trial
Z;7,
41,




--—,-tracer
Wl'44


I
I










THE
BY
COMPRESSED AIR.
BY


ROBERT ZA I1 NER, M.E.
REPRINTED FROM VAN NOSTRAND'S MAGAZINE.


NEW YORK:
D. VAN NOSTRAND, PUBLISHER,
23 MURRAY AND 2T WARREN STUZET.
18 78.




I C
L*1
11




PREFACE.


THE subject of Compressed Air and
Compressed Air Machinery offers a wide
field for useful investigation.  It has
been attempted in these pages to add
something to the scanty stock of its
literature.
Compressed Air has become a most
efficient and powerful agent in the hands
of the modern engineer. Its applicacations are rapidly growing, both in
extent and importance.   The subject
demands careful attention and study.
There can be no doubt that the great
waste of energy that to-day accompanies
the use of Compressed Air is due, not
only to sickly design and faulty -construction of machines, but very largely
also to the general ignorance of the
principles of thermodynamics. Hence,
we have started with the general equa



iv


tion of thermodynamics, which expresses
the relation between heat and mechanical energy under all circumstances, and
have deduced from it all the formulas
and results necessary to an intelligent
comprehension of our subject. We have
not tried to be simple by avoiding
the higher mathematical analysis; but
thorough and clear, by beginning at the
very bottom and fully explaining every
step and principle. It will not be necessary for the average reader to study any
work on thermodynamics or higher
mnathemratics, preparatory  to reading
this.
Zeuner's "Theorie Mechanique de la
Cihaleur," Clausius, Rankine and McCullough on Heat, Riedler's " Luftcompresslons-maschinen," have been freely used.
The works of MM, Cornet, Mallard and
Pochet and others, have all, I believe,
received credit in the text.
R. Z.
STEVENS INST. OF TECHNOLOGY,
June, 1878.




TABLE OF CONTENTS.


PREFACE.
INTRODUCTION.
I, Historical Notice; II, Its Applications and
Future.
CHAPTER I.-THE CONDITIONS MODIFYING EFFICIENCY IN THE USE OF COMPRESSED AIR.
1. Loss of Energy.
2. Methods of Cooling.
3. Conditions Most Favorable to the Highest
Efficiency.
4. Efficiency Attained in Practice.
5. Efficiency of Full Pressure and Complete
Expansion Compared.
6. Losses of Transmission.
CHAPTER II.-PHYSICAL PROPERTIES AND
LAWS OF AIR.
1. Introductory
2. Boyle's Law.




vi


3. The Law of Gay-Lussac.
4. Boyle's and Gay-Lussac's Law.
5. Absolute Temperature.
6. The Law of Pressure, Density and Temperature.
7. The Measurement of Heat.
CHAPTER III.-THERMODYNAMIC PRINCIPLES
AND FORMULAS.
1. Introductory.
2. Heat and Temperature.
3. The Two Laws of Thermodynamics.
4. Heat and Mechanical Energy.
5. The Differential Equation of the Second
Law.
CHAPTER IV.-THER[MODYNAMIC     EQUATIONS
APPLIED TO PERMANENT GASES.
1. The Determination of the Specific Heat at
Constant Volume.
2. Internal Heat.
3. Quantity of Heat Supplied.
4. Expansion with Temperature Constant.
5. Expansion in a Perfectly Non-Conducting
Cylinder.
6. Variations in the Temperature of a Gas
during Adiabatic Compression or Expansion.




vii


CHAPTER V.-THERMODYNAMIC LAWS APPLIED
TO THE ACTION OF COMPRESSED AIR.
1. Fundamental Formulas.
2. Work Spent in Compression.
3. Work Obtainable from Compressed Air.
4. The Theory of Compression.
5. The Theory of Transmission.
6. The Theory of Complete Expansive Working.
7. The Theory of Full Pressure Working.
8. The Theory of Incomplete Expansive
Working.
9. Graphical Representation for the Action of
Compressed Air.
CHAPTER VI.-THE EFFICIENCY THEORETICALLY ATTAINABLE.
1. The Efficiency of the Compressor and the
Compressed Air Engine as a System.
2. Maximum Efficiency calculated from the
Indicated Work.
3. Efficiency of Full Pressure and Complete
Expansion Compared.
CHAPTER VII.-THE EFFECTS OF MOISTURE,
OF THE INJECTION OF WATER AND OF
THE CONDUCTION OF HEAT.
1. General Statement.
2. Effects of Moisture.
3. The Injection of Water.




viii


CHAPTER VIII.-AMERICAN     AND EUROPEAN
AIR COMPRESSORS.
1. Pump Compressors.
2. Single Acting Wet Compressors.
3. Double and Direct Acting Compressors.
4. Design and Construction.
CHAPTER IX.-EXAMPLES FROM PRACTICE.
1. Republic Iron Company.
2. Economy Promoted by the use of Compressed Air.
3. Compressed Air Motor Street Cars.
TABLES.             Page.
I. Values of, -~, &c., for convenTo) V
r0 v. P
ient values o'..............72, 73
Po
II. Final Temperatures of Compressed
A ir..........................  78
IlI. Final Temperature of after Expansion............................  84
IV. Theoretical Efficiencies......... 97
V. Theoretical Efficiencies for Full
Pressure and Complete Expansion. 100
VI. Effects of Moisture on final Temperature..........................  105
VII. Work of Isothermal and AdiabaticCompression.................... 108
VIII. Quantity of Water necessary in
Compression.................... 110
IX. Quantity of Water to be Injected
into the Working Cylinder....... 112




TRANSMISSION OF POWER BY COMPRESSED AIR.
INTRODUCTION.
I.
HISTORICAL NOTICE.
The application of compressed air to
industrial purposes dates from the close
of the last century. Long before this,
indeed, we find isolated attempts made
to apply it in a variety of ways; but its
final success must be ascribed to the.
present age-the age of mechanic artsan age inaugurated in so splendid a manner by the genius of Watt, and which
has been so wonderfully productive in
good to mankind.
Without going into any details as to
its history, we shall only name the English engineers, Cubitt and Brunell,
who, in 1851-4, first applied compressed
air in its statical application to the sink



1I (


ing of bridge caissons; the Genoese Professor, M. Collodon, who, in 1852, first
conceicved and suggested the idea of employing it in the proposed tunneling of
the Alps; and, finally, the distinguished.
French engineer, Sommeiller, wrlho first
practically realized adl appllied Collodon's idea ill the boringc of the AMt. Cenis
Tunnel.
II.
Il'S APPICATION-S AND ITS FUTURE.
The applications of compressed air are
very numerous, its most imiortant one
being the transmission of power by its
ean s.
Custom has confined the term " transmission of power" to such devices as are
employed to convey power from one place
to another, without including organized:machines through which it is directly applied to the performance of work.
Power is transmitted  by means of
shafts, belts, friction-wheels, gearing,
wire-rope, and by water, steam and air.
There is nothing of equal importance




11


connected with mechanical engineering
in regard to which there exists a greater
diversity of opinion, or in which there is
a greater diversity of practice, than in
the means of transmitting power. Yet
in every case it may be assumed that
some particular plan is better than any
other, and that plan can be best determined by studying, first, the principles of
the different modes of transmission and
their adaptation to the special conditions
that exist; and, secondly, precedents and
examples.
For transmitting power to great distances, shafts, belts, friction-wheels and
gearing are clearly out of the question.
The practical incompressibility and want
of elasticity of water, renders the hydraulic method unfit for transmitting
regularly a constant amount of power;
it can be used to advantage only where
motive power, acting continuously, is to
be accumulated and applied at intervals,
as for raising weights, operating punches,
compressive forging and other work of
an intermittent character, requiring a




12


great force acting through a small distance.
Whether steam, air or wire-rope is to
be made the means of transmitting power
from the prime-mover to the machine,
depends entirely upon the special conditions of each case. In carrying steam to
great distances very important losses
occur from condensation in the pipes;
especially during cold weather.  The
wear and tear of cables lessen the advantages of the telodynamic transmission; steep inclinations and frequent
changes of direction of the line of transmission often exclude its adoption; while
it is entirely excluded when it is rather
a question of distributing a small force
over a large number of points than of
concentrating a large force at one or two
points.
Compressed air is the only general
mode of transmitting power; the only
one that is always and in every case possible, no malter how great the distance
nor how the power is to be distributed
and applied. No doubt as a means of




13


utilizing distant, yet hitherto unavailable,
sources of power, the importance of this
medium can hardly be overestimated.
But compressed air is also a storer of
power, for we can accumulate any desired pressure in a reservoir situated at
any distance from the source, and draw
upon this store of energy at any time;
which is not possible either in the case
of steam, water or wire-rope.
Larger supply-pipes are required for
steam or water transmission; the inconveniences resulting from hot steam pipes,
the leakages in water pipes, the high velocities required in telodynamic transmission are all without their counterparts in compressed-air transmission.
Compressed air is furthermore independent of differences of level between the
source of power and its points of application, and is perfectly applicable no
matter how winding and broken the path
of transmission.
But especially is compressed air adapted to underground work. Steam is here
entirely excluded; for the confined char



14


acter of the situation and the difficulty
of providing an adequate ventilation,
render its use impossible; compressed
air, besides being free from the objectionable features of steam, possesses
properties that render its employment
conducive to coolness and purity in the
atmosphere into which it is exhausted.
The boring of such tunnels as the Mt.
Cenis and St. Gothard would have been
impossible without it. Its easy conveyance to any point of the underground
workings; its ready application at any
point; the improvement it produces in
the ventilating currents; the complete
absence of heat in the conducting pipes;
the ease with which it is distributed
when it is necessary to employ many
machines whose positions are daily
changing, such as hauling engines, coalcutting machines and portable rock-drills;
these, and many other advantages, when
contrasted with steam under like conditions, give compressed air a value which
the engineer will fully appreciate.
There is every reason to believe thlat




15


compressed air is to receive a still more
extensive application. The diminished
cost of motive power when generated on
a large scale, when compared with that
of a number of separate steam engines
and boilers distributed over manufacturing districts, and the expense and danger
of maintaining an independent steam
power for each separate establishment
where power is used, are strong reasons
for generating and distributing compressed air through mains and pipes laid
below the surface of streets in the same
way as gas and water are now supplied.
Especially in large cities would the
benefits of such a system be invaluable;
no more disastrous boiler explosions in
shops filled with hundreds of working
men and women;, the danger of fire
greatly reduced; a corresponding reduction in insurance rates; an important
saving of space; cleanliness, convenience
and economy. We say economy! For
there is no doubt that a permanently
located air-compressing plant, established
on a large scale, and designed on princi



16


pies of true economy and not with reference to cheapness of construction, would
supply power at a much less cost than is
supposed. Besides, there are many natural sources of power, as water power,
which could by this means be utilized,
and their immense stores of energy conveyed to the great centers of business
and manufacture.
As affording a means of dispensing
with animal power on our street railroads, compressed air has been proposed
as the motor to drive our street cars. It
has already met with some success in this
direction, and, to-day, there are eminent
French, English and American engineers
at work upon this interesting problem.
The compressed-air locomotives of M.
Ribourt, now in use at the St. Gothard
Tunnel, give very satisfactory results.
They are compact, neat and comparatively economical.
Compressed air is also applied in a variety of other ways; in signaling, in propelling torpedo boats; in ventilating
large and confined spaces; in driving




17


machinery in confined shops; in sinking
bridge caissons.  The pneumatic dispatch system, the air brake, the pneumatic elevator and hoist, are further examples of its use.
CHAPTER I.
THE CONDITIONS MODIFYING EFFICIENCY
IN THE USE OF COMPRESSED AIR.
I.
LOSS OF ENERGY.
What is at present required in the use
of compressed air is a considerable diminution in the first cost of obtaining it
by really improving the compressor, and
a practical means of working it at a high
rate of expansion without the present
attendant losses. In the best machines
in use at the present day, the useful effect, that is, the ratio of the work done
by the air to that done upon it, is very
small. The losses are chiefly due to the
following causes:
1. The compression of air develops
heat; and as the compressed air always




