Page images
PDF
EPUB

The thermo-electric method determines temperature by measuring the electromotive force set up when the junction of two wires made of different metals is heated. For low temperatures a copper-iron junction may be used, while for high temperatures the junction of a pure platinum. wire with one of platinum-rhodium alloy is used.

The resistance method depends on the increase in the electrical resistance of a coil of pure platinum wire with rise in temperature. ($653.)

A resistance thermometer consists of a coil of platinum wire mounted in a glass or porcelain tube to protect it from injury and contamination, and provided with connections by which its electrical resistance may be tested. By means of suitable accessory apparatus the temperature of the coil may be read directly without calculations. On account of the range of temperatures that can be measured in this way (from -270° to 1500°C.), and the accuracy and ease with which the determinations may be made, this is one of the most valuable of all methods of temperature measurement.

378. High Temperatures.-For measuring high temperatures the gas thermometer, or electrical methods, or radiation pyrometers may be used.

The hydrogen gas thermometer having a porcelain bulb may be used up to 1500° C. (§376).

The platinum-rhodium thermo-couple and the electrical resistance thermometer may be used up to 1500° C. if protected by porcelain tubes.

For the highest temperatures radiation pyrometers are used. These are of two types. One depends on the heating power of the radiation from a mass of molten metal or from the interior of a furnace, and is so devised that it may be used at quite a distance from the hot body if the radiating surface is large.

The other type depends on a measurement of the intensity of the light from the glowing hot body or interior of a furnace.

Problems.

1. Find the Fahrenheit temperatures corresponding to 80°, 20°, -10°, and -50° Centigrade.

2. Find the Centigrade temperatures corresponding to 1000°, 98°. 6, 0°, and -50° F.

3. What temperature reads the same on both Fahrenheit and Centigrade scales, and at what temperature is the Fahrenheit scale-reading twice that on the Centigrade scale?

4. A temperature interval of 35° on the Centigrade scale is an interval of how many degrees Fahrenheit?

EXPANSION OF SOLIDS.

379. Expansion of Solids.-Almost all solids expand when heated. Isotropic bodies, such as glass and all liquids, expand equally in every direction. Crystals in general expand differently in different directions, and may even contract along one direction and expand in another, but in most cases the expansion more than makes up for the contraction so that there is on the whole an increase in volume with rising temperature.

380. Coefficient of Linear Expansion.-The fractional part of its length that a rod elongates when raised one degree in temperature is called its coefficient of linear expansion. Let the length of a bar at 0° be l。, and let a be its coefficient of linear expansion, then its increase in length for a rise in temperature of 1° will be la, and for t degrees its increase in length is loat, so that its total length 7 at the higher temperature is:

1=1+loat or l=l。(1+at)

In this formula 7 may be taken as the length of the bar at a temperature t degrees higher than that at which its length is l。, even though the latter may not be its length at 0° C.

It must not be supposed that the coefficient of expansion of a substance is the same at all temperatures, for in general it increases as the temperature rises. In the above formula a represents the average value of the coefficient throughout the rise in temperature represented by t.

381. Coefficient of Volume Expansion.—If a cube of substance is taken measuring one centimeter each way at 0°, and having a coefficient of linear expansion a, then its linear dimensions at to will be 1+at and its volume will be

(1+at)=1+3at +3a2t2 +a3 3

but the coefficient a is so small that the terms involving a2 and a3 may be neglected and the volume may be expressed as

1+ 3at

3a therefore represents the increase in volume of a unit cube for one degree rise in temperature and may be called the coefficient of cubical or volume expansion; hence the coefficient of cubical expansion is three times the coefficient of linear expansion in an isotropic body.

[ocr errors]

382. Measurement of Coefficients of Expansion. When the substance whose coefficient of expansion is to be obtained has the form of a long rod, its expansion may be measured by a comparator such as that shown in the figure.

