An elementary treatise on heat

Front matter

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PRESENTED 1JY

V

Chapter I

ON TEMPERATURE AND ITS MEASUREMENT. THE MERCURIAL THERMOMETER. MAXIMUM AND MINIMUM THERMOME¬ TERS.

1. If we place a poker in a fire, and after some time remove it, it feels hot The physical' cause of this sensation is called heat A piece of iron which has been exposed to the air in Britain will generally feel cold.

If we hold for some time in the right hand a piece of iron which feels hot, and then grasp the right hand with the left, the left hand will experience a sensation of heat, or the right hand will feel hot to the left, and at the same time the left hand will feel cold to the right. The same will be true if we hold for some time in the right hand any other body which feels hot. The fact that the right hand feels hot to the left after holding the hot iron, while it may have felt neither hot nor cold before, proves that the hand has re¬ ceived heat from the iron. We therefore infer that when a body feels hot to the hand it imparts heat to the hand while touching it. It then follows that, because the right hand feels hot to the left hand, heat must pass from the right hand to the left. But the left hand feels cold to the right hand and associating this sensation with what we have just proved, viz., that heat passes from the right hand to the left, we infer that a body feels cold to the hand when heat passes from the hand to the body. We may arrive at the same conclusion by holding in the right hand a piece of very cold iron, after which the right hand will feel cold to the left, and the left hand warm to the right. Now, the fact that the left hand feels warm to the right, shews that heat

G.

TEMPERATURE.

passes from it to the right hand, and we infer that this also is the reason why the right hand feels cold to the left. Also the fact that the right hand has been made to feel cold to the left by its contact with the iron, shews that heat must have left the hand and entered the iron, which ac¬ counts for the latter feeling cold to the hand.

2. We thus see that a body feels hot to the hand when heat passes from the body to the hand, and cold when it passes in the opposite direction. The sensations of heat and cold are therefore essentially relative. This may be further illustrated thus:—

Place the right hand in a mixture of ice and salt and the left hand in hot water, then place both in cold water; the cold water will feel warm to the right hand and cold to the left, shewing that the sensation of heat or cold depends on the condition of the hand relative to the hot or cold body, and not simply on the state of the body itself. The water in a bath sometimes feels warm to the hands and cold to the feet.

3. The quality of a body , in virtue of which it seems hot or cold , is called its temperature. If a body feel hot to the hand, it is said to be at a higher temperature, and if it feel cold, at a lower temperature, than the hand. Now we have seen that a body feels hot or cold according as heat passes from it to the hand, or from the hand to it. The direction of the flow of heat then, in this case, determines whether the body or the hand is at the higher temperature; and apply¬ ing the same criterion in all cases to determine whether of two bodies is the hotter, we may define temperature thus :—

Def. The temperature of a body is its thermal condition with reference to its power of communicating heat to, or of receiving heat from , other bodies; the body A being said to have a higher temperature than B ifB gain heat from A when they are placed in contact.

Hence , if when two bodies are placed in contact neither of them gain heat at the expense of the other , the two bodies are said to be at the same temperature.

4. When two bodies have the same temperature, they are said to be in thermal equilibrium with each other.

TEMPERATURE.

Now it is found experimentally that if two bodies A and O are each in thermal equilibrium with a third body B , then if A and C be placed in contact, they will be in thermal equilibrium with each other, provided no chemical action take place between them. Hence we infer that, bodies which are in thermal equilibrium with the same body , are in thermal equilibrium with each other; and our definition is consistent with itself when it directs us to assign to them all the same temperature, viz., that of the body with which they are all in thermal equilibrium. It is on this principle that the employment of thermometers depends. If two bodies act chemically upon one another they may be put into thermal communication with each other by means of a diaphragm impervious to either body, but pervious to heat. If no heat be lost or gained by either from the other the bodies are in thermal equilibrium, but it will be seen that unless radiation can take place between them all we can say respecting them is that they are each in thermal equilibrium with the dia¬ phragm, and this is no more than saying that they are in thermal equilibrium with a third body.

