90 THE STEAM ENGINE.
saturated steam, one varying with the temperatures, the other
with the pressures. The tables are made out in five unit inter-
vals ; intermediate points are proportional.
Example. Suppose we wish to find the total heat corre-
sponding to a pressure of 112.3 pounds (gage). We first add
14.7 to the 112.3 and get 127 pounds absolute pressure. The
total heat of 1 pound of steam at 125 pounds pressure is 1,186.9.
The total heat at 130 pounds pressure is 1,187.8.
Difference for 5 pounds = 1,187.8 1,186.9 = .9
Difference for 1 pound =.94- 5 = .18
Difference for 2 pounds = 2 X .18 = .36
The total heat for 127 pounds is :
Total heat at 125 pounds = 1,186.9
Difference for 2 pounds = .36
Total heat at 127 pounds = 1,187.26
This method is called interpolation, and in many complete
tables the differences for the intervals are given to facilitate the
If steam tables are not at hand, there are several approximate
formulas that may be used for rough calculations and estimates,
but it must be borne in mind that results obtained by the use of
these equations are not strictly accurate, and should not be used
if the regular tables can be had.
Probably the relation of temperature and pressure will be
most frequently needed. If the gage pressure is between 20
pounds and 100 pounds
t = 14 v/ ~p~+ 198 approximately 
where t = temperature in degrees Fahrenheit
p = gage pressure in pounds per square inch.
For pressures over 100 pounds per square inch (gage) we
must modify the equation thus :
These equations will cover a range of pressures from 20 to
340 pounds, and give an error of less than 1 J in nearly all cases.
From 35 pounds per square inch to 100 pounds the error is gen*
erally less than one-half of one degree.
THE STEAM EXGINE. 91
For pressures below 20 pounds use the constant 196 instead
The latent heat may be approximately expressed by the
I = 1,114 .7 * 
in which I = latent heat
t = temperature in degrees F.
This formula gives very good results for temperatures less
than 320 6 , corresponding to a gage pressure of about 75 pounds.
Above this pressure the formula gives slightly larger results than
are found in the steam tables. At 250 pounds (gage) the for-
mula gives 829.8 and the steam tables 825.8, so that the error
will not be large in any case.
We have defined a B. T. U. as the amount of heat necessary
to raise one pound of water from 61 F to 62 F. The specific
heat of water is nearly constant over ordinary ranges of temper-
ature and at 400 we find the heat of the liquid from the tables to
be 373.7 B. T. U. By definition, the heat of the liquid at 32 is
zero, so that a rise of 368 in temperature requires 373.7 B. T. U.
If we consider the heat of the liquid proportional to .the rise in
temperature, our error will be 5.7 units of heat in 400. At
lower temperatures the error is much smaller, so that we may
express the heat of the liquid approximately by the formula,
h = t 32 
in which h = the heat of the liquid
t = temperature in degrees as before.
The total heat is equal to the sum of the last two, or
H = h + I 
The relation of pressure and volume of steam may be approx-
imately expressed by the equation
In which P = absolute pressure
V = specific volume
C a constant =475 nearly.
n = an exponent = .
92 THE STEAM ENGINE.
We may then write the equation
This is called the equation of constant steam weight ; it may
be solved by the aid of logarithms.
The density can of course be determined from the specific
Let us apply these approximate formulas to a specific case
and see how the results compare with the actual quantities given
in the steam tables. For this purpose we will suppose steam at
70.3 pounds gage pressure or 85 pounds absolute.
Equation (3) t 14 \J~^ -j- 198
= 14 v 'Yol+ 198 = 315.40
From steam tables, temperature = 316.02
Equation (5) I = 1,114 .7 t
I = 1,114 (.7 X 315.4) = 893.2
From stea,m tables, latent heat = 892.5
Equation (6) h = t 32
= 315.6 32 = 283.4
From tables, heat in the liquid = 285.8
Equation (7) H = h -f I
= 285.8 -j- 893.2 = 1,179.0
From tables, total heat = 1,178.3
Equation (8) V = Y/l!^
V = ~V/ 475 = 5.100
From tables, specific volume = 5.125.
