different degrees of heat for comparison, so we must resort to some
other means. A simple method is to use some substance whose
volume changes a definite amount for a definite change in temper-
ature and always has the same volume for the same temperature.
Mercury and alcohol are suitable substances and may be placed in
a glass bulb, to which is connected a glass tube of small bore. All
the air is drawn out of the tube, and the end is sealed so that the
thermometric substance can expand or contract in a vacuum.
The tube having been sealed, the bulb is placed in melting ice and
the height of the mercury in the tube noted. It is then placed
THE STEAM ENGINE. 79*
in steam (or boiling water) at atmospheric pressure and the height
of the column again noted. On the Fahrenheit scale the melting
point is called 32, and the boiling point 212, and the intervening
space is divided into 180 equal parts. In the Centigrade scale
the melting point is called and the boiling point 100; there are
100 equal intervals between them. Thus we see that 180 F =:
100 C, or 1 C = 1.8 F.
Example : What is the temperature of 50 C on the F scale ?
50 C = 50 X 1.8 = 90 F above the melting point
or 90 -f 32 = 122 F above zero.
In order to compare temperatures, we place the thermometer
in contact with the substance whose degree of heat we wish to
know and then observe the height of the liquid column in the ther-
mometer. The height of this column depends upon the expansion
of the thermometric substance and indicates the intensity of heat,
or the temperature as we commonly call it. We use a thermom-
eter to measure the intensity of heat, but not the quantity of
For measuring the intensity of heat, the degree is the unit-,
for measuring the quantity of heat we have another unit, which is
the amount of heat necessary to raise one pound of water from 61
F to 62 F. This is called the British thermal unit (B. T. U.).
To raise one pound of water from 60 F to 62 F, or to raise two
pounds from 60 F to 61 F, will require 2 B. T. U.
Suppose we have a small bar of iron heated to a white heat ;
its temperature will be high, but it will contain a relatively
small quantity of heat, that is, it will not require a great many
B. T. U. to raise its temperature to this high point. But suppose
this same number of heat units were transferred to a ton of iron ;
the temperature would scarcely be changed, for the infinitely
greater number of particles would have a correspondingly less
number of vibrations.
Experience teaches us that when a rifle-ball strikes a target
it stops, and that the energy which it possesses by virtue of its
bodily motion is suddenly transformed into energy of molecular
motion. Energy is indestructible; the molecular motion of the
impinging body is at once increased and heat is developed. In
general, whenever moving bodies are brought to rest, either sud-
SO THE STEAM ENGINE.
denly as by impact or gradually as by friction, the kinetic energy
of the moving mass is transformed into molecular kinetic energy,
and we say that the bodies become heated.
We have now seen that we can transform energy of motion
into heat. Also by means of suitable apparatus we can transform
heat into energy of motion. Heat is the lowest form of energy,
and while it is comparatively easy to transform other forms into
heat, it is not as easy to change heat into the higher forms oi
energy. The principle of the transformation is simple enough, but
if we are to have an efficient engine, we must be able to extract
practically all of the heat f rom the working substance. This, how-
ever, is impossible, because the ordinary ranges of temperature
used in practice are so far removed from the absolute zero o(
temperature, that with the most perfect machines we can at best
recover but a fraction of the heat; the rest passing out of the
The transformation is accomplished by means of a working
substance which passes from the temperature of a heat generator
into a refrigerator; the heat given up during the change is trans-
formed into work. By the term refrigerator we mean the low
temperature of the working substance at exhaust. The greater
the temperature of the source of heat, or the lower the temperature
of the refrigerator, the greater will be the amount of heat that can
be abstracted and converted into useful work. If the temperature
of the refrigerator could be reduced to the absolute zero, all the
heat would be removed from the working substance, and the only
loss would be that due to mechanical imperfections of the engine ;
but since the absolute zero is 461 below the zero on the Fahren-
heit scale, or 493 below the freezing point, we must at best allow
a relatively large amount of heat to pass out of the engine into
the refrigerator without having done any work at all.
