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CHAPTER XXI

CHANGE OF STATE

Molecular states, 256. Fusion, 257. Changes in internal energy on fusion, 258. Heat of fusion, 259. Experimental method for determining the heat of fusion of ice, 260. Some effects due to heat of fusion of ice, 261. Changes in volume on solidification, 262. Effect of pressure on the melting point, 263. Undercooling, 264. Freezing points of solutions, 265. Evaporation; the kinetic theory, 266. Saturated vapors, 267. Nonsaturated vapors, 268. Dependence of pressure of saturated vapor on temperature, 269. Boiling, 270. Effect of pressure on the boiling point, 271. Why the boiling point depends on pressure, 272. Pressure of saturated vapors of different liquids, 273. The boiling points of different liquids, 274. The pressure exerted by a vapor is independent of the presence of other gases or vapors, 275. Distillation, 276. Fractional distillation, 277. The boiling points of solutions, 278. Heat of vaporization, 279. Evaporation a cooling process, 280. Freezing water by its evaporation, 281. Carbon-dioxide snow, 282. Critical temperatures, 283. The spheroidal state, 284. Ice and refrigerating machines, 285. Liquefaction of air, 286. Summary, 287.

256. Molecular states. When ice melts and changes into water, there is a change in the state of the molecules. The change of water into vapor is another type of change in state. The phenomena connected with these two changes and the reverse processes will be discussed at length in this chapter. The student will find that there are many interesting facts associated with them, and that a relatively small number of laws or principles is involved.

257. Fusion. One of the conspicuous facts connected with the change of a solid to a liquid is that for many substances this change takes place at a very definite temperature. For example, in the case of ice and water the temperature, 0° C., or 32° F., is so definite that it is used as a standard. While these temperatures are usually referred to as the melting-point temperatures, they are also the freezing, or solidifying, temperatures. For example, ice melts at the same temperature at which pure water freezes.

TABLE OF MELTING POINTS AT A PRESSURE OF 76 CENTIMETERS

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In the case of many substances the change from a solid to a liquid does not take place at a definite temperature; for example, such substances as paraffin wax, sealing-wax, and butter gradually change from a solid to a liquid. The same thing is true of iron. One reason that iron can be welded

is that it does not have a definite melting temperature, but softens and becomes plastic. If butter had a definite melting point, it would be difficult to use it as we now do.

258. Changes in internal energy

Temperature

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Time

on fusion. It is found by experi- FIG. 161. Change in temperature

ment that heat energy must be

added to all substances to change

of snow

them from solid to liquid. In the case of ice a very considerable amount of energy must be added to change it to water, even when there is no change in its temperature; hence a mass of 100 grams of water at 0° C. contains more internal energy than 100 grams of ice at 0° C.

If heat is supplied to snow or crushed ice at a uniform rate, and the temperature, as indicated by a thermometer, is observed at regular intervals, results similar to those shown in Fig. 161 will be obtained. As shown, the temperature of the snow rises quickly to 0°, when it begins to melt. The mixture of snow and water (which should be kept well stirred) will stay at that temperature, although heat is being supplied, until the snow is practically all melted. After that the temperature will rise. This experiment shows clearly that heat energy is needed to change ice to water; for during the time the ice was melting it was receiving heat from outside, and yet the temperature did not rise.

If water is taken into a cold place where the temperature is considerably lower than 0° C., and its temperature observed at regular intervals, results similar to those shown in Fig. 162 will be obtained. The flat part of the curve shows a constant temperature during the change of state from water to ice. During the time water is changing into ice it gives up heat energy.

Experiments similar to those represented by Figs. 161 and 162 are often performed in order to determine the melting, or fusing, points of substances. When a sub

stance has a definite melting point, the flat part of the curve is usually so clearly shown that there is little trouble in determining the temperature corresponding to it.