A comparison of these results shows that these formula^ can-
not b3 used when accuracy is sought ; but if only approximate
results are desired they will be found satisfactory. Whenever
possible the steam tables should be used, in preference to any
Superheated Vapor. We have seen that a saturated vapor
contains just enough heat to keep it in the form of a vapor; if it
THE STEAM ENGINE. 93
loses heat it will condense. A superheated vapor is one that has
been heated after vaporization ; it can lose this extra heat before
any condensation will take place. A vapor in contact with its
liquid is saturated; one heated after removal from the liquid is
For saturated steam there is a fixed temperature for every
pressure. If we know either the pressure or the temperature, we
can find the other in the steam tables. For instance, if the gage
pressure of a boiler is 60.3 pounds and we wish to know the tem-
perature, we simply add atmospheric pressure and turn to our
tables and find it to be 307 (about).
With superheated steam the case is entirely different, for there
is no longer the same direct relation between the temperature and
pressure. In fact, the relation between temperature and pressure'
of superheated steam depends upon the amount of superheating.
Superheated steam at 60.3 pounds gage pressure may have a tem-
perature considerably above 307 F. At a given pressure the
temperature and volume of a given weight of superheated steam
are always greater than the temperature and volume of the same
weight of saturated steam. The properties of superheated steam
at given pressure are not constant as is the case with saturated
If superheated steam were a perfect gas, we could determine
the relation of P, V and T by the equation PV = CT ; but super-
heated steam is not a perfect gas, hence we must modify our equa-
tion. By experiment it has been determined that the following
equation is nearly correct :
PV = 93.5 T 971 P*
In which P = absolute pressure in pounds per square foot
T = absolute temperature
V = volume of 1 pound in cubic feet.
THE STEAM ENGINE.
We have studied the action and formation of steam, and now
we shall consider its application to the steam engine. We know
that steam contains a great deal of heat, and that heat can be con-
verted into work by allowing a working substance to pass from
the high temperature of the heat generator to the lower tempera-
94 THE STEAM ENGINE.
ture of the refrigerator, during this change giving up heat, which
is transformed into work. There are several forms of heat engines,
all of which convert the heat contained in some substance into
work. At the present time the steam engine is the most impor-
tant. When of good size and properly designed and run, it is as
economical as any other heat engine, and it can be more easily
controlled and regulated. We shall consider first the theoretically
perfect engine and then the modifications that go to make up the
steam engine of to-day.
The theoretical engine (Fig. 3) is supposed to receive heat from
the generator at constant temperature T X until communication is
interrupted at B. The working substance expands to C without
losing or gaining any heat from external sources until the temper-
ature of the refrigerator is reached. The engine now rejects heat
at the constant temperature T 2 of the refrigerator and then com-
presses the working substance without loss or gain in the quantity
of heat until the temperature of the heat generator is reached.
These are ideal conditions, and, if fulfilled, the efficiency of the
perfect engine will depend only on the difference between the tern-
THE STEAM ENGINE. 95
perature at which heat is received and rejected, or, in other words,
it depends only upon the difference in temperature between the
generator and the refrigerator.
If Tj = absolute temperature of heat received and
T 2 = absolute temperature of heat rejected, then the ther-
mal efficiency, E, of the engine will be represented by the formula,
Or, in other words, the efficiency equals the absolute temper-
ature of the heat rejected, subtracted from the absolute temperature
of the heat received, and the remainder divided by the absolute
temperature of the heat received.
Suppose an engine is supplied with steam at 120 pounds
absolute pressure, and the exhaust is at atmospheric pressure.
What is the thermal efficiency ?
