temperature and a pyrometer being used to observe the temperature. For higher temperatures, molten lead or mineral salts, such as common salt, barium chloride, potassium chloride, and potassium cyanide, are used.

When steel and iron are heated to higher temperatures, they successively become red, orange, and white. These colors and the corresponding temperatures are approximately as follows:

118. Expansion and Contraction.-Nearly all substances expand when they are heated and contract when heat is removed from them, or they are cooled. This phenomenon is greatest in gases and least in solids, but even in solids it is of enough importance to be extremely useful at times, or to cause considerable trouble if no allowance has been made for it.

There are a few metal alloys which, within certain limits, do not change their volumes with changes of temperature, and there are also some which between certain temperatures will even expand when cooled and contract when heated. A nickel steel containing 36% nickel has practically no expansion or contraction with changes in temperature and is, therefore, used in some cases for accurate measurements where expansion of the measuring instruments would introduce serious errors.

When a solid body is heated, it expands in all directions if free to do so. As a rule, however, we are concerned only with the change of one dimension and not with the change in volume. Thus, in the case of a steam pipe we do not care about the change in thickness or in diameter, but we are concerned with the change in length. On the other hand, when a bearing gets hot and seizes, it is the change in diameter that causes the trouble. There are few machinists who have not had the experience, in boring a sleeve to fit a certain shaft, of having a free fit when tested just after taking a cut through the sleeve, and then later of finding

are.

that the sleeve fitted so tight that it had to be driven off the shaft. Of course, the explanation is that the sleeve becomes warm when being bored in the lathe, while the shaft is much cooler. When the sleeve cools to the temperature of the shaft, it contracts and seizes or "freezes" to the shaft. In accurate tool work the effect of differences in temperature between the measuring instruments and the work may become serious. For this reason many gages are provided with rubber or wooden handles which do not conduct heat readily. They thus prevent the heat of the hand from getting into the gages and expanding them. The foregoing discussion gives some idea of the troubles caused by these properties of materials; let us now see of what benefit they We have already seen the use that is made of the expansion of mercury in thermometers. There are numerous heat-regulating devices (called thermostats) which depend on the expansion or contraction of a bar to perform the desired operations. We find these used for regulating house-heating boilers and furnaces, incubators, and other devices where uniform temperatures are required. Probably the greatest shop use of expansion and contraction is in making shrink fits. When we want to fasten securely and permanently one piece of metal around another, we generally shrink the first onto the second. This process is used for attaching all sorts of bands and collars to shafts, cylinders, and the like, for putting tires on locomotive wheels, and for similar work. The erecting engineer uses it to put in the links in a sectional flywheel rim or to draw up bolts in the hub or in any other place where he wants to make a rigid permanent joint.

The amount that any substance will expand when heated, or contract when cooled, depends upon three things: the kind of material of which the body is made, the length of the body, and the amount which its temperature is changed. By "length" is meant the dimension along which the expansion is to be found. This might be the diameter, or the width, height, or any other dimension. That the expansion also depends on the temperature change is easily apparent. Thus a body heated from 60 to 80° F. has its temperature changed 20°, and its expansion will be twice as great as when its temperature change is only 10°, such as from 60 to 70° F. or from 30 to 40° F. The actual temperature of the body is ordinarily of no consequence. It will expand just as much when heated from 10 to 11° F. as when heated from 80 to 81° F., since the temperature change in both cases is 1o.

Under ordinary conditions of temperature most substances expand uniformly; that is, for each degree of temperature change the expansion (or contraction) is a definite part of the original length. This fraction of its own length which a body expands or contracts for 1° change in temperature is called its "coefficient of expansion." The coefficients of expansion for different metals have been determined by careful experiments, and complete tables of such coefficients may be found in various handbooks. In many cases the values given in different books do not agree, but this is undoubtedly due to variations in the compositions of the metals used in the tests. The following values are taken from the most reliable authorities and are sufficiently accurate for most purposes.

