American Technical Society. # Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) online

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and by transposing we obtain the corresponding formula,

C=| (F _32).

EXAflPLES FOR PRACTICE.

1. To what temperature F does 58 C correspond?

Ans. 136.4 F.

2. To what temperature C does 149 F correspond ?

Ans. 65 C.

3. The difference between the temperatures of two bodies is

45 F. What is it in Centigrade degrees ?

Ans. 25 C.

4. Lead melts at 327 C. What is its melting point o the

Fahrenheit scale ? Axis. 620 F.

14

HEAT

Temperatures below the zero point can be dealt with by call-

TTST them negative and using them with a minus sign.

Example. To what temperature F does 20 C correspond ?

Solution. F = (- of 20 \ + 32

= 4. Ans.

EXAflPLES FOR PRACTICE.

1. To what temperature F does 18 C correspond?

Ans. 0.4 F.

2. To what temperature C does 40 F correspond ?

Ans. 40 C.

The temperature T s of steam in Centigrade degrees is given

by the following formula:

where H is the barometric pressure in millimeters.

In Fahrenheit degrees the temperature T' 8 is

T' a = 212 -J- 1.71 (H" 29.92),

where H" is the barometric pressure in inches.

When the barometer stands at exactly 760 millimeters or

29.92 inches, the temperature of steam is therefore 100 C or

212 F. The Centigrade scale is used .in almost all scientific

work, while the Fahrenheit scale is more* common in daily life.

EXAMPLES FOR PRACTICE.

1. What is the temperature of steam when the barometer

reads 772.8 millimeters?

Ans. 100.48 C,

2. What is the temperature of steam when -the barometer

on a mountain stands at 27.44 inches?

Ans. 207.76 F.

EXPANSION OF SOLIDS.

When the temperature of a body rises, as a rule we find an

increase in its dimensions. This is called expansion. It depends

HEAT

OH the rise of temperature and on the nature of the body itself.

A rod whose length is unity at C will have at any other tem-

perature t the length

where a is a small constant called the coefficient of linear expan-

sion. If t= 1, then the length at 1 would be simply

l-faXl=l + a,

and the increase in length would be

We may therefore define the coefficient of linear expansion

as the increase in length per Centigrade degree of a rod whose

length is unity at C. It varies a little at different temperatures

and is usually larger at higher temperatures.

The following table gives the average value of the coefficient

of linear expansion for various solids, between and 100 C

(32 to 212 F). Different specimens of the same substance

sometimes give different results, and the figures do not hold for

temperatures much beyond the given limits. They may, however,

be used for all ordinary purposes.

COEFFICIENTS OF LINEAR EXPANSION.

Porcelain

0.00000806

0.00000448

Gas carbon

0.0000055

0.0000031

Glass

0.0000057 to 0.00000883

0.0000032 to 0.00000491

Pine wood, along grain

0.00000608

O.OC000338

Cast iron

0.00001075

0.000005972

Platinum

0.00000907

0.000005039

Steel

0.00001088 to 0.00001098

0.000006044 to 0.00000610

Wrought iron

0.00001228

0.000006822

Copper

0.00001006 to 0.00001718

0.00000925 to 0.00000954

Brass

0.00001840 to 0.00001906

0.00001022 to 0.00001059

Silver

0.00001943

0.00001079

Zinc

0.00002976

0.00001653

Ice

(12 to 0), 0.0001050

(10 to 32), 0.0000583

The coefficient of surface expansion may be found by multi-

plying the above figures by two ; and the coefficient of cubical or

volume expansion, by multiplying by three.

16

HEAT

It is clear from the table that different substances expand

very unequally ; zinc, for example, expanding over three times as

much as platinum and more than twice as much as iron. If then

B B

Fig. 2.

we make a bar like A of Fig. 2, by riveting together a strip of

zinc and one of iron, and heat it, the bar will not only lengthen

but become curved, the zinc being on the convex side. If cooled

below its original temperature, the bar curves the opposite way ;

and by fixing one end of the bar the other end may be made to

show a considerable motion for small changes of temperature.

Fig. 3.

This principle is employed in some forms of metallic thermometer

(see Fig. 3). The metal spring F G H is fastened at F, the

remaining part being free to expand or contract. To this spring,

at II, is fastened a finer spring T T, clamped at 1* to the arm A,

17

10 HEAr

which is pivoted at O. The segment C D of a gear on the arm

A operates the pinion to which the hand Z Z is attached. An

additional spring S S tends to move the hand in the opposite

direction. Heat causes expansion of the spring F G H, and the

hand L> Z moves in a direction opposite to that of the hands of

a clock. The same principle is also used in thermostats. In

these instruments the free end of the bar is sometimes made to

move between stops connected with electric circuits ; and in this

way the temperature of a furnace or a room can be easily

controlled.

With the help of the table we can calculate the expansion of

a rod of any length. Let 1 represent the length of a rod at C,

and l t its length at the temperature t ; and let us find the relation

between 1 and l t .

Since a rod of unit length at will have at t the length

l-\-at, the length of a rod 1 times as long will be 1 times as

much, or 1 (1 -|- a ) . That is,

I t =l (l + at). (0

By transposing, we may put this into the form

Example. A copper wire is 65 inches long at 30 C. How

long is it at C ?

Solution. From equation 2 we have :

nr

Length at =

1 +0.00001666 X 30

- An9 -

Example. A sheet of zinc twenty inches by thirty is heated

from 32 F to 100 F. What is its increase in area ?

Solution. The surface expansion of zinc is 2 X 0.00001653,

or 0.00003306 per degree F.

The surface of the sheet is 20 X 30 = 600 sq. in.

The sheet is heated through 100 32 = 68 degrees F.