The unit of work is the foot-pound ; that is, the work done
in raising one pound one foot. By means of careful experiments
it has been determined that for every 778 foot-pounds of work
transformed into heat there is developed one B. T. U. This value
778 is known as the Mechanical Equivalent of heat. It means
that one B. T. U. and 778 foot-pounds of work are mutually
THE STEAM ENGINE.
EXPANSION OF OASES.
A perfect gas, strictly speaking, is one that cannot be lique-
fied ; ordinarily, however, we apply the term to those gases that can
be liquefied only with great difficulty, that is, under extreme pres-
sure and a great reduction of temperature. For every perfect gas
there is a definite relation between the pressure and volume, and
what is known as Boyle's Law has been found to hold true, viz. :
The pressure of a perfect gas at constant temperature varies in-
versely as the volume ; that is, if the temperature remains constant
the pressure becomes less as fast as the volume becomes greater,
or conversely the volume becomes less as fast as the pressure
becomes greater. Now if the pressure becomes twice as great, the
volume becomes half as large, and if the volume becomes three
times as great, the pressure will be only one-third as much. Hence
we see that however the pressure may vary, the volume will change
in such a way that the pressure multiplied by the volume will
always be constant, provided the temperature remains the same,
This simple law is expressed thus :
P X V = C
P pressure in pounds per square inch (absolute)
V volume in cubic feet
C a constant which has different values for different gases.
Gases that are not easily liquefied, such as hydrogen, oxygen
and air, follow this law fairly well, but those that are easily lique-
fied, such as steam and ammonia, do not follow it at all.
The value of C is not the same for all gases, and as no gas is,
strictly speaking, a perfect gas, >ts value varies slightly with the
temperature. For air, which is nearly a perfect gas, its value is
182.08 at 32 F.
Example. What is the absolute pressure per square inch of
one pound of air if the temperature is 32 F, and the volume
4.129 cubic feet?
V = 4.129
P = 44.1 pounds per square inch, absolute.
THE STEAM ENGINE.
Let us discuss this law by means of a diagram. Fig. 1 is
drawn with O Y and O X at right angles to each other ; pressures
are measured to any convenient scale on O Y and volumes on O X.
O C represents 12.387 cubic feet and O D represents 14.7 pounds,
since P X V = 1 82.08. O F represents 24.774 cubic feet and O G
7.35 pounds. I.nlike manner O L represents 6.19 cubic feet and O N
29.41 pounds. Then if we draw perpendiculars to O X at L, C
and F, and perpendiculars to O Y at N, D and G, they will meet
in the points M, E and H. The curve A B is drawn through
these points. Then for
any pressure we can find
the corresponding volume
or vice versa. The area of
the rectangle O D E C
equals that of the rectangle
O G H F and also that of
the rectangle O N M L.
That this is so is readily
seen from the fact that the
product of the pressure and
its corresponding volume
If we plot a curve
using this equation we will
get a rectangular hyperbola, as shown in " Steam Engine Indi-
cators." This curve is called an isothermal curve or curve of
If the volume of a perfect gas remains constant, the pressure
will vary as the temperature. Or, if the pressure remains constant,
the volume will vary as the temperature. This is known as the
Law of Charles. From this we see that, as the temperature
decreases, either the pressure or the volume will decrease a pro-
portionate amount, and this must continue as long as there is any
heat in the gas; finally a low temperature (the absolute zero)
will be reached, where there is no more heat, and consequently
either the pressure or the volume must be zero, provided this law
holds true at such a very low temperature.
The law states that any change of pressure or volume is pro-
THE SfEAM ENGINE. 83
portional to the change in temperature, that is, the new volume is
equal to the first volume plus or minus some fractional part of
this volume, called the coefficient of expansion, multiplied by the
change in temperature. We may express the formula thus:
Pj Vj =P V+(PV)& X t
p V(l-f kf).
Where P l and V x are the new pressure and volume
P and V are the first pressure and volume
Jc is the coefficient of expansion for the gas
t is the change in temperature.