5. If we touch in succession several bodies all of which feel hot, some will feel hotter than others; and similarly, if we touch several bodies all of which feel cold, we shall expe¬ rience sensations of different degrees of coldness. Now if all the bodies are formed of the same material, and in the same mechanical condition, we are justified in assuming that, of two hot bodies, that is at the higher temperature which feels the hotter, and similarly for two cold bodies. But if the bodies be of different materials we are no longer justified in making this assumption, and for this reason; viz., that the power of a hot body to produce the sensation of heat does not depend entirely on its thermal condition with reference to its power of communicating heat to other bodies (that is, on its temperature), but depends also on the rate at which it can transmit heat through its substance, and this is different for different materials. Thus a piece of iron and a hollow piece of wood may both feel hot, and the iron feel much hotter than the wood; yet if the iron be placed in the hollow of the wood for some time, it may then feel hotter than before, thus shewing that heat has passed from the wood to the

1—2

MEASURE OF TEMPERATURE.

iron, and that the iron was therefore originally at a tempera¬ ture lower than that of the wood. Again, if a piece of iron and a piece of wood be in contact for a long while in a hot place, the iron will feel much the hotter though it is in thermal equilibrium with the wood, and therefore at the same temperature as the latter. This is due to the differ¬ ence in the conducting powers for heat of iron and wood, and will be discussed in a subsequent chapter. In fact, the in¬ tensity of the sensation of heat depends on the rate at which heat enters the skin, and not simply on the temperature of the body touched.

6. In order, then, to determine whether of two bodies A and B is the hotter, we ought to place them in contact, and determine in which direction the heat passes; but as this is frequently a very difficult, or impossible, operation, recourse must be had to some more convenient method. This is ge¬ nerally accomplished by taking a third body (7, very small compared with A or B } and called a thermometer. This is placed in contact with A till it is in thermal equilibrium with it, and therefore at the same temperature; and sub¬ sequently in contact with B , till it is again in thermal equi¬ librium, and therefore at the temperature of B ; and it is ascertained whether the temperature of C is higher when in equilibrium with A or with B by observation of some pro¬ perty of the body G, which changes with its temperature, as, for example, its volume.

If the body C be in precisely the same thermal condition both when it is in thermal equilibrium with A and when in thermal equilibrium with B, it follows from Art. 4 that A and B are at the same temperature. Hence, a thermometer will enable us to determine whether a number of bodies are at the same temperature or not, and if not, to arrange them in the order of their respective temperatures.

Though the changes in volume of the thermometric substance are generally taken to indicate the variations of temperature which it experiences we may avail ourselves of any other property of the thermometric substance which changes with temperature and which can be readily observed. Thus in tempering steel the colour exhibited by the thin film of oxide on its surface serves to indicate the temperature.

MEASURE OF TEMPERATURE.

Sometimes the electrical resistance of a platinum wire, which increases with the temperature, is employed to indicate the temperature to which the wire is exposed; or the thermo¬ electric current produced by a pair of dissimilar metals is employed to indicate the difference of temperature of the junctions of the metals. The 'pitch of the note of an organ pipe will indicate the temperature of the air, and as nearly all the physical properties of bodies change with the temperature almost any property may be made available for thermometric purposes.

7. All bodies, with very few exceptions, among which may be mentioned iodide of silver, stretched caoutchouc (in the direction of the tension), water at or near the freezing point and some alloys, expand when heated, and contract again on cooling, so that, other things being the same, their volumes increase as the temperature rises, and return to their original values when the bodies regain their original tempera¬ ture ; though glass presents a curious exception to the last statement as its volume does not return to its original value after expansion until a long time after the original tempera¬ ture has been restored. Suppose it possible to measure accurately the volume of a given small quantity of some substance, as, for instance, mercury. Then if the mercury be placed in contact with each of any number of bodies in succession, till it is in thermal equilibrium with it, and its volume be measured in each case, we can arrange the series of bodies in order of temperature.

8. Suppose K, L, and M to be three bodies of which K is the coldest and M the hottest. Then, although we can arrange the bodies in order of temperature by means of the small quantity of mercury, or other substance, whose volume we measure, yet we are not at present in a position to tell whether the difference between the temperatures of K and L is greater, equal to, or less than, the difference between the temperatures of L and M\ in fact we have as yet no graduated scale of temperature. Now, if our thermometer consist of a given mass of mercury, we may, if we please, define equal increments of temperature to be such as pro¬ duce equal increments in the volume of the mercury, and it will then follow directly from the definition that the differ-

MEASURE OF TEMPERATURE.

ence between the temperatures of two bodies is proportional to the difference in the volume of a given mass of mercury when in thermal equilibrium with the first and second body respectively. We are thus enabled to form an arbitrary scale of temperature which will depend upon the properties of the particular substance (in this case mercury) which forms our thermometer. As, however, the mercurial ther¬ mometer is used much more extensively than any other, before alluding to other scales of temperature we shall de¬ scribe the construction and mode of graduation of the ordi¬ nary mercurial thermometer.