Two microscopes are set on two marks on the bar, one near each end. The microscopes are firmly clamped to a solid base which is kept free from temperature change. The bar to be examined is enclosed in a box provided with glass windows through which the microscopes are set on the marks. The

[graphic][subsumed][merged small]

bar is first packed in melting ice and the micrometers attached to the microscopes are set on the two marks. Then water at a higher temperature is caused to circulate through the box, maintaining a constant higher temperature, and the micrometers are again set on the two marks. The difference between the micrometer readings gives the elongation of the bar and accurate thermometers give the change in temperature. The whole length of the bar between the marks is then carefully determined.

If this length is 1 and the elongation is e when the temperature is raised from t to t', the coefficient of expansion a is found from the relation e=la(t't), or

[blocks in formation]

This is the average value of the coefficient between the temperatures t and t'.

C

FIG. 208.

Α

B

383. Fizeau's Method for Crystals.-When only a small piece of the substance can be obtained, a method used by Fizeau in the study of crystal expansions may be used. The specimen C to be examined is placed on a plate through which pass three fine-threaded screws DD, on top of which rests a flat plate of glass. The screws DD are adjusted so that the plate A is almost perfectly parallel with the flat top of the specimen C. If the observer now looks directly down through the plate A at the top of the specimen illuminated by sodium light ($909) he sees a series of alternate dark and bright bands crossing it. These are due to the interference of light waves and depend on the thickness of the space between A and C, as explained elsewhere (see p. 644). FIG. 209. If the thickness of the space changes the bands will move across the field of view and when the thickness of this space has changed by one-half the wave length of sodium light or .000294 of a millimeter, the bands will have moved an amount equal to the distance between them, so that band 1 will occupy the position formerly held by band 2. The apparatus described is placed in a specially contrived heater where its temperature can be slowly and steadily changed or maintained constant at any desired point. As the temperature is raised a desired amount, the shift of the bands across the field of view reveals the exact change in thickness of the space between A and C. But this change is due to the difference between the expansion of the specimen and that of the screws supporting A. When once the expansion of the screws is determined, the expansion of the specimen becomes known. The expansion of the screws may be measured by substituting for the specimen C a block of some substance whose coefficient has been determined by the previous method.

384. Expansion of Crystals.-Crystals that do not belong to the regular system expand differently in different directions. A sphere cut out of such a crystal will become an ellipsoid when its temperature is raised. In some cases two of the axes of the ellipsoid would be found of the same length and in some cases all

three would be different. The directions in the crystal corresponding to the axes of the ellipsoid are called the axes of thermal expansion. In quartz the expansion at right angles to the axis of the crystal is nearly twice the expansion in the direction of the axis.

Table of Coefficients of Linear Expansion, per Degree Centigrade.

Invar

Glass

Platinum

.00000096

Brass
Silver.....
Aluminum
Lead ....

.0000189

ETET

Steel....
Iron

Copper

Ebonite

These values are approximate. The exact value for any substance depends on the state of hardness, purity, and temperature of the specimen.

385. Some Illustrations.-An iron tire when heated expands so that it can easily be slipped over the wooden rim of the wheel which it binds firmly on cooling. So the breeches of cannon are strengthened by having a series of tubes shrunk over the inner core, in this way producing an outside compression of the core which enables it to withstand the enormous pressure of the powder gas.

Allowance has to be made for expansion in case of bridges. In a steel bridge 1000 feet long the change in length between extremes of summer and winter may amount to 8 inches.

The aggregate length of the rails in a mile of track may be 4 feet longer when hottest than when coldest, so that an allowance of about 0.3 of an inch is needed for each 30-foot rail. The grate bars of furnaces rest loosely in their supports in order to allow expansion, and long steam pipes are provided with sliding or "expansion" joints unless the bends in the pipe are such as to yield elastically to elongation and contraction.

Quartz crystals have very large expansion, and when unequally heated fly to pieces because of the great strains which result in that case. When quartz is fused, however, into a glass, its coefficient of expansion is extremely small, and vessels made of fused quartz may, when red hot, be suddenly quenched in water without breaking.

« PreviousContinue »