The absolute temperature corresponding to 120 pounds pres-
sure is 341.05 -f 461 = 802.05, and the absolute temperature of
the exhaust is 212 -f 461 = 673.
Then E = 802 f " 6T8 = .16, or 16 per cent.
In actual engines this efficiency cannot be realized, because
the difference between the heat received and the heat rejected is
not all converted into useful work. Part of it is lost by radiation,
conduction, condensation, leakage and -imperfect action of the
valves. The cylinder walls of the theoretical engine are supposed
to be made of a nonconducting material, while in the actual
engine the walls are of metal, which admits of a ready interchange
of heat between cylinder and steam. This action of the walls
cannot be overcome, and is so important that a failure to consider
its influence will lead to serious errors in computations, and no
design can be made intelligently if based on the theory of the
engine with nonconducting walls. The theoretical engine carries
on its expansion without the loss of any heat, while in the actual
engine a large amount of heat is lost by radiation. There is also
a considerable loss of pressure between the boiler and engine, due
to resistance of flow through pipes and passages. In a slow-speed
engine with large and direct ports and valves this trouble may be
96 THE STEAM ENGINE.
minimized. The imperfect action of valve gears may also be
lessened with due care, but the action of the cylinder walls still
remains to be overcome.
In the theoretical card, admission is at constant boiler pres-
sure, cut-off is sharp and expansion complete, that is, expansion
continues until the temperature falls to that of the condenser and
the exhaust is at condenser pressure. The piston also sweeps the
full length of the cylinder.
In the actual engine there is a considerable loss of pressure
between boiler and engine, and the wire-drawing of the ports
and valves tends to cause a sloping steam line. Condensation
at the beginning of the stroke causes the real expansion line to
fall below the theoretical, while re-evaporation causes it to rise
above the theoretical toward the end of expansion. In the actual
engine, release takes place before the end of the stroke, expan-
sion is not complete, that is, the pressure at release is above
that of the condenser, and the resistance of exhaust ports causes
the back pressure to be above the actual condenser pressure.
Moreover, the piston does not sweep the full length of the
cylinder, and the clearance space must be filled with steam, which
does little or no work. The theoretical and actual cards are
shown in Fig. 4.
EFFICIENCY OF THE ACTUAL ENGINE.
We have seen that the efficiency of the theoretical engine is
purely a thermal consideration ; the efficiency of the actual engine,
THE STEAM ENGINE. 97
however, is a mechanical matter. The measure of the activity of
work is the horse-power which corresponds to the development
of 33,000 foot-pounds per minute. As 778 foot-pounds are equiv-
alent to one B. T. U., 33,000 foot-pounds, or one horse-power, is
equivalent to 33,000 -4- 778 = 42.42 B. T. U. Now if a certain
engine uses 84.84 B. T. U. per horse-power per minute, it is evi-
dent that its efficiency would only be |- or 50 per cent, because
42.42 -f- 84.84 = | . Hence* we may say that the efficiency of
the actual engine is equal to _ _. This
B. T. U. per H. P. per minute
efficiency is always much less than that of the perfect engine.
Let us now discuss the effects of some of the losses.
In the first place, the metal, being a good conductor of heat,
becGmes heated by the steam within and transmits this heat by
conduction and radiation to the air or external bodies. With the
cylinder well lagged much less heat is lost by radiation. If the
lagging were perfect and the temperature of the cylinder remained
the same as the temperature of the steam throughout the stroke,
there would be no loss by radiation, but we should still lose heat
by conduct' on to the different parts of the engine.
During expansion, the temperature and pressure of the steam
decrease as the volume increases, and the temperature at exhaust,
is much less than tho temperature at admission. In the perfect
engine the working substance after exhaust is compressed to the
temperature at admission, but in the actual engine much of this
steam is lost and the compression of a part of it is incomplete, so
that its temperature is less than the temperature at admission.