The problem of comparing differences of temperature in different parts of the scale, or of determining equal intervals of temperature, is comparable in difficulty with the corre¬ sponding problem in time. We meet with no such difficulty ~ in the measurement of lengths because the lengths which are to be compared may be superposed, or a third body of constant length may be superposed on each in succession. It is obvious, however, that an interval of time of to-day cannot thus be compared with an interval to-morrow, for having once elapsed it is gone for ever and some other method of com¬ paring intervals of time must be resorted to. The First Law of Motion indicates the criterion of equality in intervals of time. The principles of Thermodynamics teach us how to determine the equality of intervals of temperature but until we have studied the action of heat engines we must be content with a scale of temperature derived from the properties of some particular substance or group of sub¬ stances.

9. If we wish to detect and measure very small incre¬ ments in the volume of a substance, it is obviously most convenient to employ, when possible, a fluid as the substance whose volume is to be changed, for we can then avail our¬ selves of a large volume of fluid contained in a suitable reser¬ voir (e. g. the bulb of the thermometer), while we can cause the free surface to be contained in a tube of very small bore, and thus an extremely small increase in the volume of the fluid will be accompanied by a considerable movement of the surface in the tube. In this case it is plain that the change of volume observed is only the difference between the change

THE MERCCJIHAL THERMOMETER.

of volume of the fluid and of the envelope in which it is con¬ tained; but this is no serious inconvenience, since fluids can be found which expand very much more than glass, of which the envelope is usually made; and even if we employed solid bars, we should have to take care that our measuring instruments did not themselves expand, or we should obtain no better result.

v

10. To construct a mercurial thermometer a Fig - glass tube of very fine bore is taken, and a small bulb is blown at one end, while a cup is formed at the other extremity as shewn in Fig. 1. In this cup is placed a small quantity of mercury, and the bulb is then heated over a flame. The air in the bulb expands when heated, and a con¬ siderable portion of it escapes by bubbling up through the mercury in the cup. The bulb is then allowed to cool, when the pressure of the air within it diminishes (as explained in Chapter IV.), and the pressure of the external air drives some of the mercury in the cup down the tube and into the bulb. If it be desired to take great care in the construction of the thermometer, this process is repeated until the bulb and a portion of the tube are filled with mercury when at the ordinary temperature; but in general a more expeditious process is adopted. A small portion of mercury having entered the bulb, as described above, the latter is heated until the mercury boils, when the heavy mercury vapour drives out the lighter air at the top of the tube, and, when the whole of the air has been expelled, the bulb and tube are filled with mercury vapour (except the space occupied by the liquid mercury remaining in the bulb). The instru¬ ment is then allowed to cool, and as the mercury vapour condenses, the mercury in the cup is forced into the tube by the pressure of the external air, and, except for a very small quantity of air which may have been left behind, the bulb and tube are completely filled with liquid mercury. The instrument is then heated to a temperature somewhat higher than the highest for which it is intended to be suosequently used, when the mercury expands so as to com¬ pletely fill the tube, and drive out any residue of air which

DETERMINATION OF THE FREEZING POINT.

may have been left above it. The top of the tube is then sealed with the blowpipe while the mercury remains hot. The instrument should be kept for some months after the bulb has been blown before it is graduated, because glass after being highly heated does not acquire its permanent volume for some time, and this is the reason why, in the filling of the best thermometers to be used for moderate temperatures only, the mercury is not boiled, but the air is driven from the bulb by heating it slightly many times in succession. (See Art. 7.)

The external diameter of the tube of a thermometer is generally very great compared with the diameter of the bore. Moreover, it is of importance for many purposes that the bulb should be constructed of very thin glass. In most well-made thermometers the bulb is elongated so as to be almost cylindrical, while its external diameter is fre¬ quently not greater than that of the tube. The section of the bore of the tube is often flattened instead of circular so that the mercury may expose a broad surface to the front of the thermometer though its sectional area remains very small.

