Page:EB1911 - Volume 13.djvu/150

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WATT’S INDICATOR DIAGRAM]

HEAT

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is 0.092 a cubic centimetre for each gramme of ice melted. The method requires careful attention to details of manipulation, which are more fully discussed in the article on Calorimetry.

For measuring large quantities of heat, such as those produced by the combustion of fuel in a boiler, the most convenient method is the evaporation of water, which is commonly employed by engineers for the purpose. The natural unit in this case is the quantity of heat required to evaporate unit mass of water at the boiling point under atmospheric pressure. In boilers working at a higher pressure, or supplied with water at a lower temperature, appropriate corrections are applied to deduce the quantity evaporated in terms of this unit.

For laboratory work on a small scale the converse method of condensation has been successfully applied by John Joly, in whose steam-calorimeter the quantity of heat required to raise the temperature of a body from the atmospheric temperature to that of steam condensing at atmospheric pressure is observed by weighing the mass of steam condensed on it. (See Calorimetry.)

6. Thermometric Calorimetry.—For the majority of purposes the most convenient and the most readily applicable method of measuring quantities of heat, is to observe the rise of temperature produced in a known mass of water contained in a suitable vessel or calorimeter. This method was employed from a very early date by Count Rumford and other investigators, and was brought to a high pitch of perfection by Regnault in his extensive calorimetric researches (Mémoires de l’Institut de Paris, 1847); but it is only within comparatively recent years that it has really been placed on a satisfactory basis by the accurate definition of the units involved. The theoretical objections to the method, as compared with latent heat calorimetry, are that some heat is necessarily lost by the calorimeter when its temperature is raised above that of the surroundings, and that some heat is used in heating the vessel containing the water. These are small corrections, which can be estimated with considerable accuracy in practice. A more serious difficulty, which has impaired the value of much careful work by this method, is that the quantity of heat required to raise the temperature of a given mass of water 1° C. depends on the temperature at which the water is taken, and also on the scale of the thermometer employed. It is for this reason, in many cases, impossible to say, at the present time, what was the precise value, within 1/2 or even 1% of the heat unit, in terms of which many of the older results, such as those of Regnault, were expressed. For many purposes this would not be a serious matter, but for work of scientific precision such a limitation of accuracy would constitute a very serious bar to progress. The unit generally adopted for scientific purposes is the quantity of heat required to raise 1 gram (or kilogram) of water 1° C., and is called the calorie (or kilo-calorie). English engineers usually state results in terms of the British Thermal Unit (B.Th.U.), which is the quantity of heat required to raise 1 ℔ of water 1° F.

7. Watt’s Indicator Diagram; Work of Expansion.—The rapid development of the steam-engine (q.v.) in England during the latter part of the 18th century had a marked effect on the progress of the science of heat. In the first steam-engines the working cylinder served both as boiler and condenser, a very wasteful method, as most of the heat was transferred directly from the fire to the condensing water without useful effect. The first improvement (about 1700) was to use a separate boiler, but the greater part of the steam supplied was still wasted in reheating the cylinder, which had been cooled by the injection of cold water to condense the steam after the previous stroke. In 1769 James Watt showed how to avoid this waste by using a separate condenser and keeping the cylinder as hot as possible. In his earlier engines the steam at full boiler pressure was allowed to raise the piston through nearly the whole of its stroke. Connexion with the boiler was then cut off, and the steam at full pressure was discharged into the condenser. Here again there was unnecessary waste, as the steam was still capable of doing useful work. He subsequently introduced “expansive working,” which effected still further economy. The connexion with the boiler was cut off when a fraction only, say 1/4, of the stroke had been completed, the remainder of the stroke being effected by the expansion of the steam already in the cylinder with continually diminishing pressure. By the end of the stroke, when connexion was made to the condenser, the pressure was so reduced that there was comparatively little waste from this cause. Watt also devised an instrument called an indicator (see Steam Engine), in which a pencil, moved up and down vertically by the steam pressure, recorded the pressure in the cylinder at every point of the stroke on a sheet of paper moving horizontally in time with the stroke of the piston. The diagram thus obtained made it possible to study what was happening inside the cylinder, and to deduce the work done by the steam in each stroke. The method of the indicator diagram has since proved of great utility in physics in studying the properties of gases and vapours. The work done, or the useful effect obtained from an engine or any kind of machine, is measured by the product of the resistance overcome and the distance through which it is overcome. The result is generally expressed in terms of the equivalent weight raised through a certain height against the force of gravity.^[1] If, for instance, the pressure on a piston