Therefore the area of the heated sheet will be

600 (1 -f 0.00003306 X 68) = 600 (1 -f 0.002248) = 601.35.

The increase in area is therefore 1.35 sq. in. Ana.

is

HEAT 11

EXAMPLES FOR PRACTICE.

1. A brass disk has a diameter of four inches at 32 F.

What is its diameter at 72 F ?

Ans. 4.00164 inches.

2. A copper tank holds ten gallons of ice water. How many

gallons of boiling water vvill it hold ?

Ans. 10.05 gallons.

Suppose the length of a rod to be given at a certain tempera-

ture , and we wish to find the length at some other temperature

t fo . Inspection of equation 2 shows that we may write

l v = 1 (I + at').

We also have directly

Dividing one equation by the other, we have

fr-loG-f-aQ.-

*t lo (! + *) '

A more convenient form of this equation, which will give

approximately correct results, is as follows :

l v = J t [1 + a (f - t) ]. (4)

Equation 4 may be used to determine the length of a bar

which has been heated through a known temperature, when the

original length and the coefficient of expansion are known.

EXAHPLES FOR PRACTICE.

1. A rod of copper is 10 feet long at 25C. What will be

its length at 85?

Ans. 10.01 feet, nearly.

2. A bar of wrought iron is 200 inches long at 40 F.

What will be its length at 148 F?

Ans. 200.147 inches.

12

HEAT

3. If the extreme difference between summer and winter

temperatures is 100 degrees F, what will be the change in length

of an iron bridge which is 250 feet long in summer ?

Ans. 0.1705 foot shorter.

EXPANSION OF LIQUIDS.

In the case of liquids and gases we have to deal only with

cubical expansion, since fluids have no definite form. The expan-

sion of liquids is much greater than that of solids. For mercury

the average coefficient between 0C and 100C is 0.0001825 per

degree. For other liquids the expansion increases rapidly with

the temperature and is very great at high temperatures. The fol-

lowing table gives some values for three common liquids .

TEMP.

WA.TER.

ALCOHOL.

ETHER.

1.

1.

10

1.0001

.0105

1.0152

20

1.0016

.0213

1.0312

30

1.0041

.0324

1.0483

40

1.0076

.0440

1.0665

Water presents a partial exception to the increase of volume

by rise of temperature. As its temperature rises from (ice

just melted) to 4C, it contracts instead of expanding, the amount

of contraction being 129 parts in a million. Above 4 it expands

like any other liquid.

This curious fact is of immense importance in nature. As the

water of rivers and lakes cools, it becomes denser and sinks, the

coldest water thus going to the bottom until 4 is reached. Below

this temperature, however, the water becomes lighter as it cools,

and stays at the surface. Ice thus forms first at the surface and

the life beneath is protected, as ice is a poor conductor of heat.

If the water contracted down to the freezing point, ice would form

from the bottom up, and a pond would become a solid mass which

would probably never thaw completely.

An interesting application of the expansion of liquids is in

the mercurial pendulum used in large clocks (Fig. 4). The pen-

dulum rod carries at its end E jar of glass or iron holding a quan

HEAT 13

tity of mercury. A rise in temperature lengthens the rod and

lowers the center of gravity of the pendulum ; but the mercury also

expands and rises in the jar, producing the opposite effect.

In this way, by using the proper amount of mercury, it is

possible to make a pendulum whose vibrations are unaffected

by changes in temperature.

EXPANSION OF GASES.

If we partially fill a bladder with air and place it

near a fire, it will become distended, showing that the

air has expanded. This expansion is practically the same

for all gases, and, for each degree, is ^^-g- or 0.00366 of

their volume at 0C ; for each degree F a gas will expand

| as much, or ^A^ of its volume at 32 F. These figures

assume that the pressure on the gas remains constant.

If then we have a quantity of gas V at 0C, at 1

it will have the volume Iff V, at 2 it will have the

volume HI y, and so on. We may express the general Fio-,4.

law as follows :

If V be the volume at 0C, then the volume V t at any

other temperature t will be

Or, in decimal form,

V t = V (1 + 0.003660- ( 6 )

If t is below zero, we subtract the second term instead of

adding it.

With this formula we may work exactly as with the formulas

for the expansion of solids on page 11.

Example. Find the volume at 150C of a gas measuring 10

cubic centimeters at 15.

Solution. Applying formula 6 twice, we obtain

V 150 = V (1 -f 0.00366x150) = 1.549 V ;

V 15 = V (1 -f 0.00366x15) = 1.0549V .

14 HEAT

Therefore

v = V " S = 10 X TO. -

EXAHPLES FOR PRACTICE.

1. What will be the volume of 400 cubic inches of oxygen

at 0C, when heated to 30 ?

Ans. 444 cubic inches, nearly.

2. M 160 cubic centimeters of hydrogen be measured at

60 C, what will be the volume of the gas at 50 ?

Ans. 110.49 cub. cm., nearly.

3. If 1,750 cubic feet of coal gas at 20C are cooled to 0,

what will be the volume ?

Ans. 1,630.6 cubic feet.

If the temperatures are expressed on the Fahrenheit scale,

formula 6 becomes

V t ' = V 32 [1 -f 0.002035 (*' 32)], (7)

where t' is the temperature F.

EXAHPLES FOR PRACTICE.

1. 1,000 cubic feet of air are heated from 32 F to 90 F.

What is the increase in volume ?

Ans. 118 cub. ft.

2. 360 cubic feet of nitrogen at 70 F are cooled to 10 F-

What is the volume after cooling ?

Ans. 319.2 cub. ft.