From Boyle's Law we know that P V = C ; hence we may
write the above equation :
P 1 V,=0(l + *0
= * C(T +
From careful experiments on the expansion of air, Regnault
determined the value of the coefficient k to be .003654 for Centi-
grade units. This value is constant between freezing point, 0,
and boiling point, 100. Substituting this value of k in our last
equation, we have :
= k C (273.7 + f).
Now if we should make the change of temperature, t, equal
to 273.7 we should have:
P, Y! = k C (273.7 273.7) =
r, v t = o.
Therefore we must have reached the absolute zero at 273.7
below the freezing point, because here P l X V t has reached 0, as
we have previously seen must be the case at the absolute zero.
273.7 X 1.8 = 492.7 for the F scale. Therefore the absolute
zero is 492.7 32 = 460.7 below zero on the Fahrenheit scale.
For ordinary work 461 will be sufficiently accurate.
If we let P = absolute pressure in pounds per square inch
V = volume of one pound in cubic feet
T = absolute temperature on Fahrenheit scale,
Then, PV = CT&.
I' C equals .3693 for air.
THE STEAM ENGINE.
Example. If one pound of air occupies 16.606 cubic feet at
a pressure of 14.7 pounds per square inch, what is its temperature?
P X V = C X T
14.7 X 16.606 = .3693 X T
T _ 244.108
T = 661.
This value 661 is absolute temperature, and to find the
Fahrenheit temperature 461 must be subtracted from it. Thus,
061 461 =:200 F.
Saturated Vapor. The process of converting a liquid into
a vapor is known as vaporization; the product thus formed is
readily condensed and
therefore does not follow
the laws of perfect gases
at all. A dry saturated
vapor is one that has
just enough heat in it
to keep it in the form
of a vapor; if we add
more heat it becomes
superheated. A super-
heated vapor may lose
a part of its heat without condensation ; a saturated vapor cannot.
When a saturated vapor loses a part of its heat some of it will
condense and we say that the vapor is wet.
Steam is simply the vapor from water and we shall confine
our discussion to this alone. Suppose we have a vertical cylinder,
as shown in Fig. 2, fitted with a light piston free to move up and
down, yet so constructed that it may be loaded at will. Suppose
that there is one pound of water at a temperature of 32 F in the
bottom of this cylinder, and that the piston rests upon its surface.
Now, if we apply heat by means of a gas flame or fire, we shall
notice the following effects:
First. The temperature of the water will gradually rise until
it reaches the temperature at which steam is formed. This
temperature will depend upon the pressure, or the load on the
THE STEAM ENGINE. 85
piston. If the piston is very light, we may neglect its weight and
consider that there is simply the atmospheric pressure of 14.7
pounds per square inch acting on the water surface. At this
pressure steam will begin to form at 212 F.
Second. As soon as 212 F is reached, steam will begin to
form and the piston will steadily rise, but no matter how hot the
fire may be, the temperature of both water and steam will remain
at 212 until all the water is evaporated. We had one pound of
water at 32 F and at 14.7 pounds absolute pressure, and found
that steam formed at a temperature of 212 F and remained at
that temperature. We added 180.9 B. T. U., the heat of the
liquid, to bring the water from 32 to the boiling point. To con-
vert water at 212 into steam at 212, we added 965.7 B. T. U.
more. This quantity, known as the latent heat, or heat of vapor-
ization, makes the total heat 1,146.6 B. T. U. If we should
measure the volume carefully after all the water was evaporated,
we should find that there was just 2G.36 cubic feet of dry saturated
steam. We had one pound of water, and therefore must have one
pound of steam, for none of it could escape ; hence one cubic foot
will weigh . ; . = 0.03794 pounds, which is known as the
density of steam at 14.7 pounds absolute pressure or 212 F.
In the Table of Properties of Saturated Steam (see page 14)
all these quantities are found in the order given and at the pres-
sure of 14.7 pounds above vacuum.
Suppose now we place a weight of 85.3 pounds on the piston.
