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piston B be inserted and very suddenly depressed. Sufficient heat will be developed to ignite the vapor, and a flash will result. (If the flash does not result from the first stroke, withdraw the piston completely, then reinsert, and compress again.)
To measure the heat of compression Joule surrounded a small compression pump with water, took 300 strokes on the pump, and measured the rise in temperature of the water. As the result of these measurements he obtained 444 gram meters as the mechanical equivalent of the calorie. The experiment, however, could not be performed with great exactness.
Joule also measured the converse effect, namely, the cooling produced in a gas which is pushing forward a piston and thus doing work. He obtained 437 gram meters.
186. Significance of Joule's experiments. Joule made three other determinations of the relation between heat and work by methods involving electrical measurements. He published as the mean of all his determinations 426.4 gram meters as the mechanical equivalent of the calorie. But the value of his experiments does not lie primarily in the accuracy of the final results, but rather in the proof which they for the first time furnished that whenever a given amount of work is wasted, no matter in what particular way this waste occurs, the same definite amount of heat always appears.
The most accurate determination of the mechanical equivalent of heat was made by Rowland (see opposite p. 358) (18481901) in 1880. He obtained 427 gram meters (4.19× 10′ ergs). We shall generally take it as 42,000,000 ergs. The mechanical equivalent of 1 B. T. U. is 778 foot pounds.
187. The conservation of energy. We are now in a position to state the law of all machines in its most general form, that is, in such a way as to include even the cases where friction
FIG. 169. The fire syringe
is present. It is: The work done by the acting force is equal to the sum of the kinetic and potential energies stored up plus the mechanical equivalent of the heat developed.
In other words, whenever energy is expended on a machine or device of any kind, an exactly equal amount of energy always appears either as useful work or as heat. The useful work may be represented in the potential energy of a lifted mass, as when water is pumped up to a reservoir; or in the kinetic energy of a moving mass, as when a stone is thrown from a sling; or in the potential energies of molecules whose positions with reference to one another have been changed, as when a spring has been bent; or in the molecular potential energy of chemically separated atoms, as when an electric current separates a compound substance. The wasted work always appears in the form of increased molecular motion, that is, in the form of heat. This important generalization has received the name of the Principle of the Conservation of Energy. It may be stated thus: Energy may be transformed, but it can never be created or destroyed.
188. Perpetual motion. In all ages there have been men who have spent their lives in trying to invent a machine out of which work could be continually obtained, without the expenditure of an equivalent amount of work upon it. Such devices are called perpetual-motion machines. The possibility of the existence of such a device is absolutely denied by the statement of the principle of the conservation of energy. For only in case there is no heat developed, that is, in case there are no frictional losses, can the work taken out be equal to the work put in, and in no case can it be greater. Since, in fact, there are always some frictional losses, the principle of the conservation of energy asserts that it is impossible to make a machine which will keep itself running forever, even though it does no useful work; for no matter how much kinetic or potential energy is imparted to the machine to begin with, there
must always be a continual drain upon this energy to overcome frictional resistances, so that as soon as the wasted work has become equal to the initial energy, the machine must stop.
The principle of the conservation of energy has now gained universal recognition and has taken its place as the corner stone of all physical science.
189. Transformations of energy in a power plant. The transformations of energy which take place in any power plant, such as that at Niagara, are as follows: The energy first exists as the potential energy of the water at the top of the falls. This is transformed in the turbine pits into the kinetic energy of the rotating wheels. These turbines drive dynamos in which there is a transformation into the energy of electric currents. These currents travel on wires as far as Syracuse, 150 miles away, where they run street cars and other forms of motors. The principle of conservation of energy asserts that the work which gravity did upon the water in causing it to descend from the top to the bottom of the turbine pits is exactly equal to the work done by all the motors, plus the heat developed in all the wires and bearings and in the eddy currents in the water.