↑ Units of Work, Energy and Power.—In English-speaking countries work is generally measured in foot-pounds. Elsewhere it is generally measured in kilogrammetres, or in terms of the work done in raising 1 kilogramme weight through the height of 1 metre. In the middle of the 19th century the terms “force” and “motive power” were commonly employed in the sense of “power of doing work.” The term “energy” is now employed in this sense. A quantity of energy is measured by the work it is capable of performing. A body may possess energy in virtue of its state (gas or steam under pressure), or in virtue of its position (a raised weight), or in various other ways, when at rest. In these cases it is said to possess potential energy. It may also possess energy in virtue of its motion or rotation (as a fly-wheel or a cannon-ball). In this case it is said to possess kinetic energy, or energy of motion. In many cases the energy (as in the case of a vibrating body, like a pendulum) is partly kinetic and partly potential, and changes continually from one to the other throughout the motion. For instance, the energy of a pendulum is wholly potential when it is momentarily at rest at the top of its swing, but is wholly kinetic when the pendulum is moving with its maximum velocity at the lowest point of its swing. The whole energy at any moment is the sum of the potential and kinetic energy, and this sum remains constant so long as the amplitude of the vibration remains the same. The potential energy of a weight W ℔ raised to a height h ft. above the earth, is Wh foot-pounds. If allowed to fall freely, without doing work, its kinetic energy on reaching the earth would be Wh foot-pounds, and its velocity of motion would be such that if projected upwards with the same velocity it would rise to the height h from which it fell. We have here a simple and familiar case of the conversion of one kind of energy into a different kind. But the two kinds of energy are mechanically equivalent, and they can both be measured in terms of the same units. The units already considered, namely foot-pounds or kilogrammetres, are gravitational units, depending on the force of gravity. This is the most obvious and natural method of measuring the potential energy of a raised weight, but it has the disadvantage of varying with the force of gravity at different places. The natural measure of the kinetic energy of a moving body is the product of its mass by half the square of its velocity, which gives a measure in kinetic or absolute units independent of the force of gravity. Kinetic and gravitational units are merely different ways of measuring the same thing. Just as foot-pounds may be reduced to kilogrammetres by dividing by the number of foot-pounds in one kilogrammetre, so kinetic may be reduced to gravitational units by dividing by the kinetic measure of the intensity of gravity, namely, the work in kinetic units done by the weight of unit mass acting through unit distance. For scientific purposes, it is necessary to take account of the variation of gravity. The scientific unit of energy is called the erg. The erg is the kinetic energy of a mass of 2 gm. moving with a velocity of 1 cm. per sec. The work in ergs done by a force acting through a distance of 1 cm. is the absolute measure of the force. A force equal to the weight of 1 gm. (in England) acting through a distance of 1 cm. does 981 ergs of work. A force equal to the weight of 1000 gm. (1 kilogramme) acting through a distance of 1 metre (100 cm.) does 98.1 million ergs of work. As the erg is a very small unit, for many purposes, a unit equal to 10 million ergs, called a joule, is employed. In England, where the weight of 1 gm. is 981 ergs per cm., a foot-pound is equal to 1.356 joules, and a kilogrammetre is equal to 9.81 joules. The term power is now generally restricted to mean “rate of working.” Watt estimated that an average horse was capable of raising 550 ℔ 1 ft. in each second, or doing work at the rate of 550 foot-pounds per second, or 33,000 foot-pounds per minute. This conventional horse-power is the unit commonly employed for estimating the power of engines. The horse-power-hour, or the work done by one horse-power in one hour, is nearly 2 million foot-pounds. For electrical and scientific purposes the unit of power employed is called the watt. The watt is the work per second done by an electromotive force of 1 volt in driving a current of 1 ampere, and is equal to 10 million ergs or 1 joule per second. One horse-power is 746 watts or nearly 3/4 of a kilowatt. The kilowatt-hour, which is the unit by which electrical energy is sold, is 3.6 million joules or 2.65 million foot-pounds, or 366,000 kilogrammetres, and is capable of raising nearly 19 ℔ of water from the freezing to the boiling point.

