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rise in temperature is due to the increased rate of oxidation of the alcohol brought about by this more intimate mixture. This property of platinum is utilized in the platinum-alcohol cigar lighter (Fig. 112).
122. Absorption of gases in liquids. Let a beaker containing cold water be slowly heated. Small bubbles of air will be seen to collect in great numbers upon the walls and to rise through the liquid to the surface. That they are indeed bubbles of air and not of steam is proved, first, by the fact that they appear when the temperature is far below boiling, and, second, by the fact that they do not condense as.they rise into the higher and cooler layers of the water.
The experiment shows two things: first, that water ordinarily contains considerable quantities of air dissolved in it; and, second, that the amount of air which water can hold decreases as the temperature rises. The first point is also proved by the existence of fish life; for fishes obtain the oxygen which they need to support life from air which is dissolved in the water.
The amount of gas which will be absorbed by water varies greatly with the nature of the gas. At 0° C. and a pressure of 76 centimeters 1 cubic centimeter of water will absorb 1050 cubic centimeters of ammonia, 1.8 cubic centimeters of carbon dioxide, and only .04 cubic centimeter of oxygen. Commercial aqua ammonia is simply ammonia gas dissolved in water. The following experiment illustrates the absorption of ammonia by water:
Let the flask F (Fig. 113) and tube b be filled with ammonia by passing a current of the gas in at a and out through b. Then let a be corked up and b thrust into G, a flask nearly filled with water which has been colored slightly red by the addition of litmus and a drop or two of acid. As the ammonia is absorbed the water will slowly rise in b, and as soon
as it reaches F it will rush up very rapidly until the upper flask is nearly full. At the same time the color will change from red to blue because of the action of the ammonia upon the litmus.
Experiment shows that in every case of absorption of a gas by a liquid or a solid the quantity of gas absorbed decreases with an increase in temperature, a result which was to have been expected from the kinetic theory, since increasing the molecular velocity must of course increase the difficulty which the adhesive forces have in retaining the gaseous molecules.
FIG. 113. Absorption of ammonia by water
123. Effect of pressure upon absorption. Soda water is ordinary water which has been made to absorb large quantities of carbon dioxide gas. This impregnation is accomplished by bringing the water into contact with the gas under high pressure. As soon as the pressure is relieved, the gas passes rapidly out of solution. This is the cause of the characteristic effervescence of soda water. These facts show clearly that the amount of carbon dioxide which can be absorbed by water is greater for high pressures than for low. As a matter of fact, careful experiments have shown that the amount of any gas absorbed is directly proportional to the pressure, so that if carbon dioxide under a pressure of 10 atmospheres is brought into contact with water, ten times as much of the gas is absorbed as if it had been under a pressure of 1 atmosphere. This is known as Henry's law.
QUESTIONS AND PROBLEMS
1. Why do fishes in an aquarium die if the water is not frequently renewed?
2. Explain the apparent generation of ammonia gas when aqua ammonia is heated.
3. Why, in the experiment illustrated in Fig. 113, was the flow so much more rapid after the water began to run over into F?
WORK AND MECHANICAL ENERGY *
DEFINITION AND MEASUREMENT OF WORK
124. Definition of work. Whenever a force moves a body on which it acts, it is said to do work upon that body, and the amount of the work accomplished is measured by the product of the force acting and the distance through which it moves the body. Thus, if 1 gram of mass is lifted 1 centimeter in a vertical direction, 1 gram of force has acted, and the distance through which it has moved the body is 1 centimeter. We say, therefore, that the lifting force has accomplished 1 gram centimeter of work. If the gram of force had lifted the body upon which it acted through 2 centimeters, the work done would have been 2 gram centimeters. If a force of 3 grams had acted and the body had been lifted through 3 centimeters, the work done would have been 9 gram centimeters, etc. Or, in general, if W represent the work accomplished, F the value of the acting force, and s the distance through which its point of application moves, then the definition of work is given by the equation
In the scientific sense no work is ever done unless the force succeeds in producing motion in the body on which it
*It is recommended that this chapter be preceded by an experiment in which the student discovers for himself the law of the lever, that is, the principle of moments (see, for example, Experiment 16, authors' Manual), and that it be accompanied by a study of the principle of work as exemplified in at least one of the other simple machines (see, for example, Experiment 17, authors' Manual).
acts. A pillar supporting a building does no work; a man tugging at a stone, but failing to move it, does no work. In the popular sense we sometimes say that we are doing work when we are simply holding a weight or doing anything else which results in fatigue; but in physics the word "work" is used to describe not the effort put forth but the effect accomplished, as represented in equation (1).
125. Units of work. There are two common units of work in the metric system, the gram centimeter and the kilogram meter. As the names imply, the gram centimeter is the work done by a force of 1 gram when it moves the point on which it acts 1 centimeter. The kilogram meter is the work done by a kilogram of force when it moves the point on which it acts 1 meter. The gram meter also is sometimes used.
Corresponding to the English unit of force, the pound, is the unit of work, the foot pound. It is the work done by a pound of force" when it moves the point on which it acts 1 foot. Thus, it takes a foot pound of work to lift a pound of mass 1 foot high.
In the absolute system of units the dyne is the unit of force, and the dyne centimeter, or erg, is the corresponding unit of work. The erg is the amount of work done by a force of 1 dyne when it moves the point on which it acts 1 centimeter. To raise 1 liter of water from the floor to a table 1 meter high would require 1000 × 980 × 100 = 98,000,000 ergs of work. It will be seen, therefore, that the erg is an exceedingly small unit. For this reason it is customary to employ a unit which is equal to 10,000,000 ergs. It is called a joule, in honor of the great English physicist James Prescott Joule (1818-1889). The work done in lifting a liter of water 1 meter is therefore 9.8 joules.
QUESTIONS AND PROBLEMS
1. To drag a trunk weighing 120 lb. required a force of 40 lb. How much work would be required to drag this trunk 2 yd.? to lift it 2 yd. vertically?
2. A carpenter pushed 5 lb. on his plane while taking off a shaving 4 ft. long. How much work was done?
3. How many foot pounds of work does a 150-lb. man do in climbing to the top of Mt. Washington, which is 6300 ft. high?
4. A horse pulls a metric ton of coal to the top of a hill 30 m. high. Express the work accomplished in kilogram meters (a metric ton = 1000 kg.).
5. If the 20,000 inhabitants of a city use an average of 20 liters of water per capita per day, how many kilogram meters of work must the engines do per day if the water has to be raised to a height of 75 m.?
WORK EXPENDED UPON AND ACCOMPLISHED BY SYSTEMS OF PULLEYS
126. The single fixed pulley. Let the force of the earth's attraction upon a mass R be overcome by pulling upon a spring balance S, in the manner shown in Fig. 114, until R moves slowly upward. If R is 100 grams, the spring balance will also be found to
register a force of 100 grams.
Experiment therefore shows that in the use of the single fixed pulley the acting force, or effort, E, which is producing the motion, is equal to the resisting force, or resistance, R, which is opposing the motion.
FIG. 114. The
Again, since the length of the string is always constant, the distance s through which the point A, at which E is applied, must move is always equal to the distance s' through which the weight R is lifted. Hence, if we consider the work put into the system at A, namely, E × s, and the work accomplished by the system at R, namely, R × s', we find, obviously, since RE and ss', that
EX S = Rx s';
that is, in the case of the single fixed pulley, the work done by the acting force E (the effort) is equal to the work done against the resisting force R (the resistance), or the work put into the machine at A is equal to the work accomplished by the machine at R.