Temperature

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Time

FIG. 162. Cooling and freezing of water

259. Heat of fusion. It has just been pointed out that when ice changes into water, heat energy must be added; and that when water changes into ice, heat energy is given up. Careful experiments have shown that the amount of heat that must be added to melt 1 gram of ice at atmospheric pressure is always the same in amount. This quantity is called the heat of fusion of ice.

The heat of fusion of any substance is equal to the number of calories of heat required to melt 1 gram of the substance, its temperature remaining unchanged.

260. Experimental method for determining the heat of fusion of ice. A simple method for determining the heat of fusion of ice is based on the method of mixtures. A description of an experiment, with numerical results, will assist in a clearer understanding.

A copper vessel of mass 100 grams and specific heat 0.09 contained 400 grams of water at 25.2° C. A "dry" piece of ice (that is, one without water clinging to it) at 0° C. was dropped into the vessel, and after the ice was all melted the final temperature was 13.5° C. The mass of the vessel and its contents was found to be 550.9 grams. The increase in the mass gives the mass of ice added, which is found to be 50.9 grams.

The number of calories given up by the copper vessel and the 400 grams of water in cooling from 25.2° C. to 13.5°C. was

100 × .09 × (25.2 – 13.5) + 400 × (25.2 – 13.5) = 4785.3 cal. If the heat of fusion of the ice is represented by H, the number of calories required to melt 50.9 grams of ice and to raise its temperature to 13.5° C. is 50.9 H + (50.9 × 13.5).

Equating the heat given up by the vessel and water to the heat received by the ice, we have

whence

4785.3 = 50.9 H + (50.9 × 13.5);

H = 80.5 calories per gram.

This value is a little too high. More careful experiments, with corrections for heat received or given up to the room and for other experimental errors, give, as the heat of fusion of ice,

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261. Some effects due to heat of fusion of ice. The relatively large heat of fusion of ice (approximately 80 calories per gram) plays an important part in the use of ice in refrigerators. Ten kilos (about 22 pounds) of ice will absorb, in melting, about 800,000 calories. This is enough to lower the temperature of 50 kilos of water 16° C. If the heat of fusion of ice were as small as that of lead or mercury, the use of ice in refrigerators would be of little service.

When water changes into ice, it gives up the same number of calories as it absorbs when changing from ice to water. The reason why large masses of water tend to keep the air temperature from going much below the freezing point should be obvious. When the ground is very wet, we are not as likely to have a hard freeze as when the ground is dry, other conditions being the same. If the heat of fusion of ice were a small quantity, ponds would more frequently freeze to the bottom in winter.

262. Changes in volume on solidification. When water freezes, it expands. Two evidences of this are well known: first, the smaller density of ice, as indicated by its floating on water; second, the disastrous effects of the freezing of water pipes. The specific gravity of ice at 0° C. is 0.92.

The expansion of water on freezing disintegrates rocks and loosens up the soil, an effect which is very beneficial for plant growth. In a stony field the tendency of freezing and thawing to bring rocks to the surface is very noticeable. The freezing of the ground underneath raises the rocks; when the ground thaws, the soil is usually washed under the rocks. The raising of stakes and posts which have not been set deeply in the ground is quite common. The roots of winter wheat, blue grass, and other plants with roots which lie near the surface are raised out of the ground by frequent freezing and thawing. It is well known that the footings or foundations of buildings and monuments must be placed below the line of possible freezing. Cement steps and porches are often broken away from buildings on account of the expansion of the ground underneath on freezing.

Waxes, gelatin, and many metals-in fact, most substancescontract on solidification; water is an exception to the general rule. Gold and silver coins cannot be made by casting; they must be stamped, for the contraction on solidification prevents them from accurately fitting their molds. The manufacture, by casting, of the type used in printing requires a metal which expands on solidification.

263. Effect of pressure on the melting point. An increase of pressure lowers the temperature at which water freezes or ice melts. The effect is very easily remembered; for when water freezes, it expands, and pressure tends to prevent this.

It is a general rule that an increase of pressure lowers the temperature of the melting points of those substances that expand on

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