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RESEARCHESIN THERMUUYNAMICS

THESIS FOR DEGREE OF M: S.

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ERROL E. EMSHWILLER

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A Thesis on

BESEARCHD§ IN THERMODYNANICS

submitted to
The Department of Mechanical Engineering
(Professor H. B. Dirke)

and

The Department of Graduate werk
(Dr. Re 0. match)
Michigan state College
East Lansing.
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by

,f 1r

    

Errol E§"Emehliller
‘1?
Candidate for Degree of Master of Science
in Mechanical Engineering

June 4, 19280

PREFACE

The author, in taking graduate work in the power
production side of Mechanical Engineering, and especially
in the Thermodynamic and Engine Design divisions of said
power production, felt the necessity of getting a more
thorough understanding of the power-producing methods and
machines used and practically or theoretically capable of
being used, than can be obtained in the ordinary under-
graduate studies in Thermodynamics, Heat Engines,
Automotive Design, etc; and some of the main points brought
out by his studies towards getting this understanding are
set down in this thesis. Most of the graduate work taken
being along the lines of the relations between Heat and
other forms of Energy, and Mechanical Work, this thesis
gives the results of, and is entitled "Researches in Thermo-
dynamics."

An appreciation must be herewith expressed of the
valuable teaching and aid of Professors Dirks and Reuling
of the Mechanical Engineering Department, Professor Fields
of the Drawing Department, Professor Ewing of the Chemistry

Department, and'many others who have assisted in the
‘ preparation of this work.
--E.E.E.
313 Rapids, Michigan.
June, 1928

36059

CHAPTER I
THE TRANSFORMATION OF
HEAT ENERGY INTO MECHANICAL WGlK,

AND VICE VERSA

Energy, which is defined in Physics as the power to do work,
has several forms, including heat energy, mechanical energy,
electrical energy, chemical energy, etc. we are here concerned
with only the mechanical and heat forms of energy, neglecting the
other forms in which energy appears except as is necessary for
illustrating, aiding in, or bringing about, the transformation
of heat energy into work, and mechanical work into heat.

‘Work equals force 1 space.

" " force per unit area 3 area 2 distance.

" " unit pressure x area 1 depth-

“ " pressure x volume.

Thus we have work, or applied energy, as the product of two
factors; one an intensity factor, force or pressure; and the
other a distribution factor, distance or volume. So practically
all forms of energy may be resolved into two factors, one of
intensity and one of distribution. For instance, electrical
energy may be considered, and graphically represented, as the
product of voltage, the intensity factor, and ampere hours, the
distribution factor. Heat energy may be thus represented as the
product of an intensity factor, temperature, and a distribution

factor, which is known as entropy. Entropy was formerly called

the thermodynamic factor, but the shorter appellation "entropy,"

/’

 

 

-2-

from a Greek word meaning unknown or mystery, was applied to it and
the name is now generally accepted.

There is a definite relationship between heat energy and
mechanical work, this relation being that 1 British thermal unit of
heat equals practically 778 foot-pounds of mechanical work.
Corresponding to the law of conservation of matter is the law of
conservation of energy which states that the quantity of energy in
the universe is fixed. The thermodynamic expression of this fact
is that heat energy may be transformed into work energy, and vice
versa; in other words, that no energy is ever destroyed, its form
is simply changed. This is the first law of thermodynamics, which
is expressed in symbols by the equation:

JQ equals U2 6 U1 plus‘w,
or, in words, the quantity of heat added to a system goes to
increasing the internal energy of the system or to doing external
work.

It will be noticed, however, that this last statement and
equation did not state that all the heat added to a system went to
do mechanical work. The statement of this fact is the second law
of thermodynamics, that energy tends always to change to a degraded
form, that there is a degradation as well as a conservation of
energy. Work energy is high-grade energy, electrical and similar
energies are likewise high-grade, but heat energy is low grade;
consequently, work or electrical energy may all be transformed
into heat, but not all the heat in a system may be transformed
into work. A preportion of the heat remains heat, as unavailable

heat energy.

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The efficiency of any transformation of heat into work depends,
of course, on this remainder of unchanged energy. As the work done
can be shown by an area on the Force-Space or Pressure-Volume planes,
so the heat transformed into work may be represented graphically
on the Temperature-Entropy plane; and, if the plane is extended
far enough to show the amount of heat available to the system
studied, the preportion of heat transformed into work to heat
supplied to the system--in other words, the thermal efficiency--
may be shown.