When a quantity of gas confined in a given space is heated

its pressure rises, and if the volume of the gas is kept constant

the increase of pressure is very nearly the same as the above-

described increase of volume at constant pressure. We may

therefore deal with pressure changes due to temperature just as

with changes of volume, employirg formulas 6 and 7 as

before.

EXAHPLE FOR PRACTICE.

A closed iron tank contains air at 50 Ibs. pressure at 32 F.

What will the pressure be if the temperature rises to 68 F,

neglecting the effect of the expansion of the tank?

Ans. 53.66 Ibs.

HEAT 15

Since a reduction of temperature from C to 1 C is

accompanied by a loss of ^ ^ of the pressure of a gas, it would

appear that by lowering the temperature to 273 C (=; 459*

F) all the gas pressure would disappear, and the molecules would

come completely to rest. But this means, from our definition of heat,

the total absence of heat energy. This point, therefore, is called

the absolute zero of temperature. Of course it can never be

reached experimentally, but recent researches have carried the

range of available temperatures far down toward it. By the

evaporation of liquid and solid air and hydrogen, a temperature of

260C lias been attained.

Thus we see that to reduce ordinary temperatures .to absolute

temperature we add 273 if we are using Centigrade units, or 461

for Fahrenheit units.

LIQUEFACTION.

When heat is applied to an amorphous substance like glass or

pitch, it changes gradually from a solid to a liquid, and there is no

definite point at which melting occurs ; but for most crystalline

substances the change from solid to liquid is well marked. For

such substances, melting (also called fusion) takes place according

to the following laws :

1. Every substance melts at a certain temperature, which is

always the same if the pressure on the substance is the same.

2. After fusion begins, the temperature of fche mass remains

at the melting point until the solid is completely melted.

3. In cooling, the substance solidifies at the temperature of

melting.

TABLE OF MELTING POINTS.

Centi- II

grade. ||

Centi-

grade.

Ether,

117

Zinc,

418

Mercury,

39.4

Silver,

908

Ice,

Gold,

1072

Paraffin,

46

Copper,

1082

Wood's metal,

65 to 70

Cast iron, 1100

to 1200

Sulphur,

114

Wrought iron,

1600

Tin,

232

Platinum,

1775

Lead,

327

Iridium,

1950

* NOTK. Some authorities quote 4G1 F.

23

10 HEAT

Most substances increase in volume on melting, but some

contract. The reverse change takes place on solidifying. Good

castings can be made only from those metals or alloys which

expand on solidifying, like cast iron and type-metal. Gold,

aluminum, lead and silver must be stamped to get sharp impres-

sions.

VAPORIZATION.

Since heat is the rapid, irregular vibratory motion of the mole-

cules, it follows that if we add heat to a body we increase this

motion. At a certain stage the vibration is so vigorous that the

molecules (if the body is a solid) can no longer hold fast to one an-

other, and the solid literally falls to pieces, that is, it melts. By

applying more heat to the liquid and still further raising its tem-

perature, we may finally reach a point at which some of the mole-

cules are moving so violently as to escape into the air, altogether

free from one another's influence. We then have a vapor, and the

change into this aeriform condition is called vaporization.

If vaporization takes place slowly, and only at the surface of

a liquid, it is called evaporation. Evaporation will be hastened

by anything that facilitates the escape of molecules from the

liquid surface, as by increasing the temperature of the liquid,

lowering the pressure on it, or causing a breeze to play over the

surface.

The fact that heat is due to moleculai motion explains why

evaporation is a cooling process. Naturally those molecules will

escape first whose motion is most violent, that is,' whose tempera-

ture is highest. The more sluggish (and therefore colder) mole-

cules stay behind. Thus, as the liquid evaporates, the departing

molecules take with them more than their proportionate share of

heat, and the remaining liquid grows colder.

Cooling by evaporation may be illustrated by a simple experi-

ment. Drop about a teaspoonful of water on a table or smooth

board, and set a small tin dish on the water. Pour three or four

tablespoonfuls of ether into the dish, and blow upon it with a pair

of bellows. After two or three minutes of vigorous blowing, the

dish will be found frozen fast to the board. (Caution. Keep

etlier away from lights. Ether vapor is highly inflammable.)

HEAT 17

When water is heated over a flame, the air (or any other gas)

present is first driven off in tiny bubbles which rise to the surface

and escape without noise. When the water nearest the flame is

raised to the boiling point, bubbles of vapor are formed, which also

rise through the water, but are condensed by the cooler layers

before getting to the surface. This formation and condensation

of steam bubbles produces the sound known as singing or simmer-

ing. The " water hammer " in steam pipes is of a somewhat simi-

lar nature but on a larger scale. When the entire mass is heatea

to the boiling point, the steam bubbles rise to the surface and

break, discharging their contents into the air with a characteristic

noise. This stage is called ebullition or boiling.

Like air, steam is colorless, transparent and invisible. What

is commonly called " a cloud of steam " is really a cloud of fine

water particles condensed from steam. Observe any steam jet, and

notice that at the end of the pipe nothing whatever can be seen,

the jet becoming visible only after it has gone far enough from

the pipe to be cooled and condensed.

The increase of volume by vaporization is usually "very great.

For example, a cubic inch of water will make 1,661 cubic inches

of steam at atmospheric pressure.

By increasing the pressure on the surface of a boiling liquid,

we make it more difficult for the molecules to escape ; they cannot

escape unless given more motion, that is, unless they have a

higher temperature than before. In other words, an increase of

pressure raises the boiling point. The following table gives the

boiling point of water under different pressures, as measured by, a

steam gage :

BOILING POINT OF WATER.

GAGE PRESSURE.

TEMPERATURE, FAHR.