Suppose an engine is running with admission at 100 pounds
absolute and exhaust at 18 pounds absolute. Then from steam
tables we find the temperature at admission to be 327.6, and at
exhaust 222.4. The metal walls of the cylinder, being good con-
ductors and radiators of heat, are cooled by the low temperature
of exhaust, so that the entering steam comes through ports and into
a cylinder that is more than 100 cooler than the steam. This
means that heat must flow from steam to metal until botli are of
the same temperature. Th?s causes the steam to give up part of
its latent heat, and as saturated t team cannot lose any of its heat
without condensation, we find the cylinder walls covered with a
THE STEAM ENGINE.
film of moisture known as initial condensation. This conden-
sation in simple unjacketed engines working under fair conditions
may easily be 25 per cent or more of the entering steam. The
moisture in the cylinder has of course the same temperature as
the steam ; it has simply lost its heat of vaporization.
Although metal is a good conductor of heat it cannot give
up nor absorb heat instantly ; consequently during expansion
the temperature of the steam falls more rapidly than that of the
cylinder. This allows heat to flow from the cylinder walls to
the moisture on them. As fast as the steam expands so that the
pressure in the cylinder becomes less, this condensation will begin
to evaporate. As the pressure falls it requires less and less heat
to form steam, and therefore more and more of this moisture will
be evaporated. At release the pressure drops suddenly, and more
heat at once flows from the cylinder walls, and re-evaporation con-
tinues throughout the exhaust. Probably all of the water remain-
ing in the cylinder at release is now re-evaporated, blows out into
the air or the condenser, and is lost so far as useful work is
The steam that is first condensed in the cylinder does no
work ; its heat is used to warm up the cylinder, and later, when
it is re-evaporated, it works only during a part of the expansion
and at a reduced efficiency, because it is re-evaporated at a pres-
sure and consequently at a temperature very much lower than
that of admission. If the cut-off is short, perhaps 20 per cent of
the steam condensed may be re-evaporated during expansion ; if the
cut-off is long, 10 per cent may be re-evaporated, the rest remaining
in the cylinder at release still in the form of moisture. Thus
some of the entering steam passes through the cylinder as
moisture, until after cut-off, and still more passes clear through
without doing any work at all.
Suppose an engine is using 30 pounds of steam per horse-
power per hour and admission is at 100 pounds absolute. The
latent heat of vaporization at this pressure is 884 B. T. U. per
pound. If the condensation amounts to 331 p er cent, then 10
pounds are condensed and we lose 10 times 884, equals 8,840
B. T. U. per hour, or 147.3 per minute ; and since 42.42 B. T. U.
represents 1 horse-power, we shall lose by condensation 147.3
THE STEAM ENGINE.
divided by 42.42, equals 3* horse-power (nearly). If the cut-off is
shortened, the condensation increases and may amount to 50 per
cent at very short cut-off. Of course we use very much less
steam at short cut-off than with long cut-off, and doubtless in
many cases 50 per cent of the steam at short cut-off is not as
great an absolute quantity as 30 per cent at long cutoff. Never-
theless, in all cases it is the percentages that go to make up the
In addition to the actual loss from condensation in the cylinder
there is still another loss due to the re-evaporation. Suppose, as
before, that 10 pounds of steam are condensed in the cylinder,
and that 20 per cent of this is re-evaporated during expansion.
This will leave 8 pounds to be re-evaporated during exhaust.
Suppose the exhaust is at 3 pounds above atmospheric pressure,
or 18 pounds absolute (about). Then the heat of vaporization is
958.5 B. T. U. per pound of steam, and it will require 8 times
958.5, which equals 7668.0 B. T. U., to evaporate the 8 pounds.
All of this heat is taken from the cylinder, leaving the engine
much cooler than it would be were it not for this re-evaporatioiv
This gives some idea of the great amount of heat passing away at
exhaust, which is known as the exhaust waste.
In all cylinders it is necessary to have a little space between
the cylinder cover and the piston when at the end of the stroke.