11. It remains to graduate the thermometer. It is found that under ordinary atmospheric pressure pure ice always melts at the same temperature, which is called the freezing point, and also that the temperature of the steam above the surface of boiling water depends only on the barometric pressure to which it is subjected. A pressure of 29 905* inches of mercury at the freezing point in the latitude of London and at the level of the sea is generally taken as the standard pressure, and the temperature of the steam above the surface of water boiling under this pressure

* The pressure of the standard atmosphere is generally taken to be equal to that of 760 millimetres or 29*9215...inches of mercury at 0°C. at the sea-level in latitude 45°. On account of the variation of gravity with the latitude this is equivalent to the pressure exerted by 29'905 inches of mercury at the sea-level in the latitude of London, or by 29*898 inches of mercury in the latitude of Manchester. In order to avoid ambiguity arising from the variation of gravity, it has been proposed to adopt as the standard pressure a pressure of a megadyne per square centimetre. This is equivalent to 74*964 centimetres or 29*514 inches of mercury at 0°C. at the sea-level in the latitude of London. This would, however, necessitate a reconstruction of our thermometric scales, since the temperature of steam above water boiling under this pressure is only about 93*63° C.

DETERMINATION OF THE BOILING POINT. 9

is always the same, and is called the boiling point. If the height of the barometer differ from this standard height, in graduating the thermometer a correction has to be made in consequence. (The correction amounts to about T4° F.* for one inch of mercury.)

In order to graduate the instrument it is first placed in melting ice, and a mark made on the tube at the height at which the surface of the mercury stands. This mark corresponds to the freezing point, and should always be determined before the boiling point, because when it has been heated to the latter temperature, the glass does not .at once contract to its proper volume, and, if the freezing point were determined immediately after the boiling point, the mark would after some time be found to be too far down the tube. In determining the freezing point the thermo¬ meter should be immersed so far in the ice that the surface of the mercury is only just visible above it, in order that the whole of the mercury may have the temperature of the ice. In determining the freezing point it is not generally necessary to observe the height of the barometer, for the

1 0

melting point of ice is lowered by only F. for an increase

of pressure amounting to a whole atmosphere.

12. In order to determine the boiling point, the instru¬ ment shewn in Fig. 2 and called a hypsometer is employed. This instrument consists of a vessel A, containing water, the upper portion of which is a tube open at the top. Over this tube is placed the wider tube BO, which is closed at B by a perforated cork through which the stem of the thermometer T passes. C is a small tube for the exit of the steam, sloping downwards in order to allow the ready escape of condensed water. I) is a small bent tube containing water, which is sometimes at¬ tached to the instrument to indicate if the pressure of the steam within exceed that of the external air. When the water in A is made to boil, the thermometer soon becomes sur¬ rounded by an atmosphere of steam, which is

* For description of Fahrenheit’s scale see Art. 15.

Fig. 2.

DETERMINATION OF THE BOILING POINT.

itself surrounded by a steam-jacket, on account of the steam having to pass down between the tubes before escaping at G y and is thereby prevented from cooling. The thermometer is pushed through the cork at B till the surface of the mer¬ cury is only just visible above it, in order that the whole of the mercury may be exposed to the same temperature. The stem is then scratched at the level of the surface of the mer¬ cury (the height of the barometer being observed at the same time, in order to make any necessary correction for the pres¬ sure not being the standard pressure of 29 905 inches of mer¬ cury). The mark so placed upon the tube is called the boil¬ ing point.

13. It is important that the thermometer should be im¬ mersed in the steam and not in the water, for the tempera¬ ture at which the water will boil depends on a great many conditions. For example, the material of which the vessel is composed affects the boiling point, and water will boil in a metallic vessel at a lower temperature than in a vessel made of glass. Again, saline impurities dissolved in the water will cause the boiling point to be raised, but the temperature of the steam above the surface of the water depends only on the pressure.

If a quantity of common salt be dissolved in the water the temperature of the solution may be raised about 16° F. above the boiling point, but the temperature of the steam will be the boiling point due to the existing pressure. If two thermometers be immersed in the steam above the solution of salt, one of which has its bulb naked and clean while the other has a piece of cotton cord, which has been dipped in a strong solution of calcic chloride, twisted round the bulb, the naked thermometer will indicate 212° F. while the other may denote a temperature of 227° F. or even higher. At the same time a third thermometer immersed in the solution will read 228° F. This experiment shews that care should be taken to see that the bulb of the thermometer is clean when immersed in the steam.