(atmosphere)

50 Ibs.

100

150 "

200 "

212

297.4

337.6

365.7

387.8

The laws of vaporization are similar to the laws of fusion

given on page 15. The following table gives the boiling points io

85

IS

HEAT

degrees Centigrade of some liquids, under a pressure of .one atmos-

phere :

BOILING POINTS.

Liquid air,

188

Chloroform,

61.2

Ammonia,

38.5

Alcohol,

78.4

Sulphurous anhydride,

10.1

Mercury,

357.

Ether,

34.9

Sulphur,

444.6

DISTILLATION.

The difference in the boiling points of substances has an im-

portant application in the arts, in the separation of liquids from

Fig. 5.

solids, or of liquids from each other. The simple removal of a

liquid from a solid, as in evaporating brine to recover the salt,

needs no special appliances ; but when the evaporated liquid is to

be saved, an apparatus called a still if used, and the process is

called distillation.

A still consists essentially of two parts: a retort in which

the liquid is vaporized, and a condenser in which it is reduced to

liquid again. Fig. 5 shows a form of the apparatus for separat-

ing a liquid from a solid, or one liquid from another of different

boiling point, such as alcohol and water. The mixture is poured

into the retort B, and then heated to about 90 C, which is above

the boiling point of alcohol but below that of water. The vapor-

ized alcohol escapes through A to the worm D. This is a simple

26

HEAT . 19

helical coil of pipe surrounded by cold water, and serving to con-

dense the vapor, which runs out as a liquid at the bottom. The

cooling water is constantly changed by supplying fresh cold water

at the bottom and drawing off the heated water from the top.

This process is called fractional distillation, and is carried out

on an enormous scale in the refining of petroleum. When the dis-

tillate is to be veiy pure, it is necessary to repeat the operation one

or more times. When practicable, especially with inflammable

liquids, the heating is done by steam pipes supplied from a

distant boiler.

THE nEASUREHENT OF HEAT. Heat Units.

There are two units of measurement for determining quantities

of heat. The British thermal unit (often abbreviated B. T. U.)

is the amount of heat required to raise one pound of water from

59 to 60 Fahrenheit. The French unit, or calorie, is the amount

of heat required to raise the temperature of one gram of water

from 15 to 16 Centigrade. The former is much used in engi-

neering calculations involving steam and fuels, and the latter in all

other scientific work.

LATENT HEAT.

If we put a block of very cold ice into a vessel over a flame

and insert a thermometer into the ice, we shall observe the ther-

mometer rise to C, at which point the ice begins to melt. The

temperature of the ice and water then shows no further change

until all the ice has melted, though the heat is applied continu-

ously. Only after the melting is complete will the temperature of

the water begin to rise. It will then increase until 100 G is

reached, when ebullition begins, the temperature not rising above

100 until all the water has boiled away,

We thus see that in changing from ice to water and from

water to steam there is absorbed a considerable quantity of heat

which does not show on the thermometer. The quantities of heat

absorbed in the processes of fusion and vaporization are called

the latent heat of fusion and the latent heat of vaporization respect-

ively.

20 TIE AT

The following example shows how the latent heat of fusion

of ice may be measured. If we mix a gram of water at 80 C

with a gram at 0, we get, as we should expect, two grams at

40. But if we mix a gram of water at 80 with a gram of ice

at 0, we get two grams of water as before, but the temperature

is instead of 40. The heat which in the first case raised the

temperature of the water has in the second case been needed

merely to melt the ice. The calculation of the latent heat is

made in the following way :

One gram of water falling through 80 degrees of tempera-

ture will give out 1 X 80, or 80 calories. This quantity of heat is

required to change one gram of ice at into water at 0.

Therefore the latent heat of fusion of ice is 80 ; in other words,

the heat which will just melt a quantity of ice will raise 80 times

as much water one degree C.

By a somewhat similar method it is found that the latent

heat of vaporization of water at atmospheric pressure is 536.5.

That is, to evaporate one gram of water (already at the boiling

point) will require as much heat as would raise the temperature

of 536.5 grams one degree, or 5.365 grams from freezing to

boiling (0 to 100C).

Expressed in terms of the Fahrenheit degree and the British

thermal unit, the latent heats of fusion and vaporization are 144

and 966 respectively.

The large values of these quantities are of the greatest im-

portance both in nature and in the arts. The great amount of heat

necessary to melt the ice of winter makes the melting a slow

process, and lessens the danger of destructive floods in the spring.

In the autumn the water in freezing gives out again the heat

absorbed in melting, and the transition to winter is thus rendered

less abrupt.

Since a pound of steam in condensing will give out as much

heat as 53.65 pounds of water cooling from 100 C to 90 C, or

from 90 to 80, it follows that steam pipes for heating may be

made smaller thaa water pipes for the same service. It also

shows the value of steam as a carrier of heat; and in the arts

advantage of this is taken in innumerable ways. (See also page

19Y

28

HEAT

SPECIFIC HEAT.

When equal quantities of different substances are raised

equally in temperature, different amounts of heat are required ;

and in cooling- through equal temperature intervals different sub-

stances give out different amounts of heat.

For example, if we mix a pound of water at #0 C with a

pound at C, we get two pounds at 40 ; but if we pour a

pound of lead shot at 80 into a pound of water at 0, the result-

ing temperature will be only 2.3= A pound ol lead, therefore,

falling through 77.7 degrees of temperature, is able to raise a

pound of water only 2.3 degrees. The fall of temperature of the

hot body is nearly twice as great as in the first case, and the heat

given out in the fall only about one-seventeenth as much. The

heat capacity of the lead is therefore much less than that of the

water.

If we know how much heat will raise the temperature of a

given substance a certain amount, and how much is required to

raise the temperature of an equal quantity of water by the same

amount, then the ratio of these two quantities is called the spe-

cific heat of the substance. In other words, if we take the

C=| (F _32).