18


cools down to the temperature of the
surrounding atmosphere before it is
used, the mechanical equivalent of this
dissipated heat is work lost.
2. The heat of compression increases
the volume of the air, and hence it is
necessary to carry the air to a higher
pressure in the compressor in order that
we may finally have a given volume of
air at a given pressure, and at the temperature of the surrounding atmosphere.
The work spent in effecting this excess
of pressure is work lost.
3. The great cold which     results
when air expands against a resistance,
forbids expansive  working, which is
equivalent to saying, forbids the realization of a high degree of efficiency in the
use of compressed air.
4. Friction of the air in the pipes,
leakage, dead spaces, the resistance offered by the valves, insufficiency of
valve - area, inferior workmanship and
slovenly attendance, are all more or less
serious causes of loss of power.
The question now is, how can we get




19


rid of these losses and obtain a higher
efficiency?
The first cause of loss of work, namely, the heat developed by compression,
is entirely unavoidable. The whole of
the mechanical energy which the compressor-piston spends upon the air is coaiverted into heat. This heat is dissipated
by conduction and radiation, and its mechanical equivalent is work lost. The
compressed air, having again reached
thermal equilibrium with the surrounding atmosphere, expands and does work
in virtue of its intrinsic energy.
We proceed to the second loss, which
is the work done in driving the conmpressor-piston against the increase of
pressure due to the heat of compression.
Since the temperature increases more
rapidly than it ought, according to
Boyle's law, the work necessary to compression is greater than if the temperature were to remain constant.
The theoretical efficiency of the compressing and working cylinders, as given
further on by eq. (486), is:




'20


E= —
where rT is the absolute temperature of
the air at its exit from the compressor,
and 0& the absolute temperature at its
entrance into the working cylinder,which
in practice is that of the surrounding
atmosphere. Hence we can increase the
value of this fraction only by decreasing
the denominator r,, that is the final heat
of compression. This can only be done
by abstracting the heat during compression, or by using very low pressures.
But low pressures are excluded by other
considerations. The weight of air,.w,
needed per second to perform a given
amount of work would have to be considerably increased, and this would necessitate larger pipes, larger cylinders, and
would result in a cumbrous and expensive arrangement.
The only remaining alternative, therefore, is to bring about in the compressor
the cooling which the air now undergoes after having left it. Table VII
shows respectively the portion of work




21


lost when the air is not cooled in the
compressor and that lost when it is completely cooled, and will make manifest
the advantage there is in cooling. For
a pressure of six atmospheres the work
spent in isothermal compression to that
spent in adiabatic compression is as 3 to
4; and this ratio decreases rapidly as the
pressure increases.
II.
METHODS OF COOLING.
There are three methods in which cold
water is applied to cool the air during
its compression:
1. In case of the so-called hydraulic
piston or plunger compressors, the air is
over and in contact with a column of
water which acts upon the air like an
ordinary piston, its surface rising and
falling with the backward and forward
motion of the plunger.  It is obvious
that the cooling effect of this large mass
of water is very small. There is nothing
but surface contact, and water possesses
in a slight degree only, the property of




22


conducting, through its mass, heat received on its surface. But we obtain all
the advantages there are in having the
air completely saturated with watervapor during its compression, as well as
all the disadvantages of having saturated
compressed air to work with. What has
been here said of hydraulic plungercompressors, applies equally to hydraulic
or ram compressors (first used by Sommeiller at Mt. Cenis, but now obsolete).
2. By flooding the external of the
cylinder, and sometimes also the piston
and piston-rod. This method of cooling
presents neither the advantages nor disadvantages incident to direct intercontact between the air and water; it is that
generally adopted in American practice,
especially where it is necessary to expose
the air-pipes to the out-door atmosphere
of winter. The cooling which it effects
is, however, only an approach to that
which insures the highest efficiency.
3. By injecting into the compressorcylinder a certain quantity of water in a
state of the finest possible division,. e., in




23


the form of spray. This method of cooling
was first applied by Prof. Collodon in the
compressors used at the St. Gothard
Tunnel. It is by far the most rational,
complete and effective. In this fine state
of division the water has many more
points of contact with the air, which is
both completely cooled and kept thoroughly saturated during compression. It
is extremely important that the quantity
of water injected into the compressor
be a minimum, and hence the weight required for different tensions is given in
a table further on.
III.
CONDITIONS MOST FAVORABLE TO ECONOMY
IN THE USE OF COMPRESSED AIR.
By working air at full pressure we
avoid the formation of ice in the pipes
and exhaust ports, not so much because
the air is less cooled (for the great fall
of temperature produced by the sudden
expansion at the instant of exhaust is
almost equal to that produced by interior expansion), but because the air in




24


exhausting acquires a high velocity, and
this opposes the deposit of ice crystals
by its purely mechanical effect, and by
the heat developed by its friction.
But even at full pressure we cannot
work with high tensions without serious
drawbacks. Il England, several trials
were made at the Govan Iron Works and
other places to use air under tensions of
eight and nine atmospheres, but they
were forced to return to low pressures,
owing to the entire arrest of the machine from the formation of ice in the
ports. Hence, not taking into account
the fact that the useful effect decreases
as the pressure increases, we conclude
that it is not good practice, even at full
pressure, to work with a tension much
over four atmospheres, unless we employ
special means to reheat the working air.
But while by working at full pressure
with moderate tensions, we avoid the inconveniences of very low temperatures,
the efficiency obtained is also very low.
Notwithstanding this, even up to the
present time air is almost exclusively




25


worked at full pressure, especially in the
United States. This is because the great
cold produced by expansive working has
made its adoption impossible. With a
cut-off at ~ stroke the temperature of the
air falls 71~ C, and at J cut-off 140~ C.
Now, to avoid these low temperatures,
it is necessary either that the initial temperature of the compressed air be raised
by heating it before its introduction into
the working cylinder, or that the cylinder in which it expands be heated, or
that the compressed air be supplied with
heat directly during its expansion by
means of the injection of hot water.
In 1860, M. Sommeiller, in order to
utilize expansion, heated his working
cylinders at Bardonn6che by means of a
current of hot air circulating around the
cylinders in small pipes. By this means
he was enabled to cut off at i stroke.
In 1863, M. Devillez recommended
that the cylinder be placed in a tank
through which hot water was to circulate. Other devices were to place the
cylinder into a tank of water, into which




2G


from time to time fresh supplies of quicklime were to be thrown. Waste cotton,
soaked in petroleum, was also used to
heat the working cylinder.
Finally, in 1874, Mr. C. W. Siemens
proposed the injection of hot water into
the compressed air engine cylinder to
keep the temperature of the expanding
air from falling below the freezing point,
just as we inject cold water into the
compressor cylinder to prevent a, great
rise of temperature during compression.
This is by far the most efficient. mode of
supplying heat to the expanding air. Expansion is made completely practicable,
and hence the efficiency of the engine is
greatly increased, as was shown by M.
Cornet, who was the first to apply Mr.
Siemens' plan and to prove conclusively
its great practical utility.
The quantities of hot water to be injected into the cylinder should always be
a minimum; they are given in a table
further on.




27


IV.
EFFICIENCY ATTAINED IN PRACTICE.
It is desirable to know what efficiencies
have been attained in practice-of compressors, of compressed-air engines, and
of the two machines together as a
system.
1. By efficiency of compressor is meant
the ratio of the effective work spent upon
the air in the compressor to that developed by the steam in the driving engine; or if you choose, the resistance divided by the power.
t. In compressors without piston or
plunger, such as the hydraulic compressor of Sommeiller, the efficiency is
always less than.50. These machines
are interesting on account of their simplicity, but their useful effect is always
very small.
b. In the so-called hydraulic piston
or plunger compressor, an efficiency of.90 has been obtained when working at a
low piston-speed to pressures of four and
five atmospheres.
c. The compressors of Albert Schacht. -:-'-' -^.!




at Saarbriicken, in which the cooling is
wholly external, have shown an efficiency
of.80 when compressing to a tension of
4 effective atmospheres.
(. Prof. Collodon's compressors, into
which water is injected in the form of
spray, and which were run at a pistonspeed of 345 feet, and compressed the
air to an absolute tension of 8 atmospheres, gave an efficiency which never
descended below.80, while the temperature of the air never rose higher than
from 12 to 15 degrees C.,. The efficiency of compressed-air
engines is the ratio of the work which
they actually do, to that which is theoretically obtainable from the compressed
air. The following are examples of its
value as found by experiment:
At the Haigh Colliery, Eng.,.70
i  " Ryhope    "      ".66
M. Ribourt has found for his locomotives.50 to.60.
In general it may be said that in the
very best machines we can count upon
from.70 to.75; while in the ordinary.-..........




29


ones, working against a variable resistance, this efficiency descends to.50 and.55.
3. The efficiency of the whole system
together, that is, the ratio of the work
measured on the crank-shaft of the compressed-air engine, to that done by the
prime mover, is found to be about.20 to.25 for high pressures, and from.35 to.40 for low pressures.
Experiments made at Leeds show a
net efficiency of.255 when working with
2.75 effective atmospheres, and.455 when
with 1.33 atmospheres.
At the Blanzy mines, M. Graillot has
found for a final efficiency,.22 to.32 of
the effective work of the steam.
M. Ribourt, by experimenting on the
new compressed-air locomotives built
for the St. Gothard Tunnel, found that
the ratio of the tractive effort developed
to the original power, (in this case a
head of water), was.23; that is, after
passing the turbine, the compressor, the
expansion regulator, and the cylinders of
the locomotive, there remained.23 of
the original power.




IEEFFICIIENCY OF FULL PIZESSUREF AND'
OF E~XPANSION' COMPARED.
Le~t IV be the work spent upon tre, anr
Mf the compressor:
W1'~ the work which th-e compressed air
is theoretically able to do; thene its theoretical efficiency wvill be -U
W
If WV-the actual work donie by thie
priml-e mov0Ner, and
W' the actual work done by the air,
tben the real efficiency will be AV
w.
Now in the ordinary conditions of
practice we know that WIV is at best.70
WV; and WI' is only about.70 W2,; hience
WI.70W NV
E -real. efficiency__   ___.9-.70  ~.4E.
The value of W`(-E-the theoretical
efficiency) is.55 for full pressure and.75 for complete expansion. Hence, substituting these values of E above We




31


find for these two cases a final efficiency
of.27 and.37.
VI.
LOSSES OF TRANSMISSION.
The losses due to transmission are calculated further on.
At the works for excavating the Mt.
Cenis Tunnel, the supply of compressed
air was conveyed in cast iron pipes 7j
inches in diameter. The loss of pressure
and leakage of air, from the supply pipes,
in a length of one mile and fifteen yards,
was only 32 of the head; the absolute
initial pressure was 5.70 atmospheres,
and it was reduced to 5.50 atmospheres
whilst there was an expenditure at the
rate of 64 cubic feet of compressed air
per minute. In the middle of the tunnel, through a length of pipe of 3.8 miles,
the absolute pressure fell only from six
atmospheres to 5.7 atmospheres, or to.95
of the original pressure.
At the Hoosac Tunnel the air was carried through an 8-inch pipe from the
compressors to the heading, a distance of




7,150 feet, operating six drills, with an
average loss of two pounds pressure.
CIAPTER II.
THIE PHYSICAL PROPERTIES AND LAWS
OF AIR.
I.
INTRODUCTORY.
A fluid is a body incapable o )resisting
a change of shape. Fluids are either
liquids, vapors or gases. Water may be
taken as the type of the first; steam is
the type of all vapors, and air of all
gases.
Gases are either coercible gases, i. e.,
such as under ordinary circumstances
may be condensed into liquids or even
solids, as C02; or permanent gases, which
retain their aeriform state under all ordinary circumstances of temperature and
pressure. This distinction is convenient.
Air has been condensed, but certainly
not under ordinary circumstances.
Air then is a permanent gas, and may
be considered a perfect fluid; that is,




33


1. It is incapable of experiencing a
distorting or tangential stress, its molecules offering no resistance to relative
displacement among themselves; hence
no internal work of displacement need
be considered.
2. It has the power of indefinite expansion so as to fil any vessel of whatever
shape or size.
3. It exerts an equal pressure upon
every point of the walls of the vessel
enclosing it.
4. It is of the same density at every
point of the space it occupies.
II.
BOYLE'S LAW.
This law states that the temperature
being constant, the volume of a gas varies
inversely as the pressure; formulated:
pv'=P, V,           (1)
Where vo=the volume of a given
weight of the gas at freezing temperature and a pressure p,; and v'=the volume of the same weight of gas at the
same temperature and at any pressure p.




