of cotton soaked in ether may be used, in which case the flash is readily seen as the piston is forced down.

This experiment shows that the dynamical heating of a gas when compressed is very considerable. When air at 0° C. is compressed in a non-conducting cylinder, its rise in temperature is 90° when compressed to half its original volume, 429° when compressed to one-tenth, and 1084° when compressed to onefiftieth of its volume.

In air compressors the heat developed in this way has to be removed by a stream of cold water.

413. Cooling Due to Work of Expansion.-A gas when it expands is cooled because it does work; but is all of the cooling due to the external work done?

That is, if it were possible to pull out the piston of a cylinder containing gas so suddenly that the gas could not follow it and exert pressure against it as it moved back, would the gas be cooled or not?

This question was asked by Joule, and answered by an ingenious experiment in which he connected a copper receiver containing air at a pressure of 22 atmospheres, with another from which the air had been exhausted. On opening the stopcock between the two vessels the air expanded and filled both, but of course it did no external work in expansion since there was no piston to push back.

It was found after the expansion that the mass of gas as a whole had not changed in temperature, the gas rushing into the vacuum being heated just as much as the expanding gas in the other vessel was cooled.

More exact determinations show, however, that most gases when expanded are very slightly cooled even when no external work is done and it is this cooling of which advantage is taken in the process of making liquid air (§453).

414. Specific Heats of a Gas.-We can now see why the specific heat of a gas at constant pressure must be greater than that at constant volume. For when a mass of gas is warmed while the pressure is kept constant, it expands, doing external work. The heat supplied must therefore furnish the energy for this work as well as that which simply increases the energy of motion of the gas molecules. But when a gas is kept at

constant volume there is no external work done and the heat supplied all goes to increase the molecular energy of the gas. According to Joule's experiment (§413), the increase in molecular energy is just the same in one case as in the other, so that the difference between the heats required in the two cases is entirely due to the external work done, and is mechanically equivalent to that work.

415. Convective Temperature of the Atmosphere.-The change of temperature caused by the compression or expansion of air plays a most important part in the atmosphere. Masses of air moving upward expand and cool, while descending air masses are heated by compression. This in part serves to determine the distribution of temperature in the atmosphere, the temperature at any height tending to be equal to that which a mass of air rising to that point from the surface of the earth acquires in consequence of its expansion.

The presence of water vapor modifies what may be called the convective temperature at a given height, for the latent heat given out as the moisture in a rising mass of air condenses retards the cooling. A mass of dry air at 20° C. at the earth's surface, will be cooled to -53° C. in rising 3 miles.

When there is a downward current of air, as in case of the wind blowing over mountains and sweeping down into the valleys beyond, the compression of the air as it descends raises its temperature so that it becomes a warm wind, as in the so-called "foehn" wind of the Alps or the "dry chinook" of Montana.

416. The Nature of Heat Energy. When a body is heated it radiates heat to surrounding bodies. The rate at which a given body gives off radiation depends on its temperature. As it grows hotter the radiation may become so intense that the body glows or is incandescent. Later it will be shown that this radiation is made up of waves in which the vibrations are almost inconceivably rapid. These waves originate in the hot body and take energy from it so that it cools as it radiates. It is believed that these waves are a consequence of rapid vibratory motions in the molecules of the body, and that the heat energy of a body exists, in part at least, in the form of energy of motion of the molecules.

Radiation comes from all bodies even those that we ordinarily

speak of as cold. The molecules of all bodies are therefore considered to be in rapid vibration, though we are ignorant of the exact nature of this vibration.

But heat energy exists in bodies in another form than energy of vibratory motion, for bodies usually expand when heated, and consequently the particles or molecules are slightly moved apart. And since in case of solids and liquids there is a strong cohesive force between the particles, work must be done in separating them, and the energy which does this work comes from the vibratory energy of the molecules, which is thus transformed and stored up in the body as potential energy.

Another instance of such a transformation is in case of change of state, as when ice is melted. Here also particles which are held firmly in a comparatively fixed position in the solid state are dragged away from each other and set free to slip past each other in the liquid state, and to effect this change work must be done, and consequently in this case also a certain amount of vibratory heat energy must be changed into energy of separation or potential energy.