EXAflPLES FOR PRACTICE.

1. To what temperature F does 58 C correspond?

Ans. 136.4 F.

2. To what temperature C does 149 F correspond ?

Ans. 65 C.

3. The difference between the temperatures of two bodies is

45 F. What is it in Centigrade degrees ?

Ans. 25 C.

4. Lead melts at 327 C. What is its melting point o the

Fahrenheit scale ? Axis. 620 F.

14

HEAT

Temperatures below the zero point can be dealt with by call-

TTST them negative and using them with a minus sign.

Example. To what temperature F does 20 C correspond ?

Solution. F = (- of 20 \ + 32

= 4. Ans.

EXAflPLES FOR PRACTICE.

1. To what temperature F does 18 C correspond?

Ans. 0.4 F.

2. To what temperature C does 40 F correspond ?

Ans. 40 C.

The temperature T s of steam in Centigrade degrees is given

by the following formula:

where H is the barometric pressure in millimeters.

In Fahrenheit degrees the temperature T' 8 is

T' a = 212 -J- 1.71 (H" 29.92),

where H" is the barometric pressure in inches.

When the barometer stands at exactly 760 millimeters or

29.92 inches, the temperature of steam is therefore 100 C or

212 F. The Centigrade scale is used .in almost all scientific

work, while the Fahrenheit scale is more* common in daily life.

EXAMPLES FOR PRACTICE.

1. What is the temperature of steam when the barometer

reads 772.8 millimeters?

Ans. 100.48 C,

2. What is the temperature of steam when -the barometer

on a mountain stands at 27.44 inches?

Ans. 207.76 F.

EXPANSION OF SOLIDS.

When the temperature of a body rises, as a rule we find an

increase in its dimensions. This is called expansion. It depends

HEAT

OH the rise of temperature and on the nature of the body itself.

A rod whose length is unity at C will have at any other tem-

perature t the length

where a is a small constant called the coefficient of linear expan-

sion. If t= 1, then the length at 1 would be simply

l-faXl=l + a,

and the increase in length would be

We may therefore define the coefficient of linear expansion

as the increase in length per Centigrade degree of a rod whose

length is unity at C. It varies a little at different temperatures

and is usually larger at higher temperatures.

The following table gives the average value of the coefficient

of linear expansion for various solids, between and 100 C

(32 to 212 F). Different specimens of the same substance

sometimes give different results, and the figures do not hold for

temperatures much beyond the given limits. They may, however,

be used for all ordinary purposes.

COEFFICIENTS OF LINEAR EXPANSION.

Porcelain

0.00000806

0.00000448

Gas carbon

0.0000055

0.0000031

Glass

0.0000057 to 0.00000883

0.0000032 to 0.00000491

Pine wood, along grain

0.00000608

O.OC000338

Cast iron

0.00001075

0.000005972

Platinum

0.00000907

0.000005039

Steel

0.00001088 to 0.00001098

0.000006044 to 0.00000610

Wrought iron

0.00001228

0.000006822

Copper

0.00001006 to 0.00001718

0.00000925 to 0.00000954

Brass

0.00001840 to 0.00001906

0.00001022 to 0.00001059

Silver

0.00001943

0.00001079

Zinc

0.00002976

0.00001653

Ice

(12 to 0), 0.0001050

(10 to 32), 0.0000583

The coefficient of surface expansion may be found by multi-

plying the above figures by two ; and the coefficient of cubical or

volume expansion, by multiplying by three.

16

HEAT

It is clear from the table that different substances expand

very unequally ; zinc, for example, expanding over three times as

much as platinum and more than twice as much as iron. If then

B B

Fig. 2.

we make a bar like A of Fig. 2, by riveting together a strip of

zinc and one of iron, and heat it, the bar will not only lengthen

but become curved, the zinc being on the convex side. If cooled

below its original temperature, the bar curves the opposite way ;

and by fixing one end of the bar the other end may be made to

show a considerable motion for small changes of temperature.

Fig. 3.

This principle is employed in some forms of metallic thermometer

(see Fig. 3). The metal spring F G H is fastened at F, the

remaining part being free to expand or contract. To this spring,

at II, is fastened a finer spring T T, clamped at 1* to the arm A,

17

10 HEAr

which is pivoted at O. The segment C D of a gear on the arm

A operates the pinion to which the hand Z Z is attached. An

additional spring S S tends to move the hand in the opposite

direction. Heat causes expansion of the spring F G H, and the

hand L> Z moves in a direction opposite to that of the hands of

a clock. The same principle is also used in thermostats. In

these instruments the free end of the bar is sometimes made to

move between stops connected with electric circuits ; and in this

way the temperature of a furnace or a room can be easily

controlled.

With the help of the table we can calculate the expansion of

a rod of any length. Let 1 represent the length of a rod at C,

and l t its length at the temperature t ; and let us find the relation

between 1 and l t .

Since a rod of unit length at will have at t the length

l-\-at, the length of a rod 1 times as long will be 1 times as

much, or 1 (1 -|- a ) . That is,

I t =l (l + at). (0

By transposing, we may put this into the form

Example. A copper wire is 65 inches long at 30 C. How

long is it at C ?

Solution. From equation 2 we have :

nr

Length at =

1 +0.00001666 X 30

- An9 -

Example. A sheet of zinc twenty inches by thirty is heated

from 32 F to 100 F. What is its increase in area ?

Solution. The surface expansion of zinc is 2 X 0.00001653,

or 0.00003306 per degree F.

The surface of the sheet is 20 X 30 = 600 sq. in.

The sheet is heated through 100 32 = 68 degrees F.