34


Dry air, a mechanical mixture of
oxygen and nitrogen, being a pernlament
gas, obeys this law.
III.
THE LAW OF GAY-LUSSAC.
This second law   of gases may be
stated thus: Lhe volume of a gas tunder
constant pressure exw.ands when raised
from the frJeezig to the boiling temperature, by the same tfr'action of itself'
whatever be the nature of the gas; formulated:
v = v' (1 + at)      (2)
It has been found by the careful
experiments of MM. Rudberg, Regnault and Prof. Balfour Stewart and
others, that the volume of air at constant
pressure expands from 1 to 1.3665 between (~( C. and 100~ C. Hence for a
variation in temperature of 1~ C., the
volume varies by.003665 or -s{3 of the
volume which the air occupied at 0~ C1.
and under the assumed constant pressure.
In equation (2) the coefficient a, is therefore equal to -I-.




IV.
BOYLE'S AND GAY-LUSSAC'S LAW.
Combining the equation formulating
Boyle's law with that formulating GayLussac's, we obtain,
a1
pv-=-poVo(1 + alt)-=poVoa~ (a + t);
or letting   a=-=2'73, we have
a,
pv —~~0 (a + t)=R (a + t)  (3)
a
This last equation is a general expression for both Boyle's and Gay-Lussac's
law, and completely expresses the relation between temperature, volume, and
pressure.
R is a constant and depends upon the
density of the gas. Its value for atmospheric air is determined as follows:
The weight of the standard unit of
volume of a substance in any condition
is the specific weight of that substance in
that condition.
The specific weight of air, that is t
say, the weight of a cubic foot of air at




36


(VC. and uinder a pressure of 29.92 inches
of mercury, is, according to M. Regnault,.080728 lbs. avoirdupois.
The sjpecfi~c voluqnue of a gas is the volume of unit of weight; it is the reciprocal of the specific weight.
The specific volun-e of air, i.e., the volume in cubic feet of one pound avoirdupois at 00 C. and under the pressure of
29.92 inches mercury is:
1
0.080728=12.387 cubic feet.
Let p0 =2116.4, the mean atmospheric
pressure in lbs. per square foot. Then
P"0v0= 2116.4 X12.387
__    -        - -=9 6.0 3 76.
V.
ABSOLUTE TEMPERATURE.
Making t=-2 73 in the equation
Pv -R (a, ~ t),
the second member reduces to zero, and.
hence,
Jpv _o.




37


The distance of the freezing point
from the bottom of the tube of an air
thermometer is to the distance of the
boiling point from the bottom as 1:1.3665.
Hence, in the centigrade scale, where
the freezing point is marked 0~ and the
boiling point 100~, the bottom of the
tube will be marked-272~.85.    The
lowest reading of the scale is, therefore,
-273~. If this reading could be observed it would imply that the volume
of the air had been reduced to nothing.
This is evidently a purely theoretical
conception; but in dealing with questions
relating to gases it is exceedingly convenient to reckon temperatures, not from
the freezing point, but from the bottom
of the tube of an air thermometer. Absolute zero, therefore, is marked-273~ on
the Centrigrade scale (corresponding to
-459.~4 on Fahranheit's scale), and is
the temperature at which all molecular
motions cease, and the mechanical effect,
which we call pressure, and which is due
to these motions, becomes zero.




,38
LAW OF THE PRESSURE, DENSITY AN~D
TEMPERATURE.
Let D.-the density of a weight w~ of
air at the temperature GO C. and under
the pressurep v, c being the corresponding volume;
D -its density at pressure p-, temperature 1, zv being its corresponding volume;
D'_its density at temperature 00 C.
pressure p and volume 7'.
We shall have
or by taking vwunity,
71       D
Placing these values of r"' and 7', in
equation (1), we get
p _D'(4)
that is, the pressure of a gas is prop~ortional to its density.
From (2) we have,
D     1      a
D1+ C(t a + t          (5)




39
That is, the density of a gas is inversely
as its temperature, the latter being reconed from absolute zero.
Combining equations (4) and (5),
D    p      a
iU7 x ~ ~, or
Do  Pe   t +t
P=P.x  a+tD.         (6)
But D=-12- and hence
V)
PV 0O  (a + t)w        (6a)
(6) shows that the density of a gas is:
At constant temtperatutre, directly as the
pressure;
At constant pressure, inversely as the
absolute temperature.
DPo constant for any given gas. For
~0
air Po   2116.4 = 26216.43 (according
Do.080728
to Rankine, 26214); this is the height in
feet of a column of fluid of density Do,
which produces a pressure p0 pounds per




4()


square foot of surface; letting H be this
height, the weight of the column having
one square foot for its surface will be
DoH, or
DoH=p0.
If in (6a) we make v=1, we get
p    Da    p    1
X^+ t  P  c-axt  R    (7)
which is the weight of unit of volume,
or the specific weight of air.
Making w=1 in same equation, we
have for the volume of unit of weight,
p       Io _  a +t   t
=     =             (8)
called the specific vo,lume. (7) and (8)
are reciprocals of each other.
VII.
THE MEASUREMENT OF HEAT.
Any effect of heat may be used as a
means of measuring it, and the quantity
of heat required to produce a particular
effect is called a thermal unit. It has
been found best to take a thermal unit to
be the quantity of heat which corre



41


sponds to some definite interval of temperature in a definite weight of a
particular substance.
_Def. A British Thermal Unit is the
quantity of heat which corresponds to an
interval of one degree of Fahrenheit's
scale, in the temperature of one pound
of pure liquid water at its temperature
of greatest density (39~.1 Fahr).
Def. A Calorie, or French Thermal
Unit, is the quantity of heat which
corresponds to the Centigrade degree in
the temperature of one kilogram of pure
liquid water, at its temperature of greatest density, (3~.94 C.).
Def. The Specific Heat of a body, is
the ratio of the quantity of heat required
to raise that body one degree, to the
quantity required to raise an equal
weight of water one degree.
It has been proven for permanent
gases, that,
1. The specific heat is constant for
any given gas, and is independent of the
temperature and pressure;
2. The thermal capacity per unit of




42


volume, is the same for all simple gases
when at the same pressure and temperature;
3. The specific heat increases with the
temperature, and probably with the
pressure, when the gas is brought near
the point of liquifaction, and no longer
obeys Boyle's law.
The above three conclusions are true
of specific heat at constant volume, as
well as of specific heat at constant pr'ssMre, as far as regards simple gases and
air, (which, being a mechanical mixture,
obeys the same laws as a simple gas).
It was shown by Laplace, that the
specific heat of a gas is different, according as it is maintained at a constant
volume, or at a constant pressure, during
the operation of changing its temperature.
The specific heat of gases was independently determined by M. Regnault
and Prof. Rankine; experimentally by
the former, and theoretically by the
latter.  Their results agreed  exactly,
and are those now generally accepted.




43


As given in Watt's Dictionary of Chemistry,
The specific heat at constant pressure
is.238.
As we shall find farther on, the specific heat at constant volume is.169.
c.238.**  -J= ^1.40=y
C'.169 — 140 —Y'
CHAPTER III.
THERMODYNAMIC PRINCIPLES AND FORMULAS.
I
INTRODUCTORY.
It is well known that the cylinder of
an air compressor becomes very hot even
at a low piston-speed. This fact brings
us face to face with the doctrine of the
conversion of energy; for it is the conversion of the visible, mechanical energy
of the piston into that other invisible
form of energy called heat. Thus we
see we are at the very outset confronted
with a thermal phenomenon, whose consideration involves the science called




44


thermodynamics.   To begin with we
had no other but the visible mechanical
energy of a moving piston; but very
soon sensible heat manifests itself, and
this heat can be developed only at the
expense of part at least, of the energy of
the moving piston.
These phenomena are referable to the
two general principles which form the
basis of the science of thermodynamics,
viz:
1. All forms of energy are convertible.
2. The total energy of a substance or
system cannot be altered by the mutual
actions of its parts.
"The conversion of one form    of
energy into another takes place with as
great certainty and absence of waste,
and with the same integrity of the elementary magnitude, as the more formal
conversion of foot-pounds in kilogrammeters." "In the development of the
axioms that nothing is by natural means
creatable from nothing, and that things
are equal to the same thing only which
are equal to each other, and in the appli



45


cation to them of empirical laws with
reference to the behavior of bodies under
the action of heat and mechanical effect"*
consists chiefly the science of thermodynamics.
The general equation of thermodymamics which expresses the relation between heat and mechanical energy under
all circumstances, was arrived at independently, in 1849, by Professors Clausius and Rankine. The consequences of
that equation have since been developed
and applied by many distinguished
writers.
Of course we shall here confine ourselves to so much only of the Mechanical
Theory of Heat as is necessary to an intelligent comprehension of our subject;
and, in doing so, shall follow in outline
the treatment given by M. Pochet, in his
admirable "Youvelle Fechaniquee Indstrielle," making free use, at the same
time, of the works of Zeuner, Rankine
and Clausins.
* "History of Dymalnical Theory of leat," by the
late Porter Poinier, M.E., in Popular Science Monthly
for January, 18T8.




46


II.
HEAT AND TEMlPERATURE.
Heat denotes a motion of particles on
a small scale just as the rushing together
of a stone and the earth denotes a motion on a large scale, a mass motion. It
is due to a vibratory motion impressed
upon the molecules of a body.   The
more rapid the vibrations the more intense the heat. The quantity of heat in
a substance could be measured by multiplying the kinetic energy of agitation of
a single molecule by the number of molecules in unity of weight, supposing the
substance to be homogeneous and the
heat uniformly distributed.  Thus the
thermometer and dynamometer reveal to
us phenomena which are in reality identical, and we can establish a measuring
unit to which both effects can be referred.
Temperature is the property of a body
considered with reference to its power of
heating other bodies. It is a function of
the variables, volume and pressure, or,
t=   (7, p);




47


that is, all bodies having the same pressure and volume have the same temperature. This is expressed by the differential equation:
dt= () dp + (dv,          (9)
where (d   and ( -) are the partial differential co-efficients; dt in the former denoting the increment of t when, v remaining constant, p alone is increased by
dp; and in the latter, the increment received by t when p remaining constant,
v is increased by dv; whilst in the first
member of the equation, dt represents
the total increment of t due to the simultaneous reception by p2 and v of the increments dp and dv, respectively.
III.
THE TWO LAWS OF THERMODYNAMICS.
The whole mechanical theory of heat
rests on two fundamental theorems: *
1. That of the equivalence of heat and
* See Clausius on Heat, Memoir.




48


work; whensoever a body changes its
state in producing exterior work, (positive or negative), there is an absorption
or disengagement of heat in the proportion of one British thermal unit for every
772 foot pounds of work, (or of one
French thermal unit for every 423.55
kilogrammeters of work).
This mechanical equivalent of heat
was first exactly determined by Mr.
Joule, in honor of whom it is called
Joule's equivalent, and is denoted by the
symbol J.
2. 17w'e theorem of tAe eqtivalence of'
transfoormations; when a body is successively put in communication with two
sources of heat, one at a higher temperature t, the other at a lower temperature
to, its temperature remaining constant
and equal to that of each source during
the whole time of contact, and the body
neither receiving nor losing heat except
by reason of its contact with the two
sources, the ratio of the quantity of heat
Q given out by the higher source to the
quantity Q' transferred to the lower




49


source, is independent of the nature of
the bodies; it depends only on the
temperatures, t and to, of the two
sources.
Clausius states this as follows: In all
cases where a quantity of heat is converted into work, and where the body
effecting this transformation ultimately
returns to its original condition, another
quantity of heat must necessarily be
transferred from a warmer to a colder
body; and the magnitude of the last
quantity of heat, in relation to the first,
depends only on the temperature of the
bodies between which heat passes, and
not upon the nature of the body effecting
this transformation; or, more briefly,
heat cannot of itself pass from a colder
to a warmer body.
IV.
HEAT AND MECHANICAL ENERGY.
The quantity of heat which must be
imparted to a body during its passage,
in a given manner, from one condition to
another, (any heat withdrawn from the




50


body being counted an important negative quantity) may be divided into three
parts, viz:
1. That employed in increasing the
heat actually existing in the body;
2. That employed in producing interior work.
3. That employed in producing exterior work.
The first and second parts, called respectively the thermal and ergonal content* of the body, are independent of
the path pursued in the passage of the
body from one state to another; hence
both parts may be represented by one
function, which we know to be completely determined by the initial and
final states of the body. The third part,
the equivalent of exterior work, can only
be determined when the precise manner
in which the changes of condition took
place is known.
Let dQ-=the element of heat absorbed
during an infinitesimal change of condition;
* Clausius on Heat. Memoir.