Experiment is in complete agreement with this conclusion and shows that a considerable amount of heat energy must be given to a body to change it from the solid to the liquid form.

Therefore heat energy is thought of as existing in the body both in the form of kinetic energy or energy of motion of molecules, and as potential energy due to the separation of molecules in opposition to their mutual attractions.

417. Temperature Depends on the Kinetic Energy of the Molecules. When two bodies at different temperatures are put in contact there is a transfer of molecular energy from one to the other until equilibrium is established. When there is no longer any change taking place, it is said that both are at the same temperature. This transfer of energy is doubtless due chiefly to the energy of motion of the molecules, as it is difficult to see how the potential energy of the molecules of one body could affect appreciably the condition of a neighboring body. When ice and water are mixed together until both come to the same temperature, all flow of heat from one to the other entirely ceases and yet a gram of ice has very much less potential energy than a gram of water at the same temperature. It appears, therefore,

that temperature is chiefly, if not entirely, determined by the energy of motion, rather than the potential energy, of the molecules.

Problems.

1. The cylinder of an air compressor is cooled by a stream of water in which the flow is 1 gallon per minute. If 10 horsepower is expended in compression, find how many degrees the water is raised in temperature. 1 gallon = 3785 c.c. 1 H. P. 746 x 10' ergs

per sec.

2. How much is the water of Niagara raised in temperature by the fall of 160 ft.

3. What would have to be the velocity of a lead bullet that it may be melted on striking the target, supposing all its energy to be transformed into heat within the bullet. It takes 5.37 calories to melt one grm. of lead.

4. How many British thermal units of heat are developed by the brakes when a 100-ton train having a velocity of 20 miles per hour is brought to rest.

5. One liter of air at 0° C. is warmed to 10° C. at constant pressure. Compute the amount of heat required, and the external work done by its expansion, taking the pressure as 76 cms.

Also compute the heat that would have been required if its volume had been kept constant.

From these two results deduce the mechanical equivalent of heat (see $414).

TRANSMISSION OF HEAT.

418. Different Modes.-Three modes of transferring heat energy from one place to another are recognized, conduction, convection, and radiation.

When heat energy gradually diffuses through a mass of matter, passing from particle to particle from the warmer toward the colder parts of a body, the process is called conduction. In this case energy of motion is conceived as communicated from molecule to molecule progressively throughout the mass.

When heat is carried along by the motion of a stream of gas or liquid, the process is called convection.

In the above two cases the transference takes place in and through matter, but a hot body surrounded by a perfect vacuum

may give out energy and warm neighboring objects. In this case the energy is transmitted by waves in the ether and the process is called radiation. The term radiation is also applied to the ether waves themselves coming from the hot body.

When one end of a bar of iron is heated the other end becomes hot by conduction; the circulation in a vessel of water which is being heated carries heat from one part to another by convection; while the warmth received from a hot stove comes to us largely as radiation.

Conduction and convection are relatively slow processes while radiation is transmitted with the speed of light.

In transparent bodies, such as glass or water, heat is communicated from one part of the substance to another by conduction and radiation combined, for energy is radiated through the body directly from one part to another at the same time that it is being communicated from molecule to molecule by conduction.

While radiation originates in hot bodies and heats any body which absorbs it, radiation itself cannot be regarded as heat; for unless it is absorbed it does not affect the temperature of the bodies through which it passes. We shall study the nature of radiation in connection with light; while radiation considered as an effect of heat will be discussed in §§464-475.

419. Conduction. In general solids conduct heat better than liquids, and liquids than gases. Silver and copper are the best conductors of heat, having about 7 times the conducting power of iron, while iron conducts 100 times

as well as water, and water has 25 times the conductivity of air.

Among solids the metals are the best conductors, and it is remarkable that, generally speaking, the best conductors of heat are also the best conductors of electricity.

FIG. 224.

In crystals heat may be conducted more. rapidly in one direction than another. If a thin plate of quartz is coated with wax or paraffin and if a wire kept hot by an electric current is passed through a hole in the center of the plate, the wax will melt outward in elliptical form if the plate is cut parallel to the axis of the crystal, showing that