6. Why is a flatiron handle made of wood rather than of iron? 7. Suppose you have a quantity of hot water which you wish to cool by setting it in a cold room. Would you put it in a tin pail or in a wooden pail? Why?

8. Describe the result of the selective absorption of the glass roof of a hothouse upon the temperature within it.

9. When an arc-light lantern is used to project a microscope slide, why is a water cell put between the arc light and the slide?

10. Make a diagram of walls suitable for an ice house.

11. Why does a dead leaf resting on the snow sink into it on a sunshiny day?

12. Why does a piece of flannel lying on a marble table top feel warm while the marble itself feels cold?

13. What is best for a steam or hot water radiator, a highly polished or a dull surface?

14. Why is it that a thermos bottle will keep a liquid either hot or cold?

III. EXPANSION, FUSION, AND VAPORIZATION

278. The Measurement of Expansion of Solids. - The first demonstration in § 245 proves that when the temperature of a solid increases, the solid expands; but that demonstration gives no definite idea of the amount of this expansion. The amount of expansion varies with different substances, but for a given solid it is directly proportional to the temperature.

both the temperature of the room and the reading of the pointer. Attach a rubber tube to either end of the copper tube and send steam through it from a boiler.

After the steam has been coming through the tube freely for some time, take a second reading of the pointer and call the temperature of the steam 100° C.

From the above readings the changes in length of the tube and the changes in its temperature can be found. Then we can write the following:

The change in length of AB The change in temperature degree.

The change in length for 1 degree
The original length of AB

= The expansion of unit

length for 1 degree, and this is the coefficient of linear expansion. In general: The new length The original length + The increase in length, or L' L+ ktL,

L'

L(1 + kt),

=

Invar 1

Pine

White Glass.

Platinum

Cast Iron

=

=

The change in length for 1

or

(48)

in which L is the length of the rod at zero, L' is its length at the temperature to, and k is the coefficient of linear expansion.

=

TABLE OF COEFFICIENTS OF LINEAR EXPANSION

0.00000087 Railroad Steel
0.00000608 Copper

0.00000861 Brass

0.00000884 Aluminum
0.00001125 Ice .

0.00001320

0.00001718

0.00001878

0.00002313

0.00006400

279. Effects of Expansion in Solids. The difference in temperature between the coldest winter days and the hottest days of summer is enough to make a perceptible

1 A nickel-steel alloy containing 36 % of nickel

change in the length of long pieces of metal. Telephone and telegraph wires sag more in summer than in winter. Suspension bridges, like the Brooklyn Bridge, are several inches higher in the middle in midwinter than in summer. Bridge work and steam boilers are put together with red-hot bolts, so that the parts may be more firmly held together when the bolts are cool.

The table shows that the coefficients of expansion of glass and platinum are nearly the same. It is for this reason, and because platinum does not oxidize, that this metal is used as the sealed-in wire in incandescent lamps.

A thermostat is an example of the application of the unequal expansion of metals (Fig 244). A compound bar of copper and iron is fixed at one end and free to move at the other. When the temperature rises the point P completes the circuit through the cell C and the bell B. When the temperature falls the circuit is made through B'. By choosing bells of a different tone it is easy to tell whether a room, a greenhouse for example, is too hot or too cold.

P

B'

I

Leeteeeee

FIG. 244

COPPER

B

OF

IRON

280. Cubical Expansion. — When a solid body expands, it expands in all directions. If the form of the body is a cube and the length of each edge at zero temperature is 1, the length after expansion will be L' = 1 + Kt. The volume at t will be (1+ Kt)3 = 1 +3 Kt+3 K2ť2 + K3ť3. Since K is an extremely small fraction, as is seen from the table, the second and third powers of K are fractions so small that the terms 3 K2t2 and K33 can be neglected, and the vol

ume is considered equal to 1 + 3 Kt. Hence the coefficient of cubical expansion, or the fraction of its volume at zero temperature that a body expands on being heated 1° C., is considered to be three times the coefficient of linear expansion.

—

—

281. The Expansion of Water. - Demonstration. - Fill the bulb A, Fig. 245, with water at 4° C., up to the zero mark on B, at which point the volume of the bulb is 100 c.c. Close C and warm the water in the beaker to the temperature t° C.

Both the glass and the water expand, but the expansion of the water being much greater than the expansion of the glass, it rises in the calibrated tube. The amount of the expansion at to in cubic centimeters, divided by the product of 100 c.c. X (t 4) will give the average apparent expansion of water in glass per degree for the range of temperature tested.

FIG. 245

The coefficient of cubical expansion of ice is 0.000192; compare this with its linear expansion.

The temperature 4° is taken as a basis in the determination of the apparent expansion of water, because at that temperature water has its smallest volume and maximum density. The liquid water expands not only when its temperature is raised above 4°, but also when its temperature is lowered below 4°. In the latter, which is known as its anomalous expansion, water differs from other liquids. When winter approaches, the water of ponds and lakes becomes colder at the surface and sinks, setting up convection currents, so that, before the water at the surface becomes colder than 4°, the entire body of water is of the uniform temperature of 4°. Were it not for the anomalous expansion of water, this process

would continue down to the freezing point. This expansion, however, stops the convection currents, and when freezing begins, the water quite near the top is the only part that is colder than 4°, hence fish that are under the ice are in water of an almost uniform temperature.

Since the change in vol

ume per degree is very small, it is best shown by a curve in which the scale of volumes is taken very large. In Fig. 247

1.00200

each division in the vertical scale represents 0.00005 of the volume at 4°.

VOLUMES

The expansion of water is not uniformly proportional to the temperature. As we go from 4° in either direction, the amount of expansion per degree constantly increases. From 4° to 5° the expansion is 0.000008 of the volume at 4°; from 14° to 15°, 0.000146; from 24° to 25°, 0.000253. Liquids in general have different rates of expansion at different temperatures; in

10° 15° 20°
TEMPERATURES,
in Centigrade Degrees.

FIG. 247.- Expansion of Water

this they differ from solids and gases, which expand uniformly.

The rate of expansion of mercury, however, is nearly uniform. Its coefficient of cubical expansion, for temperatures near zero, is 0.0001818.

FIG. 246