51


Uo=the free heat present in the body
at the beginning, i.e., the body's intrinsic
energy;
U=the free heat present in the body
at the end of the change, plus the heat
consumed by internal work during the
change of state;
pdv will be the work accompanying
the passage of the body from a state
(p, v) to a state (p + dp, v + dv);
Then the heat spent while the body
passes from one temperature t to another
t+(dt, and from one state (p, v) to another (p + dp, v + dv) will be:
cQ= (U-Uo) +.pdv,
=     dU'+ -.p dv;  (10)
where dU depends upon the initial and
final circumstances, while -.pdv depends
on the intermediate circumstances of the
change of state.
We can write dU=o and entirely exclude interior work and heat by confining




52


ourselves to cyclical processes, that is to
say, to operations in which the modifications which the body undergoes are so
arranged that the body finally returns
exactly to its original condition, the interior work, positive and negative, exactly
neutralizing each other.
u=f (P, 7v),
that is, the internal heat of a body depends only upon the volume of the body,
and the pressure to which it is subjected.
Hence the increase of internal heat when
Ihe body passes from a state (p, v) to a
state (p + dp, v + dv) will be:
T=    -- )d1p + (- )-dv.  (11)
Substituting in equation (10) the value
of dcT as given by equation (11),we ha've
"    (IQ =  tp M  (t) + ^  dv (12)
an equation which is not integrable;
since this would require that the second
derivatives of the co-efficients of dp and
dac
dv (which are, respectively, d-7 and
(11). Al~




53


d'U
dvdp + J) should be equal to each
dv.dwp
other*; this would imply the impossible
condition J=o. That is, mechanically
speaking, the quantity of heat passing
cannot be expressed as a function of the
initial values of p and v. The equation
can only be integrated when we have a
relation given, by means of which t may
be expressed as a function of v, and
therefore p as a function of v alone. It
is this relation which defines the manner
in which the changes of condition take
place; the quantity of heat passing depends upon the intermediate circumstances of change of state, circumstances
which may be anything.
When a body is heated from a temperature t to another t+dt, preserving
the same volume, no external work will
be done and dv=o. Hence eq. (12) will
become:
dQ= (dU d
(dp)
=c, dt           (13)
* See Ray's Infinitesimal Calculus, p. 366; also McCullough on Heat, arts. 61 and 62.




54


which, by definition, is the speciflc heat
(ft (eOflstagit volum~e.
Trhe above equation gives:
(13at)
the partial differential co-efficient of
with respect to p.
If the body passes from t to t ~ dt
under conistntw press?tre, d1p -o, and hence
(12) becomes:
dQ= ~ (IdU)~P    clia cC (t  (14)
which, by definition, is the spqec,~ti heat
att cowstamtd pressure.
From- (14) we have:
(I U   p     (ita
Substituting these values of the partial
derivatives in eq. (12), we obtain a seeond expression for (IQ, viz.:(IQ -   c  d(/-)dp ~c(+t)dV  (15)
It is convenient to have this equation
in a f orm. involving only the ternperature




55
and specific heats, and not the quantity
Q. We obtain such a form by differentiating (13a) with respect to v, and (14a)
with respect to p and subtracting the
first result from the second. The form
obtained is:
1_ (-     dt   /c\i ct\   e \it\
J  (c- c) dv.p (+;cl);) -dv (p
(16)
V.
THE DIFFERENTIAL EQUATION OF THE
SECOND PRINCIPLE.
In the figure,
Y
Jx
0     A   D       E       B    C




1. Let OA=the initial volume of a
body whose temperature is t; it expands
in contact with a source of heat, (isothermally), from volume OA to volume OB,
when its temperature is then still t.
Q=the quantity of heat supplied by
the source.
2. It is now left to expand adiabatically, i.e., without the addition or subtraction of heat, from volume OB to
volume OC, when its temperature will
have fallen to to.
3. Now place it in contact with a
source of heat of the same temperature
to, and compress it from OC to OD,
when its temperature is still to.
Q'-the quantity of heat that has
passed into the source.
4. Compress it adiabatically from
volume OD to volume OA, when its
temperature will again be t; the body
has now undergone a complete cycle,
during which it has evidently done work
represented the area c(bed; hence,
Q- Q     heat disappeared, and from
the first law of thermodynamics,




57


Q-Q,=    xabcd=    XA.     (17)
Now the second law of thermodynamics states that Q and Q', (the heat
received and the heat given out), are
independent of the nature of the bodies,
and dependent only upon the temperature.
Suppose that the difference of temperature of the two sources of heat is
infinitely  small, t and  t+dt.  Also
consider t and v as the independent variables determining the state of the body,
p=f(v, t).
A, in the above equation, is the integral between v0 and v of the elementary
areas, such as ef. Now if Ee=p, Ef is
what p will become when the volume
remains constant, and the temperature
takes an increment dt; fe therefore
measures the differential increment
(dp
-t dt,
where dP=the partial derivative of p
with respect to t.
with respect to t.




158


Hence, Q~-QI-A.__J       (iidtdv
vo cit
taking the independent variable dt out
of the integration symbol.
Q is the heat supplied to keep at t the
temperature of the body expanding
from vo to v; and, therefore,
Q= Ck(t,i)0,v; the nature of the bodies);
also,
the variables vo, v being implicitly contained ini F.
Since Q=Q' when t becomes t+,dt we
have,
Q=-F(t+clt)=F(t)~F/(t) cit
and
Q   1+F'(t) Ct
Q1     F (t)
According to the second principle,
Qis independent of the nature of the
bodies; hence,
F (t)   J        I




59
and
Now, suppose v - v becomes indefinitely small and equal to Av; Q' will become
dQ, Q being the heat necessary to keep
at t the temperature of a body whose
volume increases by dv; hence the differential equation of the first order,
dQ={~F 4        Ad     (18)
is the differential equation of the second
principle.*
Calculation of the function 0 (t). It
may have several formns. Making dt=o
in eq. (9), we get,
~  dt)
Placing this value of dp in eq.(1)
d1Q=(c-c,) (it dv.


' See Zeuner, "1Th~orie MWchanique, de la chaleur,"
troiskione section, iii.
Also, clausius on Heat, first Memoir.




60


Moreover in (9)\!   represents the
(it
partial derivative of p with relation to t
when v is constant; making dr-o,
((P)
Hence eq. (18) may be written,
I  dV
Equating this with the value of dQ
above, we have,
1(dt\ (it\
J      C-C    -     -     I9
from which ~P (t) may be calculated.
Again, if we take Eq. (1.6) and suppose it applied to bodies whose specific
heats c and c, are independent, the first
of the pressure and the second of the
volume, as is the case in permanent
gases, these conditions give (+) and
\de  equal to zero, and the equation bedce
comes,




61


(C-cel)(d  -)1(20)
dp  J,
Dividing eq. (19) by this we get,
(dt)Qh)
dp dv
giving, 0 (t) as a function of t[f
(p v)] and of its partial derivatives.
CHAPTER IV.
THE THERMODYNAMIC EQUATIONS APPLIED TO PERMANENT GASES.
DETERMINATION OF THE SPECIFIC HEAT AT
CONSTANT VOLUME..
Forming, from eq. (3), the partial differentials
(dtv    ( dt\ -P  dt  1
dplR' dv/ R'dp. dv -R'
and substituting ia eqs. (20) and (2 1), we
have:


(22)




62


and      J()       (a +t).       (23)
1          96.0376
(22) gives,  -               1389.6 -z.169
which is the specific heat at constant voluime for atmospheric air.
IL.
INTERNAL HEAT.
Placing eqs. (12) and (15) equal to
each other and substituting the value of
c from. (22), we have
\-dpJP~ \dv!    - c(vdp1y pdv)-zAdt
according to eq. (I11).
Integrating, and substituting for R its
valuet we have,
UJ = cI- - 1J0
or           U-U0T=C/r           (24)
which shows that the internal heat for
every degree of temperature is increased
by a qnantity c' (.169), and the increase




63


of the internal heat of a gas passing from
0~C. to t~C. is always the same, whatever variations its pressure may have undergone in this passage, the volume
having been kept constant.
III.
QUANTITY OF HEAT SUPPLIED.
The partial differentials formed from
eq. (3) placed in (15) gives:
vdp + cpdv          (25)
d= —     R              (25)
which is integrable only when we have a
given relation between p and v.
1. At constant volume; make dv=o,
v being constant. Then
Q_ fpcvdpe    c'v(p-po)(0 R                 (- R)
(25a)
which defines the specific heat at constant volume.
2. At constant pressure; here dp=o,
and eq. (25) gives:
Q=-p(V-o) =c(r-Z)         (25b)




6 4


TV.
EXPANSION AT A CONSSTANT TEMPERATURE.
To find the work done by a gas expanding isother-mally, (that is, the absolute temperature is maintained at a const an t value), we must satisfy Boyle's
law and write
p~v -— pov, - con stant;
hence  p1v + vdp =o; or, v dp =-pdv.
Substituting this in (25),
R
Introducing p from eq. ()
dQ=jR a + d)v
and,
(IV0
Let W-the work done; then




W=p,,v, log. * VI        (26a.)
the ordinary form for permanent gases.
V.
EXPANSION IN A PERFECTLY NON- CONDUCTING CYLINDER.
If a gas expand( adialxttically, (i.e.,
without any passage of heat either into
the gas from without or out of the gas
into other substances), dQ =o in eq. (2 5),
and we have,
et vdp cpdAv= o.
Writing for  its value y, and integrating, we have
f    p+yJ  v A= log.?  + yog9. - =o
p5
p           V,   5
P0       Vo 5
'The logarithms, it is seen, are taken in the Naperaian
system,




66


hence,   pv" -p~vj =constant;   (2 ~)
an equation which expresses the variation of pressure as a function of volume
when the expansion or compression is
(tcliaduatw.
The external work performed during
a finite expansion is denoted by
VV
~  (y1 ~.   (28)
Since no heat is received from without,
the thermal equivalent of the work must
be estimated as intermicd heat. If, now,
Ir0 and -r are the initial and final absolute temperatures, the decrease in internal. heat will be
c'( r0,- r).
Hence we must have,




67
J  -1   oo
c,(,-.:-P        I 1-(v)     } (29)
Eq. (27) gives  v  =1; multiplying
v yY —
both members by y —     we have,
p   v v( )Y-     1 a+t     (30)
(30)
pOVO    VO     a +to  T~
also,
voy          o   (-oo)
--   and Y-=(-%.
vy   Po      v   p
hence,
(vo)Y-    p)Y     a+t   - r  (31;-   -       'Y  a+         (31)
Substituting in (28) the values of povo
from (3) and (v- )Y  from (:1), we obtain:
W= R(a + t)                  (32)
Y --- \1'-       T-     (32)
a form often used. — =.2908.
Y




6 8


VI.
VARIATIONS IN THE TEMPERATURE OF A
GAS DURING EXPANSION OR COMPRESSION IN A PERFECTLY NONCONDUCTING CYLINDER.
Placing, the second members of p~v.=
y (a  tj    and J-     in eq. (29)
we get:
which is thus interpreted
The decrease in teinperature (during
an expansion from vo to v) is proportional
to the initial absolute temperature.
The already established relation,
T   (v)7-1
expresses the final temperature as a
function of the volumes; and if we know
the initial and final pressures, the final
temperature is expressed as a function of
these pressures as follows
a+t    Tr __j),
a+t, - T    0/)  Y




69


CHAPTER V.
THERMODYNAMIC LAWS APPLIED TO THE
AcTIoN OF COMPRESSED AIR.*
I
FUNDAMENTAL FORMULAS.
The four equations formulating the
law for the expansion and compression
of dry air, are, as we have established
them,
])=Rw=-? —J(C-c')wo       (34a)
a+t         r
Po~  o~7           (34 b)
~ ~1            (34c)
TOJ1 PO       1PO         (34d)
Tlie subject of this chapter is very ably treated by M.
Mallard, in the "Bulletin de la Soci&6t de 1' industrie
mi-nerale," tome xii, page 615, to whom the writer is
greatly indebted.




