LESSON XXVI.-ON THE RELATION BETWEEN HEAT AND MECHANICAL ENERGY.

242. Heat, being a form of molecular energy, is convertible under certain conditions into the other varieties of energy, but we shall here confine ourselves to its connection with mechanical energy, which is the only form we have yet minutely described.

243. Conversion of Mechanical Energy into Heat.This conversion takes place in the phenomena of percussion, friction, and atmospheric resistance. Thus when the blow of a hammer is arrested by an anvil, its visible energy is changed into heat. Again, it is well known that savages produce fire by rubbing two dry sticks together, and this is a conversion of the energy of motion into heat through friction. We have already shown (Art. 119) that when a body in motion is resisted by the atmosphere, there is a conversion of its energy into heat. Now in all these cases visible energy is absolutely annihilated as visible energy, and at the same time heat is created. There is, however, no creation or annihilation of energy as a whole, but merely an annihilation of one species, accompanied with the simultaneous creation of another species.

The conversion of mechanical energy into heat is one that can be produced with the greatest posible ease; the difficulty, indeed, is not so much to procure this conversion as to avoid it, and to this intent we use lubricants in order to diminish the friction of machinery as much as possible. Joule was the first to establish a numerical relation between mechanical energy and heat. He conducted his experiments in the following manner.

He attached a known weight to a pulley (Fig. 66), the axis of which was made to rest on friction rollers with the object of diminishing friction as much as possible. A string passing over the pulley was connected with a vertical axis r, so that when the weight fell a rapid rotatory motion was communicated to r. Now the shaft was made to work a set of

paddles immersed in a fluid in the box B, and a vertical section of one of these paddles is given in the figure. From this it is manifest that in this experiment the fall of the weight was made to agitate the liquid in B, and to heat it through this agitation. It is, in fact, a case of the conversion of mechanical energy into heat.

5215211

PADDLE

B

WEIGHT

FIG. 66.

By means of a number of such experiments, and others of a similar nature, Joule found that it required the expenditure of an amount of mechanical energy represented by 424 kilogrammetres in order to heat a kilogramme of water one degree Centigrade. In other words, if a kilogramme of water be dropped under gravity from the height of 424 metres the velocity which it acquires will, if wholly converted into heat, raise its temperature one degree Centigrade. Further, if it be dropped from twice this height its temperature will be raised 2o C., if from three times the height 3° C., and so on.

244. Compression of Gases.-Mayer, who at a comparatively early period had divined the law of the conservation of energy, endeavoured to calculate the mechanical equivalent of heat from the heating of gases through condensation; nevertheless his proof was not quite complete, and it was reserved for Joule to furnish the link necessary to its completion.

When we compress a gas we heat it; but are we at liberty. to imagine that the heating produced is the precise equivalent of the work spent in compressing it? Let us answer this question by asking another. Suppose we drop a weight into a large quantity of fulminating powder, the result is the generation of a large amount of heat; but are we at liberty to suppose that all this heat is the mechanical equivalent of the energy of the weight? Clearly not, for the fulminating powder has altered its molecular condition, and in the process of doing so there has been the generation of a large amount of heat. Now when gas is compressed its molecules: have been brought nearer together, and hence its molecular state is different. We therefore require to know what portion of the heat developed in the compression of a gas is due to the difference in its molecular state, and what to the mechanical work spent upon the gas.

Now Joule's experiments inform us that in the case of gas the particles are so far apart as to have no perceptible action on each other, so that none of the heat produced by condensation is due to the coming together of mutually attractive particles, but this heat is entirely the equivalent of the mechanical energy spent in the compression.

We see now why a gas suddenly expanded becomes cooled. Suppose, for instance, that condensed air is contained in a vessel similar to the boiler of a steam-engine, and that the vessel has a cylinder connected with it in which a piston works. This piston has above it the pressure of the atmosphere, equal, let us say, to a weight of 1,000 kilogrammes. For the sake of simplicity we may therefore suppose that the atmosphere is done away with, and that instead a weight * of 1,000 kilogrammes is placed upon the piston. Now let the condensed air be turned on under the piston, and let us suppose that in consequence the piston is raised one metre in height. A certain amount of work has thus been done by the air in the vessel equivalent to that spent in raising 1,000 kilogrammes one metre in height. This amount of mechanical energy of position has been created, and as a consequence so much heat energy must have disappeared. The

air will therefore have become colder in consequence of this expansion.

For a similar reason, when gas is suddenly compressed work is spent upon the gas, that is to say a quantity of mechanical energy is changed into heat, and the gas becomes hotter in consequence.

245. Conversion of Heat into Work.-Suppose in the instance just now given that instead of condensed gas we use steam under a considerable pressure.

Let it be introduced below the piston (Fig. 67), which is raised in consequence up to the top of the cylinder.

AIR

BOILER

FIG. 67.

Let the supply from the boiler be now cut off by shutting the valve viv, also let the steam below the piston escape into the air by opening the valve viii. The piston is now at the top of the cylinder. Next let the steam from the boiler be introduced above it by opening the valve vi, so as to cause it to descend, and when it has got to the bottom of its stroke let this steam be disconnected from the boiler by shutting vii, and discharged as vapour into the air by opening vi, so that when the steam is introduced below the piston it will once more mount upward. An alternating motion of the piston in the cylinder may be thus produced, and a large amount of work may be accomplished if the piston-rod be connected with appropriate machinery.

This arrangement is, in fact, the high-pressure steamengine such as we see in a railway locomotive.

In the low-pressure engine the steam, when once it is cut off from the boiler, instead of being driven out into the air is driven into a vacuum chamber, in which it is cooled by a copious supply of cold water. It is thus condensed and its pressure rendered nil.

Thus in the high-pressure engine we have the force of the steam on one side of the piston, and the pressure of the atmosphere on the other, so that the steam must have a higher pressure than the atmosphere, and hence the name of the engine.

But, on the other hand, in the low-pressure engine we have the pressure of the steam on one side, and a vacuum, or nearly so, on the other.

246. It will be noticed that in both engines we obtain useful work only by cooling the steam; for had the steam not been cooled below the temperature at which it issued from the boiler, we should have been unable to obtain that difference of pressure which keeps the piston going.

In the low-pressure engine the steam is cooled by being brought into contact with cold water in the vacuum chamber of the engine, while in the high-pressure engine it is driven out into the air and cooled in consequence.

Cooling is, in fact, quite essential to the working of any heat-engine; for as long as all the parts of an engine are at the same temperature it is absolutely impossible to convert heat into work. Heat is only converted into work by being carried from a body at a higher to one at a lower temperature, and even then only a small proportion of the whole heat so carried can be changed into work.

247. Carnot, a French philosopher, who was the first to study this subject, very ingeniously likened the mechanical capability of heat to that of water, remarking that just as water on the same level can produce no mechanical effect, so neither can bodies at the same temperature; and just as we require a fall of water from a higher to a lower level in order to obtain mechanical effect, so likewise we must have a fall of heat from a body of higher to one of lower temperature.