The pressure is 85.3 pounds plus 14 7 pounds, or 100 pounds abso-
lute. We shall now find that no steam will form until a temper-
ature of 327.58 is reached. Starting with water at 32, it will
be necessary to add 297.9 B. T. U. before a temperature of
327.58 is reached, and also we must add 884.0 B. T. U. more to
vaporize it, making a total heat of 1,181.9 B. T. U. Under this
greater pressure the steam occupies a volume of only 4.403 cubic
feet, or one cubic foot of it weighs . = 0.2271 pound.
Of course it would be impossible to determine all these dif-
ferent quantities by actual experiment, and at all pressures varying
from vacuum to the high pressures, used in water-tube boilers.
86 ME STEAM
Fortunately \ve are able to compute them all from equations which
have been carefully determined by experiment. If saturated
steam were a perfect gas, we could easily calculate all the relations
of pressure, volume and temperature from the equation PV= CT,
but steam is so far removed from the state of a perfect gas that
these relations do not hold, and the true equations become very
complex. The following equation proposed by Rankine is one of
the simplest, and gives fairly good results:
, A B C
Iog 10 l = A _ _ 2
in which P = pressure in pounds per square inch above vacuum.
A = 6.1007
B = 2,732
C = 396,945
T = absolute temperature in Fahrenheit degrees.
By the aid of such equations as this, all the different quan-
tities found in the steam tables may be calculated. These equations
are based on careful experiments and give very satisfactory results.
Steam Tables. We have already seen that any change in
the temperature of saturated steam produces a change of pressure,
and that every change of pressure corresponds to a certain change
in temperature. There are several properties of saturated steam
that depend upon the temperature and pressure ; and the values
of all these different properties when arranged for all temperatures
and pressures are called Steam Tables. The following are the
principal items that are found in the tables :
1. The absolute pressure in pounds per square inch; it is
equal to the gage pressure plus the atmospheric pressure of 14.7
2. The temperature of the steam, or boiling water, at the
3. The heat of the liquid ; or the number of B. T. U. neces-
sary to raise one pound of water from 32 F to the boiling point
corresponding to the given pressure.
4. The heat of vaporization, or the latent heat ; this is the
number of B. T. U. necessary to change one pound of water, at
the boiling point, into dry saturated steam at the same temperature
THE STEAM ENGINE. 87
5. The total heat- or the number of B. T. U. necessary to
change one pound of water from 32 F into steam at the given
temperature or pressure. The total heat is evidently equal to the
sum of the heat of the liquid and the heat of vaporization.
6. The density of the steam ; that is, the weight in pounds
of one cubic foot of steam at the given temperature or pressure.
7. The specific volume ; or volume in cubic feet of one
pound of steam at the required temperature or pressure. Evi-
dently the specific volume is equal to .
All these properties have been calculated by means of various
formulas which have been deduced from the results of actual
experiment. There are several formulas for the temperatures and
pressures of steam ; as some computers have used one and some
another, there is likely to be a slight discrepancy between the
tables computed by different authors. Rankin's formula, already
given, is the simplest, but is not generally considered to be quite
as accurate as some of the later ones ; it has probably been used,
however, more than any other.
The total heat may be calculated by means of the formula
H = 1,091.7 + 0.305 (t 32) 
in which H = total heat
t =; temperature in degrees Fahrenheit.
The heat of the liquid is equal to q.
q = t + 0.00002 *a _j_ 0.0000003*3 
in which t =. temperature in degrees Centigrade.
These constants are for use in the Centigrade system only.
To calculate the heat of the liquid for any Fahrenheit temper-
ature it is necessary to change the Fahrenheit into equivalent
Centigrade degrees and then substitute in the above formula.
The formula used for the calculation of specific volume is too
complex for consideration here, but^the relation of pressure and
volume may be approximately expressed by means of an equation
of the form P V n = C, in which n is an exponent, C a constant,
P the absolute pressure, and V the specific volume ; n is usually
taken to be , and C to be 475.
On pages 14 ind 15 are given tables of the properties of
THE STEAM ENGINE.
TABLE OF PROPERTIES OF SATURATED STEAM.
of cubic ft
THE STEAM ENGINE.
TABLE OF PROPERTIES OF SATURATED STEAM.
of cubic ft