7i )


These expressions sum up the relations
existingf between the pr-)essure, volumne
aiid absolute tenype-rature, of a weight of
aiir?' compressed or exp)anded in a perfectly non-conducting cylinder.
p0, T0ro and v. have reference to the
initial state of the weight of air consider-ed, p, -z and v corresponding to the
final state.
The following table is that of MM.
Mallard and Pernolet. It gives for convenient values of -~~-the corresponding
values of    &c.   The tabular differences facilitate interpolation.
(See Tatble on patges 72 and 73.
II.
WORK SPENT IN COMPRZESSIN-,G' AIR.
The compressing-cylinder being supposed perfectly non-conducting as to
heat, our machine may be called a
"Reversible Engine;" for by reversing
the process of compression under exact



71.ly the same conditions, we get back the
exact amount of work spent in the compression.
The net work necessary to compress a
weight of air w, taken from a reservoir
(as tle atmosphere) in which the pressure p0 is kept constant, and to force it
into another reservoir in which the pressure is constantly p1, is made up of the
following parts:1. The work of compression:
2. Diminished by the work due to the
pressure p0 of the first reservoir (the
atmosphere); this work is p, v0, v0 being
the volume of weight w under pressure
p, and at the temperature to:
3. Increased by the work necessary to
force the compressed air into the receiving reservoir; this is given by the
expression p, v, v0 being the volume of
a weight of air w at the pressure p, and
temperature t,.
As no heat passes between the air and
external bodies, the thermal equivalent
of the work, according to the mechanical
theory of heat, is the difference between




TABLE L1


por-To
PO          TO             T
Num- Differ' Num- Differ- Numbers.  ences.~ bers.   ences.  bers.
1.2   1.0543   481.9485     415.0515
1.4   1.1024   4:36.9070    344.0930
1.6   1.1416   439.8762     293.1274
1.8   1.1859   367.8433    254.1567
2     1.2226   343.8179    223.1821
2.2   1.2569   321.7956    198    2044
2.4   1.80     303.7758    178.2242
2.6   1.31.93  187.7580     161.2420
2.8   1.3480   272.7419     147.2581
3     1.3752   260.7272     124.2728
3.2   1.4012   248.7138    125.2862
3.4   1.4260   238.7013    116    2987
3.6   1.4498   2 30.6897    107.3103
3.8   1.4728   220.6790    100.3210
4     1.4948   213.6690      94.3310
4.2   1.5161   206.6,596    89.3404
4.4   1.5367   200.6507     81.3493
4.6   1.5567   193.6424     79.3576
4.8   1.5760   188.6345     75.3655
5     1.5948   865.6270    322.3730
6     1.6813   769.5948     260    4052
7     1.7582   694.5684     217.4512
8     1.8276   636.5471    183.4529
9     1.8712   588.5288    159.4712
10     1.950)0  544.5128     141.4871
11     2.0044   512.4988     124.5012
12     2.0556   484 I.4.864     111.5136
13     2.1040   457.4753     101.5247
14     2.1497   434.4652      92.5348
15     2.1931.4560.5440




73


TABLE I.- Continued.


v 0
qV


V
v0.Num- Differ-     Num- 'Differbers.      ences. ~bers.     ences.


ta
7
Num- Differbers. ences.


1.1382
1.2699
1.3961
1.5179
1.6358
1.7503
1. 8619
1. 9707
2. 0772
2.1815
2.2838
2.8',843
2.4830
2.5802
2.6759
2.7702
2.8632
2.9550
3.0456
3.1352
3.5685
3.9814
4. 3772
4. 7589
5.1286
5.4869
5 8353
6.1783
6. 5123
6.8396


1317
1262
1218
1179
1145
1116
1088
1065
1043
1023
1005
587
972
957
943
930
118
906
896
4333
4129
3858
381.7
3697
3 583'
3484
343')
334
3273.8786.7875.7163.6588.6113.5713.5371.5074.4814.4584.4379.41144.4027.3876.3737.3610.3493.3384.3283.3190.2802.2512.2285.2101.1950.1824.1713.1618.15315.1462


911
712
575
475
400
342
297
260
230
205.185
167
151
139
127
117
111
101
93
388
290
227
184
1511
1.26
111
95
83
73.793.695.642.603.571.546.524.505.488.473.460
- 448. 438.428.419.410.402
3895.388.382.355.334
1.317.303.291. 281.272.263.256.250


78
53
39
32
25.22
19
17
is
13
12
10
9
9
8
7
6
27
19
19
14
12
10
9
9
7
6




74


the quantity of internal heat possessed
by the air at its entrance into the cylinder, and that possessed by it its exit.
The heat possessed by the air at its
entrance into the cylinder is,
The internal heat at its exit is,
wc'r,.
Hence the work of compression is,
Jwc'r - Jwc' o- Jwc 1(T- To),
and the net work is,
W1 =Jc'w(rl - r,) -pov +p1v1.
Substituting for pov and pv, their
values from eq. (34a) we have,
W,=Jwc(r, —r)          (35)
an equation perfectly general for dry
atmospheric air.
III.
WORK OBTAINABLE FROM THE COMPRESSED
AIR.
If, by any process, we cause a weight
of air w to pass from one reservoir, in
which there is a constant pressure po,




75


into another reservoir, in which there is
a constant pressure p, and thereby consume an amount of work WI, the same
weight of air w (supposing the air to
remain in the same physical conditions)
will restore the amount of consumed
work W, in passing back from the
second reservoir into the first. These
are the conditions of a perfect thermodynamic engine.
The work theoretically obtainable
from compressed air is therefore, eq. (35),
W, =Jwc(r1I- T0) = W,
an equation which shows how important
it is to take into account the initial and
final temperature of the air.
IV.
THE THEORY OF COMPRESSION.
1. The Work necessary, and the Volume
of the Compressing- Cylinder.-Neglecting
all dead spaces and resistances, we can
easily calculate, by the aid of our formulas and of Table I, the work necessary to
compress to a pressure p1 a weight of air




W, taken at a pressure p0, and a temperature r., as well as the volume to be given
to the cylinder of the compressor, to
compress a griven weight of air w per
second, the time T' being given in.seconds.
Our formulas are-:
WI _JWC(Tr-r0,)=Jwvcr0.{ T[k-i - (35ci)
when a final temperature -r,, which is not
to be exceeded, is assumed, the value of
IL being obtained as a function of -PI
TO                                P
from Table 1, or from an adiabatic curve.
W   _Jqwc'    Z ~91-1 ~,  (35b)
when a pressure p1-, to which we wish to
attain, is assumed.
WI pvJ~U~,      (35e)
an equation employed when we wish to
find WI as a function of the volume v. of
the air instead of as a function of its
weight. This equation is obtained by




substituting in eq. (35a.) the value of r0
from eq. (34a.), and y for c,.
From eq. (34a.) we have,
V-=Rw-XT,               (:36)
PO
an equation for the volume of the cylinder which compresses per second a
weight of air w, when the time, T, required per single stroke of the compressor (or per double stroke when the
compressor is single-acting), is given in
seconds.
2. The Final Temperature of the Compressed Air.-This is found by looking in
Table I. for the values of -  opposite
p0
the different values of P.  Supposing
the initial temperature rTo=2930=200C.,
we find for the different values of P- the
PO
values of r, in degrees of absolute temperature and degrees C., as follows:




rfA.BTA-. TI.
___           Final Temperature
PO             in Degrees C.
2      358.2           85.2
31     402.9          129.9
4      437.9          164.9
3      407.2          194.21
(I     492.0          219.6
3 15.1             242.1
8      333) 4         262.4
9      334.1          281.1
10      3 71. 3        298.3
11      5 387. 2       '2 14. 2
12~     002.2          3'29.2
13)     616. 4         343.4
1 4     0,2,9.8        356.8
1   6 42.35        309.5
V.
THE THEORY OF TRANSMISSION.
1. Loss of Pressure dlue to i'anCsmission.-The loss in pressure which results
from carrying compressed air from one
point to another point distant from the
first, is due,
1.' To the friction between the air and
the conveying pipes;




2.~ To sudden contractions in the
pipes;
3.~ To sharp turns and elbows.
From experiments made at the Mont
Cenis Tunnel, the loss of pressure from
friction in pipes was formulated thus:u2l
Ap=.00936-,          (3,)
where u=the velocity of the air per
second,
I=length of the pipes,
d= diameter "   "
Hence the loss of pressure varies,
directly as the length of pipe; directly as
the square of the velocity of the air in the
pipe; inversely as the diameter of the
pipe.
If w be the weight of air required
by the working-cylinder per second,
d2
3.1416 -u being the volume of air passing
through the pipe per second, and p, and
r1 being the pressure and absolute temperature respectively of the air in the
reservoir, we have, from eq. (34a)




80


d
3.1416- up,
-- Jw(c-c');
Solving with respect to u and substituting in (37), we have,
Ap- 13.88p B
when Joule's equivalent is taken in
French units; when taken in British
units (772 foot-pounds per British thermal unit), we have,
22
Ap=43.055-d — 1        (38)
which expresses the loss of pressure due
to friction in the pipes as a function of
the weight of air supplied per second, of
the temperature and pressure of the air
in the reservoir, and of the length and
diameter of the pipe.
2. Difference of Level.-The difference
of level which exists between the reservoir and the compressor and the compressed-air engine (as when the latter is
at the bottom of a mine) compensates in
part, at least, for the loss of pressure due




81


to the friction in the supply-pipes. The
gain in pressure due to this difference of
level is readily calculated by means of
the ordinary barometric formulae. (See
Wood's Elementary Mechanics, p. 327).
VI.
THE THEORY OF COMPLETE-EXPANSIVE
WORKING.
1. Notation.-Let 00=the absolute
temperature of the compressed air when
it enters the working cylinder;
0,=the absolute temperature of the
air after expansion;
~,=the pressure of the compressed air
on entering the working-cylinder;
0,=the pressure at the end of expansion.
2. Work theoretically obtainable.This is given in Section III, and is
W,=Jwc(o —0,)=Jwc0       1 — }
=Jwc6\l-(0      ), },  (39)




being obtained from the formula for
the final temlperatulre.
3. FPbwl Yemnperatitre.-This is given
by eq. ('-td) and is
it cane be calculated directly by the use
of Table I when we know      the ratio
of the final to the initial temperature.
4. Volume of the TWorking- Cylindler.
-The volume of the working-cylinder,
being the same as the final volume of the
air after expansion is, from eq. (34at),
V 2_Jw&-( (C-c') T       (40.)
wh'ere w -the weight of air furnished per
second and T —the time in seconds of
one stroke.
5. TMighl of Air required p)er Secod*
This is determined by the work which is
to be done by the compressed-air engine
per second. Letting. A- be a certain coefficient embracing resistances of all
kinds, we have, Section III,




83


w`2                (41)
wk Jc(-0)          (4,)
Substituting this value of w in eq. (36)
we have,
R      WT       T   Y-1
V =X2 -0                     X
Jvc  k (e0 -,)  p-x   y
WT       r
W2T    x, (42)
k (Q0-01) p,
the volume of the compressor in order to
supply the given amount of air.
6. Cold resulting from Expansion.While in the compressor there is a great
development of heat from the compression of air, in the working-cylinder there
is a great fall of temperature due to its
expansion. The final temperature 01 is
calculated from the formula of Sec. VI, 3.
The valves of, corresponding to 0,
and the reciprocals, are found from
Table I. The following table is from M.
Mallard. The initial absolute temperature is assumed 0o=293~, that is, 20~ C.