The transformation of heat energy into mechanical work requires
a medium.by which the transformation may be brought about, which
medium is called the working medium and may be any substance which
is affected as regards dimensions by the addition or subtraction
of heat; and a mechanical contrivance, as well, is required to
assist in, and make use of, the transformation, which mechanical
contrivance belongs to the class of heat engines. These have
almost unnumbered forms, and but a few of the possible forms at
that, have been constructed. There are practically no devices made
to produce heat from work for the sake of the heat produced,
although all forms of brakes and friction involve a transformation
of work energy into another form, usually heat; but devices, called
refrigerating machines, are used where work is used to extract
heat from a system, or rather the work assists in the process of

heat extraction.

Working mediums, as stated before, may be anything having a
dimensional change with the addition or subtraction of heat. First

considering solid substances, as for instance the common metals,

-4-

with definite coefficients of expansion with temperature changes,
it is quite evident that a steel object with its hard surface
resistant to pressure will do work if it expands against pressure
with the addition of heat. By giving the metal object a certain
shape and a mechanical contrivance to assist it, a larger pro-
portion of work than the preportion secured from the simpler form
of solid-expansion engine, may be got from the expansion of the
metal. Of course, some solid substances shrink with increase of
heat-~at least between certain temperature limits; but it is not
difficult to see how this property can be utilized in a heat
engine as well as the expansion of the other substances.

It is, of course, perfectly possible to have a heat engine
operating by the expansion of liquids as liquids, but the effi-
ciencies to be obtained from most liquids are not such as would
encourage the building of such engines, even just for laboratory
specimens.

When we pass from liquids to vapors, however, we enter the
field of great thermodynamic usefulness. The ability of vapors to
expand with added heat against high pressures makes them valuable
for the transformation of heat into work. Vapors are formed from
the liquid state, usually, and do not approach the condition of
perfect gases ordinarily until well beyond the vaporization point.
One trouble with vapors is that those most used and most available
require the addition of a great amount of heat to the liquid before
the substance is completely vaporized. This heat is practically all
unavailable below the amount needed to vaporize the liquid at the

lowest pressure applied in the heat engine. The efficiency of the

transformation may be and is being increased by raising the pressure

-5-

limits under which the heat engine operates.

Water vapor (steam) and mercury vapor are the most
common vapors in use; and, of the two, water vapor is by far
the more used, having the advantage over other vapors on both
commercial and available grounds.

A mixture of vapor and liquid is called wet saturated
vapor; the temperature remains constant with constant pressure
until enough heat has been added to vaporize all the liquid
present, when dry saturated vapor is secured. Further heating
at constant pressure raises the temperature and produces a
superheated vapor. Of course, the entropy increases with all
these additions of heat. The peculiarity of a vapor is that
its pressure, volume, and temperature are not mutually fixed
and interdependent as with gases; but that the quality-uper
cent by weight of vapor in the mixture of liquid and vapor-—
in saturated vapors, or the degree of superheat--number of
degrees on the temperature scale above the vaporization
temperature corresponding to the pressure-~of superheated
vapors must also be taken into account. These peculiarities
of vapors have made large sets of tables and complicated
charts showing the relations between the quantity of heat
that has been added to the vapor above a certain point--
usually the condition of the liquid at a temperature of
32 degrees Fahrenheit and zero pressure--, the entropy change
above that point, the pressure, the temperature, the density
and conversely the volume per unit mass, etc. necessary to
avoid repetition of difficult experiments and the use of

cumbersome computations.

-5-

Gases are likewise very valuable and much used in heat
engines. In the use of gases, there are two methods depending
on whether the gas is combustible or not. Air and other
non-combustible gases must be heated from an outside source.
Combustible gases are heated by their own combustion. Gases
may exist as gases before introduction into the heat engine
or may be formed from.vaporized liquid upon entrance into
the engine.

A perfect gas, that is a perfectly elastic gas, which
does not exist in fact but which is very closely approximated
by air and other common gases, follows the law that the
product of the pressure times the volume equals the weight
times a constant times the absolute temperature; expressed
symbolically this becomes the equation:

PV equals MBT.

Where P equals pressure in pounds per square foot,

V " volume in square feet, .

