It has been shown that if the specific heat of a solid be multiplied by the chemical equivalent of that solid, the result will be approximately a result that has been of some value in determining which of various values is the true chemical equivalent of the substance. For compounds the result is approximately 3. As 1 pound of water requires 1 unit of heat to raise its temperature 1°, its specific heat is thus said to be unity. All other substances are referred to water as a basis. Thus when we say that lead has a specific heat of 0.0314 we mean that to heat a pound of lead to a certain temperature only requires about 3 per cent. of the amount expressed in B.Th.U. that would be required to raise the temperature of an equal weight of water by the same amount. It is necessary to know the value of the specific heats of brick, iron, fuel and its products, in order to calculate pyrometric effects, furnace temperatures, etc. For the purpose the Table VII of specific heats will usually serve. More extended tables are found in most pocket books.

Gases have two specific heats that at constant volume and that at constant pressure, the latter being greater and due to the work done in expanding to constant pressure. Table VIII gives the specific heat of the more usual gases met with in combustion.

The specific heat of all substances appears to increase with heat, more especially in the case of the gases. This is not of much importance in boiler work but is considerable in gas engine research. In high temperature work the increase must be considered, but no error is introduced by neglecting the change when results are finally stated at low temperatures. The increase of specific heat with temperature is most marked in the case of the more easily liquefied gases.

Specific heat, then, is the relative amount of heat necessary to give to bodies a given temperature. The specific heat of water is called one, or unity, and that of other bodies is stated as the fraction of unity relative to water. Most substances about a furnace, as firebrick, have a specific heat of about 0-2. The total heat in any body is thus the product of its mass, its temperature and its specific heat as compared with some substance at another temperature and in the same state physically. Thus ice, water and steam, which are chemically identical, differ in their physical states and cannot be so compared. The specific heat of ice is only about 0.504 and that of steam is 0.480. Ice at 32°F. may have heat added to it

until it becomes water at 32°F.

In both

Water at 212°F. will absorb heat and become steam at 212°F. these cases we see no change of temperature due to the additional heat, but we see a change of physical condition. One pound of ice has absorbed 142 B.Th.U. of heat to enable it to exist as water. Any further heat then added will increase the temperature until 212°F. is reached. Then we may add 965-7 B.Th.U. to the water with no change of temperature, but we get the water in the still higher physical state of steam. In each case the heat has become hidden or latent. It is not apparent as temperature, but is occupied in keeping the molecule liquid or gaseous as the case may be. Heat which thus disappears in changing the

state of a body is termed latent heat.

Latent Heat.

Latent heat is thus the specific heat of the changed state of a body. It is not stated, however, as is specific heat, in terms of the ratio to water, but in actual

heat units per unit of weight, as in calories per kilogram or B.Th. U. per pound. Thus the latent heat of water is said to be 142-6, because the melting of 1 pound of ice demands 142-6 B.Th.U. It is important to know the latent heat of a few substances. Some are given in Table IX below, those marked § being hypothetical and not definitely determined.

Heat becomes latent not merely by such a process as actual boiling of water by heat. It becomes latent equally when water is converted to vapour by absorption in dry air the heat must come from somewhere in such a case, and it comes primarily from the air or from the wooden floor on which water has been sprinkled for cooling purposes. If steam be heated above its saturation temperature it will now only absorb about 0.480 of a unit. Hence the specific heat of steam is barely half that of liquid water. After a very considerable further addition of heat, a point is reached where the temperature again ceases to rise; but again here is a change of state. The water is split up into constituent elements of oxygen and hydrogen, and one pound of steam will absorb 6,900 thermal units during the splitting up of its chemical affinities, showing the great energy of chemical changes, for to melt ice requires 142 heat units per pound; to vaporize the water requires 965-7 heat units, and to decompose it demands 6,900. No matter how it occurs that a body changes its state, heat is given out or absorbed. To set free the solid hydrogen or solid water locked up in a piece of coal demands heat which is rendered latent. Thus heat is rendered latent when carbon is vaporized, and when again carbon is reduced from its state of carbonic acid gas to the solid form of wood by the action of the living forces of a tree, the heat is again set free by the solidification of the carbon; but the heat rendered latent in the decomposition of a body is known as the heat of dissociation, and, like latent heat, is expressed in actual heat units.

Dissociation.

The heat absorbed in any process of chemical dissociation is an exact equivalent of the heat which is set free when the same substances combine. Thus if 1 pound of hydrogen unites with 8 pounds of oxygen to produce 9 pounds of water, the heat of combination is 62,100 B.Th.U., and therefore the heat of dissociation of water is 62,100÷9-6,900 B.Th.U.

There now remains to consider only the

Unit of Heat.

The unit of heat is merely an arbitrary measure of comparison. In British

1 From solid condition in coal.

measures it is the amount of heat necessary to raise the temperature of 1 pound of water through 1°F. at or near 32°F.

In the metric system it is the amount of heat necessary to raise the temperature of 1 kilogram of water through 1°C.

9

As 1 kilogram=2.204 pounds and 1°C.=3°F. the ratio of the two units is 2-204 × 9÷5=3-968, the reciprocal of which is 0-252.

The British Thermal Unit is written B.Th.U., and the metric unit is called the calorie and is written cal. Therefore 1 cal. 3.968 B.Th.U., and 1 B.Th.U= 0.252 cal. For near approximation the ratio of 4 : 1 may be employed.

The heat unit is employed to express latent heat of combustion of or dis

sociation.

It is necessary to have a statement of the relation of the heat form of energy or

Unit of Work.