84
TABLE III.
Final Temperature.
Absolute 0.     Degrees C.
2        239.6        - 33.4
3        213.0        - 60.0
4        196.0         - 77.0
5        183.7        - 89.3
1 1      74.2         - 98.8
7        166.6        -106.4
8        160.3         -112.7
9        154.9        -118.1
10       150.1         -122.9
11       146.1         -126.9
12   i   142.5         -130.5
13       139.2     i   -133.8
14       136.3         -136.7
15       133.6         -139.4
This table shows what very low temperatures are reached when we work full
expansion with air at a high pressure.
Ice is formed from the water-vapor
present in the air, and seriously interferes
with the action of the working engine.




85


VII.
THlE THEORY OF FULL PRESSURE WORKING.
1.Work obtainable.-This is, in the
present case, expressed by the equation,
Placing in this equation the value of V.
from eq. (40) we have,
The general expression for the work
restored has been given by eq. (39),
where 0, is the temperature of the air
after it has been exhausted and has assumed the pressure of the atmosphere 0J,*
2. Final Temperatnre.-Placing eqs.
(44) and (39) equal to each other,
& -1   y-l (P
or,  =- _+   ~    =.'7102+.29-:1- (45)
3. TWeight of Air necessary per Seeond.-This is given by eq. (4 1).




86


4. Volume (f Cylindee.-Substituting
w, eq. (41), in eq. (34at), we have,
xv rj                  (46)
THEORY OF INCOMPLETE EXPANSIVE
WORKING.
1. Work attain able.-This is given by
eq. (3 9).
2. Fin~al Temiperature.-'We have, eq.
(34d),
from which we get 01' (the temperature
at the end of the stroke). 0, is then
found from the equation,
+ y-l        i
y         ' 0.
3. Ike weight of' air- used.-This is
given by eq. (41.)
4. Volume of the Cylinder.-Eq. (34a),
written to satisfy our conditions, becomes:




87


0'
V,=J(c-c')wT,',
or, substituting the value of w from eq.
(41),
V    y-1     WT          (47)
IX.
GRAPHICAL REPRESENTATION FOR THE
ACTION OF COMPRESSED AIR.
Let abscissas, in diagram on next page,*
be volumes, and ordinates pressures;
taking 0 for the origin. Through B
(povo) construct an adiabatic curve from
its equation, (eq. 27).
" The intrinsic energy of a fluid is the
energy which it is capable of exerting
against a piston in changing from a given
state as to temperature and volume, to a
total privation of heat and indefinite expansion." The intrinsic of 1 lb. of air
at p, and v0, will be represented by the
area included between the axis of
* For which we are indebted to Professor Frazier.




88




89
abscissas, the ordinate AB=p0, (at a
distance from the origin OA=v0,), and
the portion of the adiabatic curve extending indefinitely from B until it becomes tangent to the axis of abscissas
when x= cc. The algebraic expression
for this area (found by integrating eq.
(27 a) between the limits oo and v0, is,
- Y-1(48a)
PO=mean pressure of atmosphere in
lbs. per square foot=2116.3;
VO=volume in cubic feet of 1 lb. of air
at pressure po and temperature r,
= 12.387;
r0= 493.0~2 corresponding to 320 F;
y=1.4O8; hence
1_P _= 64250 foot -pounds;
3/-I
that is, one pound of air, at mean barometer pressure and 320F, possesses an
intrinsic energy of 64250 foot-pounds;
and it is upon this store of energy that
we draw, when, after abstracting in the,
fo rm of' heat all the work we had ex



90


pendedl in, eompressing the air, we yet
cause it to pemiform work by exspansion.
Through B construct an isothermal
curve f rom its equation (eq. 1.). At a
point (as L —) chosen arbitrarily upon
this curve to correspond to a desired
pressure we can construct another adiabatic curve LEN. Then wvili the relations exist, expressed as follows, and
given by Prof. Frazier
Area ABDC prolonged indefinitelyintrinsic energy possessed by the
air before compression=IL
Ar-ea ABLPA —the work performed in
comnpressilng the air.
Area DBLRiN prolonged indefinitely=ABLPA~energy in the form of
heat abstracted by the cooling
water; consequently, BSND prolonged indefinitely —ASLPA.
Area (CKRN prolonged indefinitely=
intrinsic energy of the air after
expansion.
Area KRLPK~work performed by
the air in its expansiol).




91


Area ABRKA= work performed by
the air after it leaves the workingcylinder.
Area DBRSN prolonged indefinitely=
ABRLPA=the      heat absorbed
by the air after leaving the working - cylinder.
For isothermal compression, we have,
Area ABLHOA=total work performed in the compressing-cylinder.
Area ABLPA= work performed in the
compression of the air.
Area PLHOP=work performed in the
expulsion of the air from the compressor.
Area ABUOA=work performed by
the atmosphere.
Area UBLHU=ABLPA=the work
performed by the motor.
Area UTLHU= useful work performed
by the air (full pressure).
Area UBLHU - UTLHU = TLBT=
amount of work lost.
For adiabatic compression we have:




92


Area ABXYA=work performed in
the compression of the air.
Area YXHOY=work performed in
the expulsion of the air from the
compressor.
Area ABUOA= work performed by
thde atmosphere.
Area BXHUB= work performed by
the motor.
Area TLHIUT =useful work performed
by the air (full pressure).
Area BXLTB = BXHUB-TLHUT=
amount of work lost.
When the air is allowed to expand
fully (to its original pressure p),
Area RTLR=-useful work of expansion.
Area UHLRU= total useful work (=
UTLHU + RTLR).
Area BXLRB= — BXHUB- UHLRU
= amount of work lost where air
is cooled after leaving the compressor.
Area BLRB = UBLHU-UHLRU=
amount of work lost where air is
cooled completely in compressor.




93


The area BLRB represents, then, the
excess of work performed on the air
above that per:ornled by it, or the
amount of work permanently transformed into heat. It is, therefore, not possible, even by preventing any rise of temperature during compression and allowing the air to expand to its full extent,
to obtain from the compressed air as
much work as was expended in the compression. We can obtain from compressed air all the work expended upon
it, only by causing it to reproduce exactly during its expansion the changes of
condition it underwent during compression. This may theoretically be accomplished in three ways.
1. By allowing the compressed air to
become heated during compression, and
preventing all transmission of heat until
it leaves the working cylinder. It will
be compressed and will expand in this
case following the curve BX.
2. By cooling the air during compression and heating it during its expansion,
in such a manner that its temperature




94


shall remain constant during both operations. The air will be compressed and
will expand in this case, following the
curve BL. The heat abstracted during
compression will equal that supplied
during expansion.
3. By cooling the air before its compression to such a degree that after it is
compressed it will have the temperature
of the media surrounding the working
cylinder. The air will be compressed
and will expand in this case, following
the curve RL.
CHAPTER VI.
EFFICIENCY  THEORETICALLY ATTAINABLE.
I.
EFFICIENCY OF TIHE AIR-COMPRESSOR AND
COMPRESSED-AIR ENGINE AS A SYSTEM.
Work performed on the air
Work performed by the air
the efficiency =E;
hence,




95


EWJc(r0o-rO)w    = '
WI JC(T,-O)WI
To
=-. x,             (48.)
In practice, -~and -P differ very little
in value, their difference being due to
the loss of pressure from the friction between the air and the supply-pipe, a loss
which is very small if the pipes are of
sufficient diameter.
Hence we may write,
E= 0,               (48a)
0T
that is to say, when compressed air is
made to expand completely, and when
the ratio of its pressure to the pressure
of the surrounding atmosphere is the
same when the air leaves the compressor
as when it enters the cylinder of the
compressed-air engine, the efficiency of




96
the system is the ratio of the temperature
of the compressed air when it leaves the
compressed-air-engine cylinder to the temperatere of the air at its entrance into
the compressor.
This law is independent of any heat
lost by the air in passing from one cylinder to the other.
Since we have just admitted that,
(~ _Po
00 P.
we have,
o0-     t       Pt~hence,
E= — W  - 01-o        (48b)
showing that the loss of work is proportionral to the loss of heat undergone by
the compressed air in its passage from
the compressor to the working-cylinder.
The efficiency will be a maximum
when r,=0o; that is, when the loss of
heat is nothing. Of course, this condition cannot be realized. Generally the




97


compressed air reaches the working
cylinder with a temperature equal to
that of the surrounding atmosphere.
The temperature 0, is therefore given,
and the efficiency can only be increased
by diminishing r,.
The following table is calculated from
(eq. 48b) for different values of P-, the
po'
temperature of the compressed air at
entering the working cylinder being
taken 0-=293~, that is, '20~ C.
TABLE IV.
P~          P.
E.            pE.
Po                Po
2.82        9.53
3.72       10.51
4.67       11.50
5.63       12.49
6.60       13.48
7.57       14.47
8.55       15.46
The table shows that when the pressure has reached four atmospheres, even




a considerable increase of it does not
much effect the efficiency.
II.
MAXIMUM EFFICIENCY CALCULATED FROM
THE INDICATED WORK.
Let p = the pressure of the compressed
air,
Letp0,=the pressure of the atmosphere,
v and vo=the corresponding volumes;
also let p = i-p0; then v h v,
The work spent upon the air to compress it, is, (eq. 2Gca),
V
W,=p~v nap. log.   =p'v x
2.303 comn. log. 9t
The work performed by the air is:
W2 =(p -1j)0)v
and as pv0-v~v and v=nv., we have
hence,




99


-W1- v vX 2.303 com. log. n2.303 corn. log. n (49.)
Substituting different values of n in
this formula we get the corresponding
values of E.
III.
THE EFFICIENCY OF COMPLETE EXPANSION
AND OF FULL PRESSURE COMPARED.
To show the comparative merits and
demerits of full pressure and complete
expansion in the use of compressed air,
we present a table prepared by M. Mallard:                   *......




* o..     TABLE V.,..


I


By, Final tempera-I Th ep2ical effi6 ture. Degrees    cit.oy with
9    C(. Complete comrplete expanexpansion.. sibb.
_ ~5....


Final temperature. Degrees
C. Full pressure.


I


Theoretical efficiency with
full pressure.


I


Ratio of efficiency
at full pressure to
efficiency at complete expansion.