The above values are based on a temperature rise of 1° F. For 1° C. change in temperature the coefficients would be of those just given. The student is not expected to memorize these values. It must be remembered that if the length is given in feet, the expansion calculated will be in feet; and if the length is in inches, the expansion calculated will be in inches. To get the actual expansion (or contraction) of any body for 1° change in temperature, multiply the length of the body by its coefficient of expansion. The expansion for a change of temperature of 10° will be 10 times that for 1°; for a change of temperature of 50°, the expansion will be 50 times as great, etc. Example:

What will be the expansion in a steam pipe (steel) 200 ft. long when subjected to a temperature of 300° F. if erected when the temperature was 60° F.?

Coefficient of expansion = .0000065 (from table)

The law of expansion and contraction may be expressed by a formula as follows:

ETXCXL

where E is the change in length

T is the change in temperature

C is the coefficient of linear expansion

L is the original length of the body

2. The piston of a gas engine when running has a temperature about 400° higher than the cylinder in which it is running. What allowance must be made for expansion when fitting the piston if the cylinder is 12 in. in diameter? (The piston is made of cast iron.)

The piston must be made smaller than the cylinder by the amount that a 12-in. piston would expand with a temperature rise of 400°.

Coefficient of expansion = .000006

Expansion per degree = .000006 X 12 = .000072 in.
Total expansion

= .000072 X 400 = .0288 in., Answer.

119. Allowances for Shrink Fits.-In making a shrink fit, the collar or band, or whatever is to be shrunk on, is bored slightly smaller than the outside diameter of the part on which it is to be shrunk. It is then heated and thus expanded until it can be slipped into place. When it cools, it cannot return to its original size but is in a stretched condition. It, therefore, exerts a powerful grip on the article over which it has been shrunk.

1

Practice differs considerably in the allowances that are made for shrink fits. A rule which has been widely and successfully used is to allow in. for each inch of diameter. According 1000 to this rule, if we were shrinking a crank on a 6-in. shaft, the crank should be bored .006 in. small or else the shaft turned .006 in. oversize and the crank bored exactly 6 in. For a 10-in. shaft we would allow .010 in, and so on for other sizes.

This could be expressed by the following formulas:

Assuming that an allowance of .001 inch per inch of diameter is used in shrinking a steel tire onto a locomotive wheel, let us see what temperature change is required to perform this operation. Since the tire is of steel, each inch of diameter will expand .0000065 in. for every degree of temperature rise. The total expansion for each inch of diameter must, of course, be .001 inch. Therefore, the number of degrees temperature rise required will be

If the wheel and tire were at a temperature of 70° F. to begin with, the final temperature of the tire would be 70 + 154 224° F.

=

In practice, the tire would be heated to a still higher temperature in order to expand it enough so that it could be slipped on easily and quickly before it had time to cool off or to warm the wheel.

120. Unit of Heat.-Although heat is not a substance nor can it be weighed, still it is possible to measure heat through its effect upon the temperature of a body. In English-speaking countries the unit of heat in general use is known as the British thermal unit, or "B.t.u." The B.t.u. is that quantity of heat required to raise the temperature of 1 lb. of pure water 1° F. In other words, when 1 lb. of pure water is heated so that its temperature rises 1°, say, for example, from 60 to 61° F., the amount of heat absorbed by the water equals 1 B.t.u. It follows, then, that 2 lb. of water heated so that its temperature rises 1° will absorb 2 B.t.u.'s, and 3 lb. of water so heated will absorb 3 B.t.u.'s, etc. Similarly for each degree of temperature rise, a pound of water will absorb 1 B.t.u. Thus if the above pound of water is heated from 60 to 70° F. it will absorb 10 B.t.u.'s, etc.

121. Efficiencies of Boilers and Engines.-We have already mentioned the manner in which heat is transformed into work in the steam engine and the gas engine. In these two cases, through the effect of heat, we obtain a working fluid (steam or gas) under high pressure, and this working fluid by virtue of its pressure exerts a force upon the piston of an engine and performs work.

In the case of the steam engine, for example, heat is obtained by burning coal, oil, or gas in a suitable furnace or "firebox."