Therefore the area of the heated sheet will be

600 (1 -f 0.00003306 X 68) = 600 (1 -f 0.002248) = 601.35.

The increase in area is therefore 1.35 sq. in. Ana.

is

HEAT 11

EXAMPLES FOR PRACTICE.

1. A brass disk has a diameter of four inches at 32 F.

What is its diameter at 72 F ?

Ans. 4.00164 inches.

2. A copper tank holds ten gallons of ice water. How many

gallons of boiling water vvill it hold ?

Ans. 10.05 gallons.

Suppose the length of a rod to be given at a certain tempera-

ture , and we wish to find the length at some other temperature

t fo . Inspection of equation 2 shows that we may write

l v = 1 (I + at').

We also have directly

Dividing one equation by the other, we have

fr-loG-f-aQ.-

*t lo (! + *) '

A more convenient form of this equation, which will give

approximately correct results, is as follows :

l v = J t [1 + a (f - t) ]. (4)

Equation 4 may be used to determine the length of a bar

which has been heated through a known temperature, when the

original length and the coefficient of expansion are known.

EXAHPLES FOR PRACTICE.

1. A rod of copper is 10 feet long at 25C. What will be

its length at 85?

Ans. 10.01 feet, nearly.

2. A bar of wrought iron is 200 inches long at 40 F.

What will be its length at 148 F?

Ans. 200.147 inches.

12

HEAT

3. If the extreme difference between summer and winter

temperatures is 100 degrees F, what will be the change in length

of an iron bridge which is 250 feet long in summer ?

Ans. 0.1705 foot shorter.

EXPANSION OF LIQUIDS.

In the case of liquids and gases we have to deal only with

cubical expansion, since fluids have no definite form. The expan-

sion of liquids is much greater than that of solids. For mercury

the average coefficient between 0C and 100C is 0.0001825 per

degree. For other liquids the expansion increases rapidly with

the temperature and is very great at high temperatures. The fol-

lowing table gives some values for three common liquids .

TEMP.

WA.TER.

ALCOHOL.

ETHER.

1.

1.

10

1.0001

.0105

1.0152

20

1.0016

.0213

1.0312

30

1.0041

.0324

1.0483

40

1.0076

.0440

1.0665

Water presents a partial exception to the increase of volume

by rise of temperature. As its temperature rises from (ice

just melted) to 4C, it contracts instead of expanding, the amount

of contraction being 129 parts in a million. Above 4 it expands

like any other liquid.

This curious fact is of immense importance in nature. As the

water of rivers and lakes cools, it becomes denser and sinks, the

coldest water thus going to the bottom until 4 is reached. Below

this temperature, however, the water becomes lighter as it cools,

and stays at the surface. Ice thus forms first at the surface and

the life beneath is protected, as ice is a poor conductor of heat.

If the water contracted down to the freezing point, ice would form

from the bottom up, and a pond would become a solid mass which

would probably never thaw completely.

An interesting application of the expansion of liquids is in

the mercurial pendulum used in large clocks (Fig. 4). The pen-

dulum rod carries at its end E jar of glass or iron holding a quan

HEAT 13

tity of mercury. A rise in temperature lengthens the rod and

lowers the center of gravity of the pendulum ; but the mercury also

expands and rises in the jar, producing the opposite effect.

In this way, by using the proper amount of mercury, it is

possible to make a pendulum whose vibrations are unaffected

by changes in temperature.

EXPANSION OF GASES.

If we partially fill a bladder with air and place it

near a fire, it will become distended, showing that the

air has expanded. This expansion is practically the same

for all gases, and, for each degree, is ^^-g- or 0.00366 of

their volume at 0C ; for each degree F a gas will expand

| as much, or ^A^ of its volume at 32 F. These figures

assume that the pressure on the gas remains constant.

If then we have a quantity of gas V at 0C, at 1

it will have the volume Iff V, at 2 it will have the

volume HI y, and so on. We may express the general Fio-,4.

law as follows :

If V be the volume at 0C, then the volume V t at any

other temperature t will be

Or, in decimal form,

V t = V (1 + 0.003660- ( 6 )

If t is below zero, we subtract the second term instead of

adding it.

With this formula we may work exactly as with the formulas

for the expansion of solids on page 11.

Example. Find the volume at 150C of a gas measuring 10

cubic centimeters at 15.

Solution. Applying formula 6 twice, we obtain

V 150 = V (1 -f 0.00366x150) = 1.549 V ;

V 15 = V (1 -f 0.00366x15) = 1.0549V .

14 HEAT

Therefore

v = V " S = 10 X TO. -

EXAHPLES FOR PRACTICE.

1. What will be the volume of 400 cubic inches of oxygen

at 0C, when heated to 30 ?

Ans. 444 cubic inches, nearly.

2. M 160 cubic centimeters of hydrogen be measured at

60 C, what will be the volume of the gas at 50 ?

Ans. 110.49 cub. cm., nearly.

3. If 1,750 cubic feet of coal gas at 20C are cooled to 0,

what will be the volume ?

Ans. 1,630.6 cubic feet.

If the temperatures are expressed on the Fahrenheit scale,

formula 6 becomes

V t ' = V 32 [1 -f 0.002035 (*' 32)], (7)

where t' is the temperature F.

EXAHPLES FOR PRACTICE.

1. 1,000 cubic feet of air are heated from 32 F to 90 F.

What is the increase in volume ?

Ans. 118 cub. ft.

2. 360 cubic feet of nitrogen at 70 F are cooled to 10 F-

What is the volume after cooling ?

Ans. 319.2 cub. ft.

When a quantity of gas confined in a given space is heated

its pressure rises, and if the volume of the gas is kept constant

the increase of pressure is very nearly the same as the above-

described increase of volume at constant pressure. We may

therefore deal with pressure changes due to temperature just as

with changes of volume, employirg formulas 6 and 7 as

before.