_. 1      I


-I


I


2
3
4
5
6
7
8
9
10
11
12
13
14
15


- 33.4
- 60.0
- 77.0
- 89.0
- 98.0
-106.0
-112.7
-118.1
-122.9
-126.9
-130.5
-133.8
-136.7
-139.4.855.806.782.768.758.751.746.742.739.736.734.732.730.729


-22.4
-36.9
-43.2
-48.0
-51.0
-53.0
-54.5
-55.6
-56.5
-57.4
-58.0
-58.6
-59.2
-59.5.82.72.67.63.60.57.55.53.51.50.49.48.47.46.95.90.86.82.79.74.73.71.69.68.66
65.64.63


I






101


The initial temperature is assumed at
20~C.
The table shows that by working nonexpansively we avoid very low temperatures of exhaust; but this is of little
practical importance when we take into
account the low efficiency of full pressure,
as compared with complete expansive
working. Also when working at full
pressure, the higher the working pressure
the lower the efficiency.
CHAPTER VII.
THE EFFECTS OF MOISTURE, OF THE
INJECTION  OF WATER, AND     OF
THE CONDUCTION OF HEAT.
I.
GENERAL STATEMENT.
In dealing with compressed air we
must always keep in view the very important consideration of the initial and
final temperature of the air.
There are two principal causes tending




102


to vary the amount of heat present in
the compressor or absorbed in the working-cylinder:1. The water or water-vapor of which
atmospheric air always contains more or
less, and which is purposely introduced
into the cylinder of the so-called wetcompressors.
2. The conduction of heat by the
cylinders, supply-pipes, reservoirs, &c.
1I.
THE EFFECTS OF MOISTURE.
Atmospheric air always contains more
or less moisture. We wish to consider
the effects of this moisture upon the air
undergoing compression or expansion,
The injection of water into the cylinders
and its cooling or heating effects are left
out of the question altogether, as they
will receive attention further on.
In all conditions of temperature and
pressure practically realizable, a mixture
of air and saturated water-vapor will
remain saturated when the mixture ex



103


pands against a resistance, a certain
quantity of water being thereby condensed; on the contrary, compression
superheats  the  vapor,  which  then
becomes non-saturated, and non-saturated vapors follow the laws of permanent gases.
1. Influence of 'water-vapor upon the
work spent on the air and upon that
performed by it.-The presence of moisture in the air has been found to be
favorable both in the compressor-cylinder and in the working cylinder. In both
cases, however, the gain in work spent
or performed is so slight that it can be
entirely neglected, and the formulas
already established for dry air become
applicable with a sufficiently close
approximation. In tile case of compression, the vapor is superheated and
therefore comports itself very much like
the air itself; while in the working-cylinder, the increase of work performed,
when the initial temperature of the
compressed air does not exceed 30~ C.,
is very small; and, as the temperature at




104
which compressed air is used, is rarely
higher than 20~ C., the influence of the
water-vapor can be safely neglected.
2. Influence of the moisture of the air
upon the SFinal Temperatare.-The presence of the moisture in the atmospheric
air introduced into the compressor tends
to lessen the heat of compression; this
effect, however, is very slight, and, in a
practical point of view, is not worth
considering.
When compressed air is completely
expanded in a working-cylinder, the
presence of moisture in it tends to lessen
the cold produced.   M. Mallard has
found what the initial pressure would be
for certain initial temperatures, so that
the final temperature should not fall
below 0~ C. He has found this for both
dry and saturated air, and his results are
tabulated as follows:



105


TABLE VI.
Value of -p with the
Final tern- Initial tern-    air.
perature.  perature.           -____
Degrees C. Degrees C.  Sat urated
withi water-  Dry.
vapor.
00        200        1. 50    1.276
00        300        1.89      1 432
00        40*        2.39      1.602
1    500        3.06      L~780
This table shows that, if compressed
air at 500C and at a pressure of three
atmospheres be introduced into a workilug-cylinder, this air, if satni-ated with
aqueous vapor, can be completely expandled without falling to a temperature
below O'C; and that this air, if dry, dare
not exceed an initial pressure of.'78
atmospheres if its final temperature is
not to fall below O'C.
3. Voltmne of the Cylinders.-'I his is
calculated as for dry air, since the effect
of the m. isture is too slight to be taken
into account.




106


III.
TIE INJECTION OF WATER.
1. The Effect of IJotroducing Water
into the Compressor- Cylinder.-It is of
great advantage in practice to introduce cold water into the compressor.
It carries away the heat of compression
to a very great extent. It acts as a lubricant, and, by cooling the cylinder, it
prevents the destruction of any organic
material, such as packing, valves, &c.,
that may be employed upon it.
If in addition to the atmospheric
moisture present in the air at its entrance
into the compressor, water be introduced
in quantities just sufficient to keep the
air saturated with water-vapor during
the compression, the work spent upon
the air and the final temperature at the
end of compression will both be less than
if the air had not been kept saturated
while being compressed. It is unnecessary to calculate the amount of work
saved or the extent to which the temperature is reduced by the presence of




107
this saturated water-vapor; for if water
is at all to be introduced into the compressor, it may as well be thrown in in
larger quantities, that is, in quantities
sufficient to absorb and carry off the
greater part of the heat of compression.
The effects of the heated air in the
compressor is a great cause of loss of
motive power, and it is very desirable to
cool the air during its compression.
The final temperatures for different
pressures have already been given in
Table II. We repeat them here in connection with the quantities of work
spent when the compression follows
Boyle's law and when it is effected without any removal of heat.




TABLE VII.


Coim pression with
Q  temperature constant.
*  Volume    Work in
' g   in cubic  kilogramE    meters.   meters.
1    1.00
2.50        7,199
3.333     11,356
4.250      14,200
5.200     16,580
6.167      18,475
7.143      20,038
8.125     21,422


Compression with increase of
tenmperature.


Tempera- Volume in
ture in   cubic
Degrees C. meters.
20       1.
85~.5.612
130~.4.459
165~.6.374
195~.3.320
220~.5.281
243~.2.252
263~. 6.229


Work in
kilogrammeters.
7,932
13,360
17,737
21,209
24,310
27,048
29,518


Loss of work  Fraction of the
due to the    total work
heat of con-   required for
pression.    compression,
kilogram-    which is conmeters.    verted into heat.
733.092
2004.150
3477.196
4629.213
58035.240
7040.260
8096     i.274




109
The Quantity of Water to be Injected.
-We have found eq. (26), that the
quantity of heat developed by compression is given by the formula,
Q=J nap. log. -~,
where r0 is the absolute final temperature
=273~ +40~=313~. From this formula
the quantity of heat, Q, is calculated for
different pressures. We then find the
weight of water, which, if introduced at
20~C and removed when it has taken up
enough heat to raise its temperature to
40~C, would absorb this quantity of heat
Q. Under these conditions we find that
each kilogramme of water will absorb 20
calories. Dividing Q by 20 we get the
weight of water to be introduced in
kilogrammes. In this way the following table was prepared:




110


TABLE VIII.


Absolute
pressure to
which the
air is compressed.
atmospheres.
2
3
4
5
6
8
9
10
11
12
13
14
15


Weioht of water at
Heat devel- 20~ C. to be injected
oped by com- into the compressor
pression and' per kilogramme of
to be carried air compressed in
off by the' order to keep the
injected  final temperature
water.    from rising above
40~ C.
calories.   kilogrammes.
14.695.734
23.284         1.164
29.392         1.469
34.120         1.701
37.979         1 891
41.264         2.063
44.087         2.204
46.589         2 329
48.816         2.440
50.849         2.542
52.694         2.634
54.391         2 719
55.962         2.798
57.425         2.871


2. The Injection of Hlot Water into
the  Cylinder of the    Compressed-Air
Engine.-In the production of compressed air, the great cause of loss of motive
power, as we have seen, is the development of heat. Analogous to this is the




L11


loss which occurs in the use of compressed air.  Great cold is produced by
expansive working, and this has long
forbidden its adoption. The injection
of hot water into the working-cylinder,
has now made it possible to attain the
desirable result of working expansively.
The Quantity of.Hot Water to be
Introduced.-The quantity of heat, Q, to
be supplied to keep the temperature of
the expanding air constant is found from
eq.(26), to be,
Rr. nap.
Q=     nap.log.
The expansion being supposed to follow
Boyle's law, we have,
pi'1-=p-poV or - -P
V0 P
Hence we have,
Q-RJ nap. log. 4.
p,=l in this case since the air is expanded down to atmospheric pressure. From
this formula the weight of water to be
injected is calculated as in table. The
results are given in the following:




TABLE IX.


Absolute pressure at which
the compressed
air is introduced into
the working
cylinder.
2
3
4
5
6
7
8
9
10
11
12
13
14
15


Quantity of heat to
be supplied to keep
the temperature of
the air from falling
below 0~ C. during
its expansion down
to atmospheric
pressure.
13.280
21.030
26.550
30.828
34.334
37.285
39.833
42.094
44.106
45.945
47.612
49.145
50^.62
51.885


Weight of water to be injected into the working cylinder per kilogramme of compressed
air introduced to keep the final temperature
from falling below 0~ C.
The temperature of the water introduced being


20~ C..134.212.262.311.346.376.402.425.445.464.480.496.510.524


50~ C..103.163.206.240.266.289.309.326.342.356.369.381.392.402


100~ C..074.117.148.178.192.208.223.235.247.256.266.274.282.290




113


The quantities of water here given are
the minima values, since the latent heat
which is released by the water in freezing
has not been taken into account. Hence
to avoid the formation of ice we must
add a slight excess of hot water.
3. The Efect of the Conduction of
Heat by the Cylinders, Pipes, &c.-Since
the  temperature. of the  compressed
air when used is most always that
of the surrounding   atmosphere, the
result of the conduction of heat by the
contaiining vessels is the dissipation of
the total heat of compression. T'he mechanical equivalent of this heat is, of
course, lost work, and, as it is most
economical to get rid of this heat during
compression, conduction and radiation
from the compressor is an advantage.
Since, in working expansively, there is a
tendency for the cylinder to become
colder than surrounding bodies, the conduction and radiation of heat is here too,
if anything, an advantage.
In all our formulas and results hitherto
established, the cylinders have been sup



114


posed non-conducting; and the investigations of M. Mallard have shown that
this hypothesis is justified. For the heat
leaving the compressor by conduction
and radiation is in part compensated for
by that developed by the friction of the
piston; and the heat conducted through
the working cylinder is very small relatively to that converted into work.
Hence, any passage of heat by conduction of the cylinders belongs to those
secondary quantities which are always
omitted in the general theory of motors,
except so far as allowed for by proper
coefficients.
CHAPTER VIII.
AMERICAN   AND EUROPEAN    AIR-CoIMPRESSORS.
I.
PUMP COMPRESSORS.
Pump or plunger compressors are
generally in high repute in Germany and
Austria, especially in mines, and they




115


seem to give very satisfactory results.
In the United States they never have
been used to any considerable extent and
are now not at all used.
It must be said to the prejudice of
these compressors, that, in consequence
of the large mass of water to be pushed
back and forth by the plunger, a large
per-centum of power is wasted in overcoming inertia; that high piston speeds
are, in consequence of the violent shocks
which result, utterly impossible; that
they are very heavy and hence require
expensive foundations; that when the
prime mover is run at a high speed, a
more or less cumbrous, expensive, and
wasteful machinery of transmission is
necessary; that their use is limited, pressures of 5 or 6 atmospheres being their
utmost capability, on account of the
large quantity of cooling water taken up
by the air at even moderately high tensions; that a large amount of coolingwater is required to produce a comparatively small effect in the abstraction of
heat.




I [6


On the other hand, it must be admitted that these compressors are liable
to very few repairs, that they are simple
ji- constiruition. and that " dlead spaces
are avoided.
rrhe hydraulic or ram compressors
first used b)y Sommeiller at the Mt.
Cenis Turmel have become obsolete.
HI.
SI1N ("LE-ACTING WET COMPRESSORS.
The~ aII' compressors now used in the
UnitedI States are either-, -Dry Comupressors in which the cooling is effected by
floodinLgr the external of the cylinder, and
somnetitnes also the piston and piston-hiead
witli waiter-; Wet Compressors, by the injecti"Iil of water into the cyliIIder-slpaee,
as wed ais, 1y external floodingr; coinpressors with no cooling alrrangremneit are
sel~loini tiied, and only in tempor-ary and
cheap) plan~ts.
Coini r-essors with a partial injection
of water have been used to very,. good
effect in the United States. Most of




117


these are single-acting, and are represented by the machines of Burleigh, of
Fitchburgh, Mass. The cooling is very
efficient and hence the useful effect is
considerably increased. They are very
durable and not liable to get out of repair, as is shown by the record of Burleigh's machines, which have stood the
test of years of steady work.
The use of single-acting compressors
renders it necessary that, in all cases
where anything like a uniform supply of
air is needed, to have two compressorcylinders.  These  cannot be   driven
directly from the piston-rod of the
driving engine, but necessitate an indirectly coupled-connection of some sort.
All this makes single-acting compressors
somewhat cumbrous and expensive.
As built to-day, the evils of dead
spaces, and of jars and shocks resulting
from water in the cylinder, have not been
duly considered. There are also a few
cases when the sectional area of the
inlet-valves is insufficient; and in general those parts which are most liable to get
out of repair are most difficult of access.




