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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Font size 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

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

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

Centi-

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

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
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