14. It is very important that when the fixed points are marked upon a thermometer tube the tube should be in the same position relative to the vertical as that in which it is to

SCALES OF TEMPERATURE.

be subsequently used. For if a thermometer be observed in a horizontal position, and be then turned into the vertical position, the reading will be lowered in consequence of the increased pressure in the bulb, and the effect will be greater the longer the column of mercury and the thinner the walls of the bulb.

As the air has no access to the interior of a thermometer it follows that the reading of a thermometer will depend to some extent on the barometric pressure, for the pressure of the air will compress the bulb of the thermometer diminish¬ ing its volume by an amount depending on that pressure. This can be rendered very apparent by placing a thermometer in the receiver of an air pump and exhausting the air when the thermometer will continue depressed after sufficient time has been allowed for the interior of the receiver to regain its original temperature, the depression being due to the ex¬ pansion of the glass under the diminished pressure of the air. When self-registering mercurial thermometers are employed for determining the temperature at considerable depths in the sea great care must be taken to protect the bulbs from the great pressure to which they would otherwise be exposed.

15. It remains now to subdivide the stem of the ther¬ mometer between the freezing and boiling points into de¬ grees, and to mark off degrees above the higher and below the lower of these temperatures. There are three different modes of doing this in general use in different parts of Europe, in other words, there are three distinct scales of temperature. In Fahrenheit’s scale, which is chiefly adopted in England, the freezing point is marked 32° and the boiling point 212°. The tube between these points is then divided into 180 equal portions, and divisions equal to these marked off above 212° and below 32°. In the scale of Celsius, better known as the Centigrade scale, the freezing point is marked 0°, and the boiling point 100°, the tube between these points being divided into 100 equal parts and equal divisions marked off along the rest of the tube. This scale of temperature is now almost universally adopted by scientific men. The third scale of temperature, viz. that of Reaumur, is in very general use in ordinary life on the Continent. In it, as in the centigrade scale, the freezing

CALIBRATION OF THE TUBE.

point is marked 0°, but the boiling point is marked 80°. This scale, like that of Fahrenheit, has little to recommend it in preference to the centigrade, except its general use in some localities.

16. We shall now suppose that we are graduating a centigrade thermometer, and that the freezing and boiling points have- been marked upon its stem as described above. If the thermometer is not required for very accurate mea¬ surements the remainder of the work is very simple. The length of tube between the freezing and boiling points is divided into 100 equal parts, and these are marked off upon the tube, or on a box-wood or metal scale attached to it, by means of a dividing engine or otherwise, equal divisions being then carried on throughout the remainder of the tube. Each division thus' marked is called a degree, and those de¬ grees which lie below the are marked negative.

17. Now it is obvious that if there be any inequalities in the bore of the thermometer tube in different parts, equal lengths of the tube will not always correspond to equal increments in the volume of the mercury relative to that of the glass. The above mode of graduation is therefore not sufficiently exact for accurate instruments. In order to remove this cause of error, a small pellet of mercury, of a convenient length, is detached from the rest of the column, and by inclining and gently tapping the tube, is made to occupy different positions within it. The length of the pellet in each position is carefully measured, and, since its volume is constant, it follows that, if the length of a degree at any part of the tube is made proportional to the length of the pellet when occupying this position, each degree will correspond to the same increment of the apparent volume of the mercury in the glass. This process is called cali¬ brating the tube. The division of the tube is then conducted on this principle, and it is obvious that care and calculation are required in effecting it. A small pellet of almost any desired length can generally be removed from the rest of the column by tapping it so as to remove a long pellet, warming it, re-uniting the pellet to the column, cooling it and again tapping the tube. A pellet will then break off at the same freezing point, or zero of the scale,

SCALES OF TEMPERATURE.

point of the tube at which the last united to the column, and the column being shorter in this case, the pellet will be shortened by an equal amount. By carefully repeating this process we can remove a very short pellet.

All thermometers pretending to accuracy should be graduated on the glass tubes themselves, and not on a scale which can be detached from the instrument.

It has been remarked (Art. 9) that the expansion of the mercury with which we have been dealing, is not its actual increase of volume, but its apparent expansion when con¬ tained in a glass vessel, and is the difference between the actual increase of volume of the mercury and that of the in¬ terior of the part of the glass vessel which originally con¬ tained it.