M " the molecular weight in pounds,

and T " the absolute temperature in degrees Fahrenheit,

the constant B equals 1544 for all gases. From this the value
of B for any given weight of gas may be computed. Air, while
not a compound, may be assigned a molecular weight by taking
air as a mixture of 77 parts by volume of nitrogen, N2, with
a molecular weight of 28 and 23 parts of Oxygen, 02, molecular
weight 32, and finding the average molecular weight of the
mixture. This gives

77 x 28 equals 2156

23x52 " __'_I_§_e__
100 1 average molecular weight " 2892
Molecular weight of air " 28.92

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n7.-

Value of B for air where M equals 1 pound equals 1544
divided by 28.92 equals 53.4. The same procedure may be
followed in other cases.

From the above statements it is evident that the deter-
mination of any two of the three conditions or qualities,
pressure, volume, and temperature, governing a gas decides
the third condition or quality; that is, the pressure is
dependent only on the volume and temperature for a given
.weight, and so on. Other ways of stating the same thing are
Boyle's Law, "If the temperature is kept constant, the
volume of a given weight of gas varies inversely as the
pressure,” and Charles‘ Law, "The increase of pressure when
the gas is heated at constant volume is proportional to the
increase of temperature." Expressed by symbols Boyle's Law
becomes:

PV equals C, or

equals sz " P V equals - - -.

Plvl 2 3 3

and Charles' Law is:

P - Po equals K(T - To).
Charles' Law plotted on rectangular graph paper indicates
that there is a point at which the pressure becomes zero
when the temperature reaches said point, and this locates
the absolute zero of temperature, or zero on the gas scale,
which zero is 460 degrees below zero Fahrenheit; so that
460 degrees must be added to the Fahrenheit readings to

obtain absolute temperatures or temperatures on the gas

scale. This leads to still another form of the statement

I,

 

 

 

 

~8-

of the relation betweenthe three coordinates defining the

state of a gas, that is, that expressed as an equation,

PV PV P'V‘
‘T equals K, or TV equals T" .

Where but one unit of weight of gas is considered, it may be
seen that this is the same as
PV equals BT, B equaling the constant K,
or for M units of weight, we again reach the expression
PV equals MET.

Gases are rather seldom.simp1e compounds, but are
usually mixtures in which the relations between the pressure,
volume, and temperature must be determined by methods similar
to that used in figuring out the value of B for air. That
is, the average quality, whether it be molecular weight,
.specific heat, density, or what not, must be taken from.the
proportions of the various compounds or elements present in
the gaseous mixture; and computations are then made using
this average quality. Whether the quality refers to volume,
as in the case of molecular weights, or to weight, as in
the case of specific heats, determines whether the proportions
of the constituent compounds are to be taken by volume or by
weight.

In computations dealing with the products of the comp
bustion of combustible gases, the question of mixtures looms
large; for there is, besides the compounds of oxygen with
carbon, hydrogen, sulphur, etc., the nitrogen of the atmosphere
that is admitted with the oxygen required for combustion and

-9-

also in most cases an excess of air of from 10 to 100%
necessary to insure complete oxidation.

One difficulty with combustible gases used in heat
engines has been that the temperatures produced have been so
high that the metal of the mechanical device has been weakened
or destroyed by the heat unless means were taken to carry
away some of the heat, which was thereby rendered useless for
producing work. The best metal now produced can not stand
constant exposure to the high temperatures of the uncooled
combustible-gas heat engine.

- However, the maximum temperatures obtainable from gaseous
combustion have not been as high as were originally calculated
from the heats of combustion of the different gases and
elements, determined experimentally by various kinds of
calorimetry. This is because in making these original
calculations it was assumed that:

The specific heats of the gases evolved remained
constant, whereas they increase greatly in value with
high temperatures.

No heat was supposed to be lost during the
combustion process, whereas, in reality a great deal
of heat energy is lost by radiation and conduction
during combustion.

The process of combustion was carried to

_completion; while, in fact, especially at high

temperatures, there is dissociation of the pro-

ducts of combustion back into the original elements

or compounds, or into others.