EXAHPLE FOR PRACTICE.

A closed iron tank contains air at 50 Ibs. pressure at 32 F.

What will the pressure be if the temperature rises to 68 F,

neglecting the effect of the expansion of the tank?

Ans. 53.66 Ibs.

HEAT 15

Since a reduction of temperature from C to 1 C is

accompanied by a loss of ^ ^ of the pressure of a gas, it would

appear that by lowering the temperature to 273 C (=; 459*

F) all the gas pressure would disappear, and the molecules would

come completely to rest. But this means, from our definition of heat,

the total absence of heat energy. This point, therefore, is called

the absolute zero of temperature. Of course it can never be

reached experimentally, but recent researches have carried the

range of available temperatures far down toward it. By the

evaporation of liquid and solid air and hydrogen, a temperature of

260C lias been attained.

Thus we see that to reduce ordinary temperatures .to absolute

temperature we add 273 if we are using Centigrade units, or 461

for Fahrenheit units.

LIQUEFACTION.

When heat is applied to an amorphous substance like glass or

pitch, it changes gradually from a solid to a liquid, and there is no

definite point at which melting occurs ; but for most crystalline

substances the change from solid to liquid is well marked. For

such substances, melting (also called fusion) takes place according

to the following laws :

1. Every substance melts at a certain temperature, which is

always the same if the pressure on the substance is the same.

2. After fusion begins, the temperature of fche mass remains

at the melting point until the solid is completely melted.

3. In cooling, the substance solidifies at the temperature of

melting.

TABLE OF MELTING POINTS.

Centi- II

grade. ||

Centi-

grade.

Ether,

117

Zinc,

418

Mercury,

39.4

Silver,

908

Ice,

Gold,

1072

Paraffin,

46

Copper,

1082

Wood's metal,

65 to 70

Cast iron, 1100

to 1200

Sulphur,

114

Wrought iron,

1600

Tin,

232

Platinum,

1775

Lead,

327

Iridium,

1950

* NOTK. Some authorities quote 4G1 F.

23

10 HEAT

Most substances increase in volume on melting, but some

contract. The reverse change takes place on solidifying. Good

castings can be made only from those metals or alloys which

expand on solidifying, like cast iron and type-metal. Gold,

aluminum, lead and silver must be stamped to get sharp impres-

sions.

VAPORIZATION.

Since heat is the rapid, irregular vibratory motion of the mole-

cules, it follows that if we add heat to a body we increase this

motion. At a certain stage the vibration is so vigorous that the

molecules (if the body is a solid) can no longer hold fast to one an-

other, and the solid literally falls to pieces, that is, it melts. By

applying more heat to the liquid and still further raising its tem-

perature, we may finally reach a point at which some of the mole-

cules are moving so violently as to escape into the air, altogether

free from one another's influence. We then have a vapor, and the

change into this aeriform condition is called vaporization.

If vaporization takes place slowly, and only at the surface of

a liquid, it is called evaporation. Evaporation will be hastened

by anything that facilitates the escape of molecules from the

liquid surface, as by increasing the temperature of the liquid,

lowering the pressure on it, or causing a breeze to play over the

surface.

The fact that heat is due to moleculai motion explains why

evaporation is a cooling process. Naturally those molecules will

escape first whose motion is most violent, that is,' whose tempera-

ture is highest. The more sluggish (and therefore colder) mole-

cules stay behind. Thus, as the liquid evaporates, the departing

molecules take with them more than their proportionate share of

heat, and the remaining liquid grows colder.

Cooling by evaporation may be illustrated by a simple experi-

ment. Drop about a teaspoonful of water on a table or smooth

board, and set a small tin dish on the water. Pour three or four

tablespoonfuls of ether into the dish, and blow upon it with a pair

of bellows. After two or three minutes of vigorous blowing, the

dish will be found frozen fast to the board. (Caution. Keep

etlier away from lights. Ether vapor is highly inflammable.)

HEAT 17

When water is heated over a flame, the air (or any other gas)

present is first driven off in tiny bubbles which rise to the surface

and escape without noise. When the water nearest the flame is

raised to the boiling point, bubbles of vapor are formed, which also

rise through the water, but are condensed by the cooler layers

before getting to the surface. This formation and condensation

of steam bubbles produces the sound known as singing or simmer-

ing. The " water hammer " in steam pipes is of a somewhat simi-

lar nature but on a larger scale. When the entire mass is heatea

to the boiling point, the steam bubbles rise to the surface and

break, discharging their contents into the air with a characteristic

noise. This stage is called ebullition or boiling.

Like air, steam is colorless, transparent and invisible. What

is commonly called " a cloud of steam " is really a cloud of fine

water particles condensed from steam. Observe any steam jet, and

notice that at the end of the pipe nothing whatever can be seen,

the jet becoming visible only after it has gone far enough from

the pipe to be cooled and condensed.

The increase of volume by vaporization is usually "very great.

For example, a cubic inch of water will make 1,661 cubic inches

of steam at atmospheric pressure.

By increasing the pressure on the surface of a boiling liquid,

we make it more difficult for the molecules to escape ; they cannot

escape unless given more motion, that is, unless they have a

higher temperature than before. In other words, an increase of

pressure raises the boiling point. The following table gives the

boiling point of water under different pressures, as measured by, a

steam gage :

BOILING POINT OF WATER.

GAGE PRESSURE.

TEMPERATURE, FAHR.

