CHAPTER III

EXPANSION OF SOLIDS

14. Linear Expansion of Metals, etc.-The following is one of the simplest ways of observing the increase in length of a metal bar when it is heated.

EXPT. 5.-Lay a flat bar of iron, about 1 ft. long, across two wooden blocks, as in Fig. 8.

Under one end (between it and

the block) place a fine sewing-needle at right angles to the length of the bar. On the other end place a weight, so as to keep it fixed, and make the bar bear well down upon the needle. Attach a light straw pointer by sealing-wax to the eye end of the needle, and at right angles to it.

Heat the bar with a spirit-lamp or Bunsen burner as it expands the free end moves forward and rolls the needle round.

Since the needle is small, a very slight movement of the end will make the pointer move through a sensible arc.

Repeat the experiment with strips of glass (which should be heated cautiously), copper, zinc, etc.

15. Unequal Expansion of Metals.-Different metals do not expand equally when heated. The following experiments show that brass expands more than iron when both are heated through the same interval of temperature.

EXPT. 6. Cut off from a thin iron rod a piece about 6 inches long and file the ends square. Cut a 66 gauge" out of thick sheet-brass, so that the iron rod just fits into it lengthways when cold (Fig. 9). By filing the inside of the gauge or tapping it with a hammer on the outside you can adjust it so that it grips the iron rod firmly. Suspend the gauge and rod in a sauce-pan or tin dish filled with water, and heat the water to boiling. You will find that the rod soon drops out, thus showing that the brass expands more than the iron.

Fig. 9 [1/8].

EXPT. 7.— Take two thin strips of iron and brass respectively: solder or rivet them together, hammer the compound strip

straight, and then heat it by holding it over a fire or passing it through a gas-flame. On account of the unequal expansion of

the metals the strip bends, the more expansible metal (brass) being on the outside of the curve (Fig. 10).

16. Coefficients of Expansion.—Experiment shows that when a metal bar is heated it expands uniformly, and the expansion or increase in length is proportional (1) to the original length of the bar, (2) to the interval of temperature through which it is heated, and (3) to a certain fraction which depends upon the nature of the substance, and which is called the coefficient of linear expansion of that sub

stance.

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The coefficient of linear expansion of copper is about or 0.000017. If a bar of copper 30 inches in length at o° be heated to 1°, its length will become 30 +- inches or 30 (1+0.000017) inches; and, since the expansion is proportional to the rise of temperature, at 10° its length

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will become 30 (1+ inches or 30 (1+0.000017 × 10) inches, and

so on.

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The coefficient of linear expansion of a substance may be defined in any of the following ways:

Definition 1.—If a bar of any substance be heated through 1o, its length will increase by a certain fraction, and this fraction is called the coefficient of linear expansion of the substance.

Definition 2.-The coefficient of linear expansion is the ratio of the increase of length produced by a rise of 1° to the original length.

Definition 3. -The coefficient of linear expansion is numerically equal to the increase in length produced in unit length of the substance by a rise in temperature of 1°.

Let a denote the coefficient of linear expansion of a body whose length at o° is : starting with any one of the above definitions you will easily see that the expansion produced by heating the body to t° will be lat, and that its length ' at t° will be given by the equation

You will find examples of the use of this equation at the end of the chapter, and you should make yourself thoroughly familiar with it.

You

17. Examples and Applications of Expansion. will see by the above table that glass and platinum have the same coefficient of expansion. These two substances expand and contract at the same rate, so that if a platinum wire is fused into a glass tube the joint will remain good on cooling. It is mainly on this account that whenever a metallic wire has to be fused through the side of a glass vessel platinum is always used. If you try to fuse a copper wire into a piece of glass tubing, you will find that on cooling the copper contracts more rapidly than the glass, and so a crack is started which makes the joint leaky.

Boiling water may be poured into thin glass vessels such as beakers and flasks without much danger of cracking them. But glass is such a bad conductor of heat that, if boiling water is poured into a thick-bottomed tumbler, the inside of the tumbler expands before the heat has had time to reach the outside, and in consequence of this irregular expansion the glass cracks.

The best way of loosening a glass stopper when it has stuck fast in the neck of a bottle is to make use of the expansion of glass by heat. Hold the neck of the bottle over a small gasflame, turning it round so as to heat it gently and uniformly : the neck expands before the heat has time to penetrate farther, and after tapping the stopper with a knife or key it can generally be pulled out.

EXPT. 8.-Stretch an iron or platinum wire, two or three feet in length, horizontally; if you have no suitable clips for holding it, support it on bricks with heavy weights placed on top. Heat it by means of a long burner placed underneath, or, better still, by passing an electrical current from a battery through it. As the wire expands it bends or 'sags' under the influence of its own weight on cooling it tightens up again. This sagging can be observed in telegraph wires, and is more noticeable in summer than in winter.

Standard yard-measures and metre-scales are constructed so as to be of a given length at a definite temperature: thus the metre is defined as being the distance between the ends of a rod of platinum made by Borda, the rod being at the temperature of melting ice. A scale which is correct at o° will not be correct at 15°, for it will have expanded, and its real length

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will be greater than its apparent length: to make allowance for this we require to know the coefficient of expansion of the material of the scale, and then we can calculate its real length at any temperature according to equation (1) Art. 16. Such corrections have to be applied to all brass and glass scales affixed to barometers, etc.

18. Force exerted in Expansion and Contraction.Great force is required to stretch a bar of iron appreciably, and when such a bar is made to expand by heat a correspondingly large force is exerted against any obstacle which resists its expansion.

If the bars of a furnace were firmly fixed at both ends, they would, in endeavouring to expand, either loosen the masonry on either side, or else the bars themselves would bend. Instead of this, they are fixed at one end only and are free to expand at the other end; or, as in boiler-furnaces, the fire-bars are not fixed at all at the ends, but simply rest upon cross-bars.

Wheelwrights employ the force of contraction in making cart-wheels. When the wooden framework of the wheel is ready it is placed in position on the ground: the tire or iron rim, which is made somewhat smaller in diameter, is heated until it has expanded sufficiently to allow the wheelwright to slip it on. Cold water is now poured over the iron, and as it shrinks it binds the parts of the wheel firmly together.

In making railways, especially if the rails are laid in cold weather, a space of about a quarter of an inch is left between each rail and the next in order to allow for expansion in summer. In all large metal structures engineers endeavour to obtain freedom of movement under changes of temperature. In the Britannia tubular bridge over the Menai Straits this is secured by resting the metal tubes on rollers at one end; and in the huge Forth bridge, which has recently been constructed, the rails on the 1700-feet span are free to slide to the extent of 18 inches.

19. Compensation of Clocks and Watches.-The rate at which a clock goes is controlled by the movements of its pendulum, and the time taken by the pendulum to swing backwards and forwards depends upon its length. You can test this with a pendulum consisting of a bullet hung from a string. If the string is a metre (or about 39 inches) in length, the