 

 

 

 

-10—

The first two false assumptions were strictly thermo—
dynamic errors; but chemistry had an important part to play
in correcting the third. ‘In any chemical reaction-~and
combustion is, of course, and essentially, a chemical
reaction-~there is an action proceeding each way, but with
most reactions at ordinary pressures and temperatures the
force driving one phase or action is insignificant compared
to the force driving the opposite action, and the reaction
goes to practical completion in the direction of the over-
whelmingly larger driving force. But the relations between
these driving forces change with the temperature so that a
point or temperature is reached where the opposing forces
Just balance each other; and the reaction halts. A con~
dition of chemical equilibrium has been established and
complete combustion is prevented. This condition of
equilibrium.is determined by the partial pressures of each
of the substances in the mixture at the time of reaching
the equilibrium. For instance in the combustion of carbon
monoxide, CO, to form.002, a constant K.p equals P'002

 

(p.co)(p.02)%
called the equilibrium constant, represents the product

of the partial pressures of the products of reaction
divided by the product of the partial pressures of the re-
acting substances, each partial pressure having an exponent
equal to the coefficient applied to the substance to Which
the partial pressure relates, the equation for the reaction

mentioned being: CO plus % 2 equals 00 This is the same

2.
as the chemical equilibrium.obtained in a solution when the

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concentrations of the resultant compounds divided by the
concentrations of the reacting compounds equals a constant K.

The Law of Mass Action to the effect that the speed or rate

 

of any chemical change is proportional to the active masgL

 

that is, the molecular concentration of each substance engaged

in the reaction, which holds for all chemical reactions,

 

whether reversible or not, is the basic statement from which
those relating to the equilibrium constant are derived. The
values of K and KP are always constant at a given pressure
and temperature when the condition of equilibrium is reached.
By very lengthy equations involving the heats of combustion,
the intrinsic energies, and the thermal potentials above the
standard conditions of 32 degrees F. and atmospheric pressure,
Goodenough and Felbeck arrive at a relation between the
values of Kp’ for each of several combustion processes, and
the temperature. Having this, the direction in which the
reaction will progress at any given temperature can be
determined; and the temperature at whichthe state of
equilibriumfis reached may be calculated. This is theoret-
ically the maximum temperature attainable, and may be
reached with rich mixtures of fuel and air and rapid comp
bustion; but can-hardly be obtained with thin mixtures and
slow'burning.

To boost this maximum temperature and with it the
pressure and thermal efficiency-~at least, theoretically to

boost the efficiency-~a means must be found of keeping down

the concentration of the products of combustion, thereby

-1a-

causing the reaction to proceed further towards completion
in an attempt to maintain the value of the constant Kb at
the point it attains at equilibrium. In gaseous combustion
this means decreasing the partial pressure of the product
of combustion. This can be done by adding some element or
compound that will combine with the products of combustion
in such a manner as to prevent the reaction from proceeding
backwards. That is, the new compounds formed must have no
tendency to return to the original states, or at least

must have a much slighter tendency to revert than the
common products of combustion.

Mixtures of gas and vapor, such as atmospheric air,
damp gas, etc. furnish problems combining the features of
both vapor problems and gas problems; and such mixtures are
becoming increasingly important with the adeption of the
system of keeping the temperature down in gas engines by
spraying water in with the hot gases. In the case of the
atmosphere, the amount of water vapor is so small, comp
paratively, that it may be neglected in ordinary heat
engine computations; although it must be figured on quite
closely in problems concerning heating and ventilation,
where relative humidity is important. For close work, the
temperature of the air must be taken, and then a reading
taken of the temperature of‘a wick soaked in water and
circulated freely in the air. An instrument called the sling
psychrometer is made to take both these temperatures simul-

taneously, and from this pair of temperatures, the relative

~13—

humidity may be found by reference to charts Which have

been formulated, or by the use of Carrier's Formula:

e equals e' - (P -e'2 (t - t|2 , where

t equals dry—bulb temperature in degrees F

t' " wet-bulb temperature in degrees F
e' " vapor pressure in #/0' corresponding to t'
e " vapor pressure in #/0" corresponding to to,

the dew point, and
P equals barometric pressure in pounds per sq. in.

The steam in the air is always dry saturated or superheated
except when actual condensation in the form of rain, mist,
dew, etc. is occurring, for at the low partial pressure of
the water vapor in the atmosphere, the boiling point, or
perhaps more correctly stated, the vaporization point is
below ordinary temperatures. When the vapor pressure rises
with an excess of moisture, or the temperature of the air
falls below the vaporization point, part of the water in
the air condenses as one of familiar forms of rain, snow,
etc. The wet-bulb temperature never falls quite to the
dew point, however, if the air is at all above saturation
temperature due to conduction of heat away from the cold
bulb by the warmer air.

