CHAPTER III

EXPANSION OF SOLIDS

THE dimensions of all bodies are altered more or less by an increase or decrease in temperature. Solid bodies have the property of retaining their shape without the support of a containing vessel. Hence in the case of a solid bar we may measure the increase in length, breadth, or thickness due to a given rise of temperature, and thus determine the increase in length which a bar of 1 cm. long would experience if heated through 1°C. This is defined as the coefficient of linear expansion of the substance of which the bar is composed.

On the other hand, fluids take their shape from the vessel in which they happen to be contained. It would therefore obviously be useless to make measurements of the linear dimensions of a fluid, unless to obtain its volume. A certain mass of water, for instance, may be poured into vessels of various shapes and sizes, its linear dimensions being thus capable of modification in an infinite number of ways. But through all these modifications the volume of the water will remain the same, providing its temperature is not altered; whilst every alteration in temperature of the water will produce a corresponding alteration in its volume. Hence it is rational to confine our attention, in the case of a fluid, to the alteration in volume which accompanies an increase in temperature.

Fluids are divided into liquids and gases. The volume of a gas is altered, not only by an increase or decrease of temperature, but also, and to an equal extent, by changes of pressure.

The contraction which occurs when a metallic body is cooled is frequently utilised by engineers. A good example is afforded

in the manufacture of large cannon. The general shape of one of these is shown in the sectional drawing (Fig. 18).

FIG. 18.-Section of Cannon.

An inner tube of steel is first turned accurately cylindrical on the outside, and bored internally. This tube, though sufficiently strong to guide the projectile in a straight course, is not strong enough to withstand the great force suddenly called into play by the explosion of the powder. To furnish sufficient strength a number of steel coatings are successively shrunk on to the tube. Each of these coatings is bored internally to such a diameter that, when at the same temperature as the rest of the cannon, it is too small to fit in place. On being heated, however, (the rest of the cannon remaining cold) it just slips into position, and when cooled is held tightly there.

EXPT. 11. The enormous force called into play when the expansion of a metal rod is resisted by mechanical means is illustrated in the following experiment. A rod of steel or

wrought iron is provided, at one end, with a nut which can be screwed on to it, and at the other with a hole through which a small bar of cast iron can be placed. A strong metal stand is furnished with two upright pillars, provided at their upper extremities with knife edges against which the cast-iron bar and the nut can respectively rest. The nut is screwed up tightly so as to put some compressional strain on the bar. If the latter be now heated, the force called into play will be sufficient to break the cast-iron rod.

A simple modification of this experiment shows that an equally great force is called into play when the contraction, due to cooling a heated rod, is resisted by mechanical

means.

FIG. 19.-Compound strip, showing differential expansion.

EXPT. 12. Take a strip of ebonite, about a foot long and an inch broad, and as thin as can be procured, and glue this on to a strip of wood (pine by preference) of similar dimensions, so that the two form a compound strip of double

the thickness of the wood or the ebonite. (A thin strip of wood such as here required can be easily obtained by the use of a circular saw.) If this compound strip, Fig. 19, be heated, it will be found to bend into a curve such as shown by the dotted lines. The reason of this is, that the increase in length of a strip of ebonite is greater than that of a simi. lar strip of wood when both are subjected to the same rise of temperature. The compound strip can only remain straight when both of its components are of equal length; if the length of one component becomes greater than that of the other, the compound strip will assume a curved form, with the longer strip on the convex side of the curve.

Strips of brass and steel may be substituted for the ebonite and wood, when it will be found that for a given rise of temperature brass expands more than steel.

EXPT. 13. Take about a foot of indiarubber pressure tubing (the kind containing an internal layer of canvas is unsuitable), and fix a

FIG. 20.-Arrangement for showing the effect of heating on stretched india-rubber.

small piece of open glass tube into one end, a small wooden rod being placed in the other end. Bind both in position by means of this copper wire. A loop of copper wire is attached to the glass tube, and

another to the wooden rod. A fine sewing needle is driven through the wooden rod at right angles to its length, and a mass of about a pound having been hung from the loop at this end of the tube, the other end is attached to a horizontal arm of a retort stand, Fig. 20. A straw has two holes burnt through it at right angles to its length by means of a hot needle, the distance between the holes being about a quarter of an inch. The needle A, projecting through the wooden rod at the lower extremity of the indiarubber tube, is placed through that hole in the straw which is nearest to the centre of the latter. Another needle B, driven into a block of wood C, is placed in the other hole in the straw, and the whole is adjusted so that the straw is horizontal.

If the indiarubber tube is now heated by the flame of a Bunsen burner, the straw will indicate that a contraction takes place in the indiarubber.

It must not, however, be concluded from this experiment that indiarubber contracts when heated. As a matter of fact, if a mass is employed only just sufficient to keep the tube straight without stretching it, it will be found that the indiarubber expands when heated.

The legitimate conclusion to be drawn from this experiment is that though indiarubber expands when heated, a given stretching force will produce a smaller extension when the temperature is high than when it is low.

Coefficient of Linear Expansion of a Metal.—In order to determine the coefficient of linear expansion of a metal, the usual method is to observe the elongation produced by a given rise of temperature in a bar of known length. The chief difficulty lies in measuring the small elongation.

EXPT. 14. Take a straight piece of brass tube of circular section, of length about 120 cm., and diameter about 2 cm. Take two pieces of flat sheet brass, of dimensions about 5 cm. x 2 cm. x 3 c.m. These two pieces must be soldered, one at each end, to the curved surface of the brass tube, so that they lie in one plane, a part of each projecting beyond the end of the tube. This may easily be done by placing the two pieces of brass on a flat table, laying the brass tube upon them, and effecting the soldering by means of a bit and the ordinary flux (zinc chloride solution.) Blanks must be soldered into the ends of the tube, and two side tubes, C, D, (Fig. 21) also soldered in position, so that water or steam may be passed through them.

The arrangement to be made may be understood from Fig. 21. AB represents the tube, with the side tubes C, D, and

the brass plates E, F. E is placed on a block of wood, and held in position by means of a weight W1. F rests on a needle N, which in turn rests on a piece of flat glass supported on a block of appropriate height. The needle N has one end inserted at right angles into a counterbalanced straw P, which is to serve as a pointer. The needle may be fixed tightly to the straw by means of a little sealing wax. A weight W2 serves to press the brass plate F on to the needle.

On starting the experiment, arrange the pointer P so that it is vertical, and points to o° on the circular scale graduated in degrees. Observe the temperature of the room (†。 C)3.

Now pass steam through the tube AB by means of indiarubber tubes joined to C and D; that joined to C being con

C

As

FIG. 21.-Arrangement for measuring the expansion of a metal tube. nected at its other end with a piece of glass tube thrust through the cork in the mouth of a tin can in which water is boiled. the tube AB is heated it will increase in length, and the end A being fixed, the end B will roll on the needle N and thus cause the pointer P to revolve.

Let us suppose that when steam has passed freely through AB for ten minutes or so, it is found that the pointer indicates o. Further, let d the diameter (in cms.) of the needle, as measured

=

by a micrometer gauge.

Now for a complete rotation of the needle (i.e., through 360°), the end of the brass tube would advance through ad cms. Therefore for a rotation through 0°, the end of the tube would advance through

πα χ

0 360

cms.