mercury, the imagined inventor of chemistry.'—Johnson's Dict.
* ↑ Ann. de Chimie et de Physique, xxi. p. 333 (1822).
* ↑ Dr. Joule, however, finds that the rise of the freezing point of a delicate thermometer has been going on for twenty-six years, though the changes are now exceedingly minute.—Phil. Soc. Manchester, Feb. 22, 1870.