118


We are inclined to think that the
claim of the Burleigh Co., that their
compressor is the most efficient, economical, and durable of any built in this
country, cannot be far from the truth.
III.
DOUBLE AND DIRECT-ACTING COMPRESSORS.
Up to within several years ago, singleacting compressors have been used
almost exclusively.  Now the double
and direct-acting compressor seems to
be superseding it. This is now the
leading type of American compressor,
although hitherto it has given at least no
better results than the best single-acting
machine.
Superiority in the double-acting compressor is found in its simplicity. The
piston of the engine drives the compressor by a direct connection. All wasteful
and cumbrous machinery of transmission
is at once unnecessary and high pistonspeeds are possible; in the United States
from five to seven feet.




119


Most American double and direct-acting compressors are of the dry kind.
These have the advantage that the air is
delivered without having any water
mechanically mixed with it.   Hence
very much ice cannot be formed when
the air is worked expansively. Higher
rates of expansion are possible than with
air from a wet compressor.
One of the very best American double
and direct-acting dry compressors is the
"National," built by Allison & Brannan,
Port Carbon, Pa., (Office, 95 Liberty St.,
N. Y.). Steam cylinders of the mediumsized duplex machine are 12 X 42", and
the air cylinders 15"X42".   The air
pistons work to within one sixteenth of
an inch of the cylinder heads.  The
water circulation. for cooling passes
spirally around the air cylinder from the
center to each end.  The engine will
compress air to the same pressure as that
of the steam used. The amount of free
air compressed at a piston speed of 350
feet is about 1000 cubic feet per minute.
A greater pressure of air than the press



120


ure of steam used is obtained by increasing the size of the steam cylinder, or
decreasing that of the air cylinder.
The best double and direct acting
compressor of the wet kind is undoubtedly that of Dubois-Francois, built in
Seraing, Belgium, and exhibited at the
Centennial Exposition, in 1 86.
Dry compressors, although the cheapest as regards first cost, are not the most
economical in working. But where air
is to be carried through pipes exposed to
great cold they are the only alternative.
IV.
DESIGN AND CONSTRUCTION.
The efforts of builders and engineers
should be directed to the attaining of a
higher efficiency, and they should not, as
is now often the case, sacrifice the latter
to cheapness and small dimensions. To
attain such desirable efficiency the heat
of compression must be more effectually
abstracted. This must be done by a
more ingenious and rapid circulation of




121


water around the cylinder, and injection of water in the form of spray into
the cylinder. But the injection of water
in some efficient and practical manner,
which is so essential to the reaching the
highest efficiency, introduces the great
disadvantage of having to work with
wet air. Hence we see how important
would be an invention of means or apparatus for separating the water from
the air when direct intercontact has
been had to keep down the temperature.
We must also remember the important
physical fact that water absorbs very
considerable volumes of air-volumes
dependent upon the pressure of the air
and the amount of surface of water exposed to the fluid contact, time being
also an important factor.
Clearance must be reduced to the
smallest possible amount. It has been
brought down in a few cases to 0.39
inch.  A  long stroke, one from 2 to
to 3 times the diameter of the cylinder,
is another means of avoiding loss from
dead spaces, since here the air which




1 22


fills the dead space is small in comparison with that actually delivered. The
valves must be so placed that, between
their seats and the piston-head at the
end of the stroke there shall be the
smallest possible clearance.
The valves themselves, to close the
more rapidly, are made to have only a
very small travel. (This has been made
as small as.08 to.12 inch.)     The
valve-area must be made large enough
by  increasing  the  number of    the
valves.  It should   be amply large,
generally from  - to -l of the sectional
area of the cylinder. The valves should
be so attached to the cylinder-head that
they may be removed and repaired without taking off the latter or otherwise
taking the machine apart.
Great care must be taken to have the
piston head fit the cylinder accurately
and closely, since, especially in dry compressors, great losses result from any
looseness. The piston-heads should be
made so that they can be adjusted to
preserve a nice fit, as in steam engine




123


practice. Lubrication of the cylinder in
case of the dry compressor should be
effected by automatic oil cups placed
upon it.
It must also be borne in mind that the
working pressure is that which most
influences the physical conditions of
working, and the suitable mode of construction.  And, although the loss of
work increases with the pressure, yet the
rate of variation of the loss of work
decreases as the pressure increases. As
great a proportion of work is lost by
increasing the pressure from two to three
atmospheres as by increasing it from
five to ten atmospheres.
The tendency in Germany and France,
as well as here, is for the wet compressor
entirely to supersede all others. But it
is scarcely too much to say that the
air-compressor of the future has yet to
be invented.




124


CHAPTER IX.
EXAMPLES FROM PRACTICE.
I.
The Republic Iron Company of Marquette, Mich., have done away with the
use of steam, by utilizing the power of.a
water-fall situated about a mile from
their works. The power is transmitted
by means of compressed air which drives
all their machinery, and thus saves the
cost of fuel.
There are four compressors, 24" diameter and 5/ stroke, driven by two turbine
Swain water-wheels 5W' diameter, under
16 feet head of water. As near as has
been ascertained, they have about 450
horse power at the wheels. The air is
carried one mile in a pipe built of boiler
iron, 15" inside diameter. About 66 per
cent. of the effective power of the wheels
is obtained at the mines and shops.




125


II.
ECONOMY PROMOTED BY THE USE OF
COMPRESSED AIR.
To show the great saving of both time
and money since the introduction of
compressed-air machinery we will give a
few figures.
It cost the Golden Star Mining Co., of
Sacramento $12 to $15 per foot to run a
tunnel 7 X 7 feet, when employing hand
labor; after introducing air machinery
it cost them  $6 to $7 per foot; with
hand labor they made a distance of two
feet per day; with machine labor, a distance of six feet per day.
Another instance, among many, is
that of the Sutro Tunnel Company of
Nevada;
Expense by hand labor per
month.................. $34,000 to $50,000
Expense by machine labor
per month................ $14,000 to $16,000
III.
COMPRESSED-AIR MOTOR STREET CAR.
The pneumatic engine which has been




126


on trial by the Second Avenue Railroad
Company, on the Harlem portion of their
road, from the Station at Ninety-Sixth
Street, to Harlem River, at One-Hundredand-Thirtieth Street, has proved so satisfactory to the company that it has authorized the construction of five more
engines.
These are to be used exclusively on
the upper part of the road, where it is
proposed to dispense entirely with the
use of horse power, so soon as the
requisite number of engines shall be procured. It was stated at the company's
office, that the most sanguine expectations had been fulfilled; the new
engine could be run at a trifling cost,
and without the noise and smoke and
smell of oil which accompany the use of
steam; any rate of speed which was
likely to be required could be maintained, and the engine was under as complete
control of the engineer as one propelled
by steam or a car drawn by horses.
The new engines are manufactured by
the Pneumatic Tramway Engine Com



127


pany, whose office is at No. 317 Broadway. Some time ago two Scotch engineers, Robert Hardie and J. James, invented a system of propelling cars by
means of compressed air. The invention
was examined by a number of practical
railroad men who were visiting Scotland.
Hardie and James were induced to visit
this country and the company was organized. Experiments have been making
for a year, resulting in improvements
which now seem likely to render the invention serviceable to the public. The
motive power is condensed air, contained
in two reservoirs, placed one under each
end of a car, which is similar in construction to those in ordinary use on
street railways. The air is pumped in by
a stationary engine at one hundred and
twenty-seventh street, and this has been
so far improved that the reservoirs in
the cars now used are filled in a few
minutes. These are of steel, and are
tested up to a strength many times
greater than their working pressure, and
it is claimed that there is no danger of




128


explosion. The machinery is simple and
not liable to get out of order. The airtanks of the experimental car are only
sufficiently large to enable it to make
one round trip   between Harlem   and
Ninety-Sixth Street stations; but the
cars now building will be larger and will
contain  reservoirs of  much   greater
capacity; and it is claimed that there
will be no difficulty in constructing them
so that the round trip from   Harlem
river to Peck Slip can be made without
replenishing.
Mr. Henry Bushnell, of New Haven, is
the inventor and constructor of another
new compressed air motor street car, the
chief peculiarity of which is that he is able,
as he says, to force air into his receivers
until his gauge registers the enormous
pressure of more than 3,000 pounds per
square inch. His receivers are tubes, the
largest of which are twenty feet long, and
only eight inches in diameter, inside measurement. There are four of these, two
lying side by side above the axles, and
next to the wheels on either side of the




129


car. Between them at one end are four
other tubes, each six feet long and six
inches in diameter, inside measurement.
The material is wrought iron threeeighths of an inch thick, and are welded
in. The double cylinder engine which
utilizes this air in turning the wheels of
the car does not differ materially from a
steam engine, except that its two cylinders are only two and three-fourths
inches in diameter, inside measurement.
The machine built by Mr. Bushnell to
compress the air consists of three steam
air pumps.   The first and largest is
merely a feeder to the second. The air
that comes from it is condensed to a
pressure of about six pounds. This denser air is more worthy the prowess of
the second pump, which in turn crushes
it into a greatly smaller compass. The
third pump gives the final pressure.
The gauge on the compressing machine
has registered 3,500 pounds per square
inch. The plungers of the second and
third pumps have no heads. They are
merely rods of steel forced into vessels




130


containing oil. As the plungers move
out and in, the surface of the oil falls
and rises, admitting the air through one
valve and forcing it out of another. It
is, therefore, necessary to have the packing of the plungers only oil tight, not air
tight, tinder the tremendous pressure.
The chamber that first receives the air
from the third pump is cooled by
a covering of cotton waste saturated
with water. On the other hand, the expansion of the air as it is given off at
each half revolution of the car engines
absorbs heat, and after running the car
for a short time the engine cylinders and
escape pipes are whitened with frost.
To remedy this Mr. Bushnell will surround the cylinders with stout metal
jackets, beneath which he will force air
with the aid of a small pump geared to
the machinery of the car. This newlycompressed air, he says, will supply heat
enough to keep the cylinders warm.
The writer rode recently on the new
car as far on the Whitneyville road as
Mr. Bushnell could go without interfer



131


ing with the trips of the horse cars. The
motion was easy, and at times about
twice as rapid as that of a horse car.
The new vehicle obeyed the engineer
promptly in starting and stopping. The
distance traveled in going and returning
was a little over a mile. At the start
the guage registered 1,800 pounds. At
the return the pressure indicated was
1,500 pounds. When the air was allowed to escape from a turned cock the
roar was frightful and was as irritating
to the ear as escaping steam. In running, however, very little noise is heard
from the escape-pipe, because the escaping air is made to pass through a
mass of ordinary curled hair. This device
Mr. Bushnell esteems one of the most
important of his inventions. He has no
doubt that it would prove equally efficacious in deadening the sound of escaping
steam.
Friends of Mr. Bushnell claim that he
could never make a receiver capable of
retaining air at the high pressure he had
in view. The air that was in the tubes




132


was pumped in, he says, on the 25th of
June. The gauge then showed 2,100
pounds. The pressure gradually lessened
until it was ],900. After that time a
small leak was discovered. This leak
was closed with a turn of the wrench,
and after that not a pound was lost up
to the trial, when 100 pounds was
allowed to blow off to gratify the curiosity of visitors just previous to the
short trip referred to.
Mr. Bushnell called attention to the
small diameters of his largest tubes.
He said that a pressure of 2,000 pounds
per square inch would give, by calculation on the head of each tube, an aggregate pressure of fifty tons; while the
two-feet heads used by the inventor of a
rival compressed air motor would have
to withstand an aggregate pressure of
180 tons, if a pressure of 800 pounds per
square inch should be put on, as the inventor claimed was possible. The heads
were necessarily the weakest parts of the
tubes. A welded joint, such as his were,
was usually reckoned twice as strong as
a riveted one.




133
On a previous occasion Mr. Bushnell
made a round trip on his car on the
Whitneyville road, a distance of a little
over four miles. The pressure was then
reduced from 1,950 pounds at the start
to 750 pounds on the return. A company called the United States Motor
Power Company has been formed, and
Mr. Bushnell is its president.




I




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BELL. CHEMICAL 1PHIENOMEN_,A  OF  IRON
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JANNETTAZ. A GUIDE TO THE DETERMINATION
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MOTT. A PRACTICAL TRE ATISE ON CHEMISTRY
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