(atmosphere)

50 Ibs.

100

150 "

200 "

212

297.4

337.6

365.7

387.8

The laws of vaporization are similar to the laws of fusion

given on page 15. The following table gives the boiling points io

85

IS

HEAT

degrees Centigrade of some liquids, under a pressure of .one atmos-

phere :

BOILING POINTS.

Liquid air,

188

Chloroform,

61.2

Ammonia,

38.5

Alcohol,

78.4

Sulphurous anhydride,

10.1

Mercury,

357.

Ether,

34.9

Sulphur,

444.6

DISTILLATION.

The difference in the boiling points of substances has an im-

portant application in the arts, in the separation of liquids from

Fig. 5.

solids, or of liquids from each other. The simple removal of a

liquid from a solid, as in evaporating brine to recover the salt,

needs no special appliances ; but when the evaporated liquid is to

be saved, an apparatus called a still if used, and the process is

called distillation.

A still consists essentially of two parts: a retort in which

the liquid is vaporized, and a condenser in which it is reduced to

liquid again. Fig. 5 shows a form of the apparatus for separat-

ing a liquid from a solid, or one liquid from another of different

boiling point, such as alcohol and water. The mixture is poured

into the retort B, and then heated to about 90 C, which is above

the boiling point of alcohol but below that of water. The vapor-

ized alcohol escapes through A to the worm D. This is a simple

26

HEAT . 19

helical coil of pipe surrounded by cold water, and serving to con-

dense the vapor, which runs out as a liquid at the bottom. The

cooling water is constantly changed by supplying fresh cold water

at the bottom and drawing off the heated water from the top.

This process is called fractional distillation, and is carried out

on an enormous scale in the refining of petroleum. When the dis-

tillate is to be veiy pure, it is necessary to repeat the operation one

or more times. When practicable, especially with inflammable

liquids, the heating is done by steam pipes supplied from a

distant boiler.

THE nEASUREHENT OF HEAT. Heat Units.

There are two units of measurement for determining quantities

of heat. The British thermal unit (often abbreviated B. T. U.)

is the amount of heat required to raise one pound of water from

59 to 60 Fahrenheit. The French unit, or calorie, is the amount

of heat required to raise the temperature of one gram of water

from 15 to 16 Centigrade. The former is much used in engi-

neering calculations involving steam and fuels, and the latter in all

other scientific work.

LATENT HEAT.

If we put a block of very cold ice into a vessel over a flame

and insert a thermometer into the ice, we shall observe the ther-

mometer rise to C, at which point the ice begins to melt. The

temperature of the ice and water then shows no further change

until all the ice has melted, though the heat is applied continu-

ously. Only after the melting is complete will the temperature of

the water begin to rise. It will then increase until 100 G is

reached, when ebullition begins, the temperature not rising above

100 until all the water has boiled away,

We thus see that in changing from ice to water and from

water to steam there is absorbed a considerable quantity of heat

which does not show on the thermometer. The quantities of heat

absorbed in the processes of fusion and vaporization are called

the latent heat of fusion and the latent heat of vaporization respect-

ively.

20 TIE AT

The following example shows how the latent heat of fusion

of ice may be measured. If we mix a gram of water at 80 C

with a gram at 0, we get, as we should expect, two grams at

40. But if we mix a gram of water at 80 with a gram of ice

at 0, we get two grams of water as before, but the temperature

is instead of 40. The heat which in the first case raised the

temperature of the water has in the second case been needed

merely to melt the ice. The calculation of the latent heat is

made in the following way :

One gram of water falling through 80 degrees of tempera-

ture will give out 1 X 80, or 80 calories. This quantity of heat is

required to change one gram of ice at into water at 0.

Therefore the latent heat of fusion of ice is 80 ; in other words,

the heat which will just melt a quantity of ice will raise 80 times

as much water one degree C.

By a somewhat similar method it is found that the latent

heat of vaporization of water at atmospheric pressure is 536.5.

That is, to evaporate one gram of water (already at the boiling

point) will require as much heat as would raise the temperature

of 536.5 grams one degree, or 5.365 grams from freezing to

boiling (0 to 100C).

Expressed in terms of the Fahrenheit degree and the British

thermal unit, the latent heats of fusion and vaporization are 144

and 966 respectively.

The large values of these quantities are of the greatest im-

portance both in nature and in the arts. The great amount of heat

necessary to melt the ice of winter makes the melting a slow

process, and lessens the danger of destructive floods in the spring.

In the autumn the water in freezing gives out again the heat

absorbed in melting, and the transition to winter is thus rendered

less abrupt.

Since a pound of steam in condensing will give out as much

heat as 53.65 pounds of water cooling from 100 C to 90 C, or

from 90 to 80, it follows that steam pipes for heating may be

made smaller thaa water pipes for the same service. It also

shows the value of steam as a carrier of heat; and in the arts

advantage of this is taken in innumerable ways. (See also page

19Y

28

HEAT

SPECIFIC HEAT.

When equal quantities of different substances are raised

equally in temperature, different amounts of heat are required ;

and in cooling- through equal temperature intervals different sub-

stances give out different amounts of heat.

For example, if we mix a pound of water at #0 C with a

pound at C, we get two pounds at 40 ; but if we pour a

pound of lead shot at 80 into a pound of water at 0, the result-

ing temperature will be only 2.3= A pound ol lead, therefore,

falling through 77.7 degrees of temperature, is able to raise a

pound of water only 2.3 degrees. The fall of temperature of the

hot body is nearly twice as great as in the first case, and the heat

given out in the fall only about one-seventeenth as much. The

heat capacity of the lead is therefore much less than that of the

water.

If we know how much heat will raise the temperature of a

given substance a certain amount, and how much is required to

raise the temperature of an equal quantity of water by the same

amount, then the ratio of these two quantities is called the spe-

cific heat of the substance. In other words, if we take the

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