The unit of work is expressed in the form of the earth's attraction.

For the purpose of the engineer the attraction of the earth is measured by the pull exerted at sea level in the latitude of London upon a piece of metal which is called the pound. The work done in lifting one pound through a height of one foot is a unit of work and is called the foot pound. Heat and mechanical work are mutually convertible. Dr. Joule, of Manchester, by the agitation of water by means of falling weights, ascertained that the unit of heat or B.Th.U. is the equivalent of 772 pounds raised one foot, or 772 foot pounds at the latitude and elevation of Manchester, and, with very slight variation, of no account in engineering, at any spot on the earth's surface. Joules' determination of 772 was made by means of thermometers less perfect than those now procurable, or his figure would have been 778 foot pounds, as since found by Rowland.

The mechanical equivalent of 772 foot pounds per degree Fahrenheit becomes 1,389.6 foot pounds per degree Centigrade.

Expressed in terms metrical altogether or in kilogram Centigrade units, the equivalent is 3,063-54 foot pounds or 423.55 kilogram metres.

Thus the calorie is 423-55 km. =3-968 B.Th.U.

With the more modern figure of 778 foot pounds =1 B.Th.U.=3,087-3 foot pounds. Per calorie=426-84 kilogram metres, so that 1 B.Th.U.=107.78 metre kilograms.

Weight.

Like the British pound, the kilogram is simply a piece of metal, and work units are done in raising it against the pull of gravity.

whose relation to the foot pound is 7.231.1.

kilos.

The kilogram is 2-2 pounds (actually 2.2046212).

Hence the kilogram metre

The pound is thus 0-4536

The metre or unit of length is 39.370432 inches, or say 3 feet 3 inches, and very nearly for easy remembrance and mental calculation.

The American yard is said to be 36-001 British inches, an inappreciable difference in engineering but noticeable in mechanical fine work.

Errors in converting units are most likely to occur when units are compound, as when converting pounds per square inch to kilos per cm.2

Very closely the English ton of 2,240 pounds resembles the French tonne of 1,000 k.=2,204-6 pounds.

Also 1 k. per linear metre is equal nearly to 2 pounds per linear yard, and 9 calories per cube metre is very closely 1 B.Th.U. per cubic foot.

Gravity.

Gravity G at Greenwich is 32-19078 feet per second acceleration per second, usually written 32-2 per sec.2

2

The expression /2G may be approximated as 8.

Metrically, G=9-8117 metres per second at Greenwich.

The true value at any other latitude (L), in centimetres per second' is980-6056-2.5028 Cos.2 (L)-0-000003 H,

where H is the height above sea level in centimetres.

Other compound units that are useful are as follows

To find the number of cubic feet of air at 62°F. chemically consumed for one pound of fuel, take the percentage of carbon, hydrogen and oxygen in fuel. To the carbon add three times the hydrogen and subtract four-tenths of the oxygen and multiply the remainder by 1.52. The product is the cubic feet of air (A). Thus A 1.52 (C+3 H−0·4 O).

The weight of air per cubic foot is Ax 13-14 in pounds.

The total weight of gaseous products per pound of fuel is found by multiplying the percentage of carbon by 0-126 and that of the hydrogen by 0-358. The sum gives the total gases (W), thus W=0.126 C + 0.358 H.

The total volume is found by multiplying the carbon percentage by 1·52 and the hydrogen by 5.52; the sum of these is the total volume (V) in cubic feet at 62°F., thus V=1·52 C+5·52 H.

The volume at any other temperature (T) is V' =

=

Chapter XII

THE CALORIFIC POWER OF FUEL

Calorific Formula.

ULONG and Petit and subsequently Favre and Silbermann determined the

DUL

calorific capacity or heat of combustion of many substances with more or less accuracy. Dulong endeavoured to find a formula for calculating the heat of combustion of any fuel of which the chemical composition was known.

The capacity given by him to carbon was 7,295 calories. The latest determination of Berthelot is 8,137 and that for hydrogen is 34,500.

Dulong's formula for fuel according to its composition was with the correction to modern coefficients.

Cal. =8,137 C +34,500 (Hg) where

C is the carbon in 1 kilogram of fuel and H and O are the hydrogen and oxygen respectively, it being assumed that the oxygen is already combined with hydrogen and that so much of the hydrogen is already useless. Any error would appear to be on the safe side, and the formula assumes the return of all the gases to 0°C.

In actual practice, of course, the gases pass at a temperature of over 100°C., and the water is in the form of vapour, and the calorific capacity of hydrogen is often taken as only 29,150 B.Th.U. to allow for the heat absorbed in vaporization of the water.

In Germany, Dulong's formula is used in the form

Cal. = 8,100 C +29,000 (H-9)+2,500 S-600 W.

where S is the sulphur present, and W is the weight of hygroscopic water.

Seeing that in coal the hydrogen is as solid apparently as the carbon, it appears correct to take something off the co-efficient of hydrogen to allow for the heat absorbed in gasefying it, and in the above formula the subtraction of 150 calories perhaps helps to make this formula coincide very closely with calorimetric results.

Possibly also the rounding off of the co-efficient for carbon from 8,137 to 8,100 helps to correct for the vaporization of the carbon compounds which are exothermic when first formed and do not give up the full heat value of their separate hydrogen and carbon. Thus both marsh gas, CH,, and ethane, CH,, give out heat when formed and require it again when dissociated, and coal is so complex a body, as are also liquid fuels, that very little positive knowledge can be assumed: it is sufficient to know that the formula last given is a very fair approximation to

the truth.