Let us next consider where the water at the top of the falls obtained its potential energy. Water is being continually evaporated at the surface of the ocean by the sun's heat. This heat imparts sufficient kinetic energy to the molecules to enable them to break away from the attractions of their fellows and to rise above the surface in the form of vapor. The lifted vapor is carried by winds over the continents and precipitated in the form of rain or snow. Thus the potential energy of the water above the falls at Niagara is simply transformed heat energy of the sun. If in this way we analyze any available source of energy at man's disposal, we find in almost every case 'that it is directly traceable to the sun's heat as its source. Thus, the energy contained in coal is simply the energy of separation of the oxygen and carbon which were separated in the processes of growth. This separation was effected by the sun's rays.
The earth is continually receiving energy from the sun at the rate of 342,000,000,000,000 horse power, or about a quarter of a million horse power per inhabitant. We can form some conception of the enormous amount of energy that the sun radiates in the form of heat by reflecting that the amount received by the earth is not more than
of the total given out. Of the amount received by the earth not more than 1 part is stored up in animal and vegetable life and lifted water. This is practically all of the energy which is available on the earth for man's use.
QUESTIONS AND PROBLEMS
1. Show that the energy of a waterfall is merely transformed solar
2. Analyze the transformations of energy which occur when a bullet is fired vertically upward.
3. Meteorites are small, cold bodies moving about in space. Why do they become luminous when they enter the earth's atmosphere?
4. The Niagara Falls are 160 ft. high. How much warmer is the water at the bottom of the falls than at the top?
5. How many B. T. U. are required to warm 10 lb. of water from freezing to boiling?
6. Two and a half gallons of water (= 20 lb.) were warmed from 68°F. to 212°F. If the heat energy put into the water could all have been made to do useful work, how high could 10 tons of coal have been hoisted?.
190. Definition of specific heat. When we experiment upon different substances, we find that it requires wholly different amounts of heat energy to produce in one gram of mass one degree of change in temperature.
Let 100 g. of lead shot be placed in one test tube, 100 g. of bits of iron wire in another, and 100 g. of aluminium wire in a third. Let them all be placed in a pail of boiling water for ten or fifteen minutes, care being taken not to allow any of the water to enter any of the tubes. Let three small vessels be provided, each of which contains 100 g. of water at the temperature of the room. Let the heated shot be poured into the first beaker, and after thorough stirring let the rise in the temperature of the water be noted. Let the same be done with the other metals. The aluminium will be found to raise the temperature about twice as much as the iron, and the iron about three times as much as the lead. Hence, since the three metals have cooled through approximately the same number of degrees, we must conclude that about six times as much heat has passed out of the aluminium as out of the lead; that is, each gram of aluminium in cooling 1° C. gives out about six times as many calories as a gram of lead.
The number of calories taken up by 1 gram of a substance when its temperature rises through 1° C., or given up when it falls through 1° C., is called the specific heat of that substance.
It will be seen from this definition, and the definition of the calorie, that the specific heat of water is 1.
191. Determination of specific heat by the method of mixtures. The preceding experiments illustrate a method for measuring accurately the specific heats of different substances; for, in accordance with the principle of the conservation of energy, when hot and cold bodies are mixed, as in these experiments, so that heat energy passes from one to the other, the gain in the heat energy of one must be just equal to the loss in the heat energy of the other.
This method is by far the most common one for determining the specific heats of substances. It is known as the method of mixtures.
Suppose, to take an actual case, that the initial temperature of the shot used in § 190 was 95° C. and that of the water 19.7°, and that, after mixing, the temperature of the water and shot was 22°. Then, since 100 g. of water has had its temperature raised through 22° - 19.7° = 2.3°, we know that 230 calories of heat have entered the water. Since the temperature of the shot fell through 95° 22° 73°, the number of calories given up by the 100 g. of shot in falling 1° was = 3.15. Hence the specific heat of lead, that is, the number of calories of heat given 3.15 up by 1 gram of lead when its temperature falls 1o C., is = .0315. 100
Or, again, we may work out the problem algebraically as follows: Let x equal the specific heat of lead. Then the number of calories which come out of the shot is its mass times its specific heat times its change in temperature, that is, 100 × × × (95 −22); and, similarly, the number which enter the water is the same, namely, 100 × 1 × (22 – 19.7). Hence we have
100 (95 — 22) x = 100 (22 19.7), or x = .0315.
By experiments of this sort the specific heats of some of the common substances have been found to be as follows:
mx H x C - Ye