In vertical engines the space is greater at the bottom than at the
top. The volume of this space, together with the volume of the
steam ports, is called the clearance. It varies from 1 to 20 per
cent, depending upon the type and speed of the engine ; the higher
the speed, the greater the clearance. This clearance space must
be filled with steam before the piston receives full pressure, but
this steam does no work except in expanding, and the volume of
the clearance offers additional surface for condensation.
Another important loss is that due to friction. We know that
it takes considerable power to move an unloaded engine; if fitted
with a pLun, unbalanced slide valve, the power necessary to move
the valve alone is considerable. The piston is made steam tight
by packing rings, and leakage around the piston rod is prevented
by stuffing boxes. All these devices cause friction as well as wear
at the joints. The amount of power wasted in friction varies
100 THE STEAM ENGINE.
greatly, depending upon the kind of valves, general workman-
ship, state of repair and lubrication.
Two engines may be used together on the same shaft, partly
expanding the steam in one of the cylinders, and then passing it
over to the other to finish the expansion. One advantage from
this arrangement is that the parts can be made lighter. The high-
pressure cylinder can be of much less diameter than would be
possible if the entire expansion were to take place in one cylinder.
This, of course, makes the pressure exerted on the piston rod
much less, and the piston rod and connecting rod can thus be
made much lighter. The low-pressure cylinder must be larger
than it otherwise would be, but its parts need not be much heavier,
because the pressure per square inch is always low.
This arrangement gives not only the advantage of lighter
parts, but a decided increase of economy over the single cylinder
type. If attention is given to the matter, a loss of economy would
be expected, because the steam is exposed to a much larger surface
through which to lose heat, but the gain comes from another
source, and is sufficient to entirely counterbalance the effect of
a larger cylinder surface.
When very high pressure steam and a great ratio of expan-
sion is used, the difference between the temperature of the enter-
ing and that of the exhaust steam is great. For instance, suppose
steam at 160 pounds (gage) pressure enters the cylinder and the
exhaust pressure is 2 pounds (gage), the difference in temperature
is, from steam tables,
370.5 218.1= 152.4
This difference becomes nearly 230 if the steam is con-
densed to about three pounds absolute pressure. The cylinder and
ports of the engine are cooled to the low temperature of the
exhaust steam, and, as we have seen, a considerable quantity
of the entering steam is condensed to give up heat enough to
raise the temperature of the cylinder to that of the entering
steam. As the ratio of expansion increases, the difference in
temperature increases, and consequently the amount of steam
thus condensed also increases. To keep this initial condensation
THE STEAM ENGINE. 101
as small as possible we must limit the temperature, that is, we
must not have as great a difference between admission and
exhaust. To do this we must divide the expansion between two
or more cylinders.
It will be remembered that the great trouble Watt found with
Newcomen's engine was its great amount of condensation, and he
stated as the law which all engines should try to approach, " that
the cylinder should be kept as hot as the steam which enters it."
This is to avoid condensation when steam first comes in. If,
instead of expanding the steam in one cylinder, we expand it
partly in one and then finish the expansion in another, we shall
have passed it out of the first cylinder before its temperature falls
a great deal, and consequently the cylinder walls will be hotter
than they would be if we had expanded it entirely in one cylinder.
This would then reduce the amount of steam condensed. The
importance of this may not be evident at first, but it makes a
great difference in the economy of the engine. If there is less
condensation, there will be less moisture to re-evaporate, and con-
sequently less exhaust waste ; hence we shall save in two ways at
the same time.
In a compound engine we admit the steam first to the smaller
or high-pressure cylinder, and exhaust it to the larger or low-
Suppose steam at 160 pounds (gage) pressure is admitted
to a cylinder, and the ratio of expansion is such that the steam
is exhausted at about 60 pounds (g a g e ) pressure; then the dif-
ference of temperature is
370.5 307 = 63.5.
If, now, the steam when exhausted from the first cylinder