[f1-1] Units of Work, Energy and Power.—In English-speaking countries work is generally measured in foot-pounds. Elsewhere it is generally measured in kilogrammetres, or in terms of the work done in raising 1 kilogramme weight through the height of 1 metre. In the middle of the 19th century the terms “force” and “motive power” were commonly employed in the sense of “power of doing work.” The term “energy” is now employed in this sense. A quantity of energy is measured by the work it is capable of performing. A body may possess energy in virtue of its state (gas or steam under pressure), or in virtue of its position (a raised weight), or in various other ways, when at rest. In these cases it is said to possess potential energy. It may also possess energy in virtue of its motion or rotation (as a fly-wheel or a cannon-ball). In this case it is said to possess kinetic energy, or energy of motion. In many cases the energy (as in the case of a vibrating body, like a pendulum) is partly kinetic and partly potential, and changes continually from one to the other throughout the motion. For instance, the energy of a pendulum is wholly potential when it is momentarily at rest at the top of its swing, but is wholly kinetic when the pendulum is moving with its maximum velocity at the lowest point of its swing. The whole energy at any moment is the sum of the potential and kinetic energy, and this sum remains constant so long as the amplitude of the vibration remains the same. The potential energy of a weight W ℔ raised to a height h ft. above the earth, is Wh foot-pounds. If allowed to fall freely, without doing work, its kinetic energy on reaching the earth would be Wh foot-pounds, and its velocity of motion would be such that if projected upwards with the same velocity it would rise to the height h from which it fell. We have here a simple and familiar case of the conversion of one kind of energy into a different kind. But the two kinds of energy are mechanically equivalent, and they can both be measured in terms of the same units. The units already considered, namely foot-pounds or kilogrammetres, are gravitational units, depending on the force of gravity. This is the most obvious and natural method of measuring the potential energy of a raised weight, but it has the disadvantage of varying with the force of gravity at different places. The natural measure of the kinetic energy of a moving body is the product of its mass by half the square of its velocity, which gives a measure in kinetic or absolute units independent of the force of gravity. Kinetic and gravitational units are merely different ways of measuring the same thing. Just as foot-pounds may be reduced to kilogrammetres by dividing by the number of foot-pounds in one kilogrammetre, so kinetic may be reduced to gravitational units by dividing by the kinetic measure of the intensity of gravity, namely, the work in kinetic units done by the weight of unit mass acting through unit distance. For scientific purposes, it is necessary to take account of the variation of gravity. The scientific unit of energy is called the erg. The erg is the kinetic energy of a mass of 2 gm. moving with a velocity of 1 cm. per sec. The work in ergs done by a force acting through a distance of 1 cm. is the absolute measure of the force. A force equal to the weight of 1 gm. (in England) acting through a distance of 1 cm. does 981 ergs of work. A force equal to the weight of 1000 gm. (1 kilogramme) acting through a distance of 1 metre (100 cm.) does 98.1 million ergs of work. As the erg is a very small unit, for many purposes, a unit equal to 10 million ergs, called a joule, is employed. In England, where the weight of 1 gm. is 981 ergs per cm., a foot-pound is equal to 1.356 joules, and a kilogrammetre is equal to 9.81 joules. The term power is now generally restricted to mean “rate of working.” Watt estimated that an average horse was capable of raising 550 ℔ 1 ft. in each second, or doing work at the rate of 550 foot-pounds per second, or 33,000 foot-pounds per minute. This conventional horse-power is the unit commonly employed for estimating the power of engines. The horse-power-hour, or the work done by one horse-power in one hour, is nearly 2 million foot-pounds. For electrical and scientific purposes the unit of power employed is called the watt. The watt is the work per second done by an electromotive force of 1 volt in driving a current of 1 ampere, and is equal to 10 million ergs or 1 joule per second. One horse-power is 746 watts or nearly 3/4 of a kilowatt. The kilowatt-hour, which is the unit by which electrical energy is sold, is 3.6 million joules or 2.65 million foot-pounds, or 366,000 kilogrammetres, and is capable of raising nearly 19 ℔ of water from the freezing to the boiling point.

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