The preportions of gas and vapor in a mixture are made
manifest through partial pressures. Dalton's Law, that
the pressure of the mixture is the sum of the pressures of
the constituents, gives a basis for comparing pressures;

and, if an idea can be obtained of the degree of superheat,

—1 4-.

or the quality, of the vapor or of the composition of the
gas, the remaining weights, volumes, or preportions may

be secured easily. Should the exact composition or qualities
not be obtainable, an estimate of partial pressures may be
made from the weight of the constituents and the mixtures.

By the use, then, of gas constants for the ingredients and
the mixture as a whole, accurate enough results may be
obtained for ordinary heat-engine work involving gas-vapor
mixtures.

'The Thermal Efficiency of Heat Engines for any and all
working mediums is limited to that of what is called the.
Carnot Cycle, which is expansion at constant temperature,
further expansion at constant entropy, compression at
constant temperature, and compression at constant entropy
back to the starting point. Many proofs are given that
there can be no cycle of greater thermal efficiency than
this one, but one of the simplest and most sufficient is
that furnished by the temperature-entropy diagram, on which
the cycle named is a rectangle bounded on top and bottom
by constant temperature lines and on the sides by constant
entropy lines. »The area beneath this rectangle is unavail-
able energy. Since a rectangle possesses the maximum
volume possible between two straight parallel lines, it
is plainly seen that the Carnot cycle represents the most
heat converted into work between any two given temperatures

or between any two given entrepies.

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-15-

Likewise it can be seen upon further investigation of
the diagram that this represents the most heat put into the
system, represented by the area under the upper constant
temperature line, and the largest prOportion of that taken
out between the temperatures fixed by the Operating con-
ditions; therefore the Carnot cycle is the most efficient
thermally, between any given temperature limits, of all
possible cycles.

The point of absolute zero entropy evidently lies at
negative infinity as far as regards the range of temperatures
with which we have to deal; so, entrOpy having an infinitely
large value at any point we have occasion to consider in
heat engine operation and design, we select for it an
arbitrary starting point, usually the liquid line of water
at zero pressure and 52 us rees F. The energy head or
thermal potential of a working substance, representing the
energy in work and heat required to bring it (the working
substance) to a given point or condition is likewise taken
from an arbitrary zero, at 52 degrees F. and zero or
atmospheric pressure usually. This is represented by the
symbol 1, while entropy is variously represented by ¢, N,
or S, the latter of which will oe used here. Expanding
gases have different specific heats, also, according to the
line they follow in expansion, while there is another
Specific heat for the increase of temperature without expan-
sion. For gases whose molecules consist of single atoms the
ratio between the specific heat at constant pressure and
that at constant volume, Cp/Cv, equals 1 2/5 or 1.67; for

diatomic gases it is approximately :1 2/5 or 1.40; and for

-15-

triatomic gases it is about 1 2/7 or 1.28. For air, for
instance, which is a mixture of two diatomic gases, oxygen
and nitrogen, Cp equals .242, and Cv equals .175, and
“242/,173 equals 1.40 approximately, although of course the
values of the specific heats vary slightly with the tempera-
tures. Other terms used in connection with working mediums
are: change in intrinsic energy, V2 - V1, which relates to
the energy which the medium has stored within it; external
work, which represents the work, W, done on or by the
substance in reaching a certain state or condition from
another state or condition; and quantity of heat added or
abstracted, Q if measured in B.t.u. or JQ if considered as
foot-pounds, which is practically equal to the thermal
potential 1 when both are considered above the same zero,
except that i includes the work energy necessary to put the
working medium into the heat engine equipment and Q includes
only the heat and other energy added to it after it (the
working substance) gets into the heat engine equipment. There
are other coefficients connected with the working mediums,
such as the amount of heat required to raise the pressure
one unit at constant volume and again at constant tempera-
ture, etc.; but problems necessitating the use of such

constants are more rare than those requiring C and Cv and

P
K equals Cp/Cv : so they are not discussed further here,
except to say that such problems are probably more readily
solved from the tables or charts than from the use of con-
stants which vary widely as other conditions vary.

The first practicable heat engine made use of water-

vapor or steam as the working medium, and steam still does

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-17—

more work than all other working substances together that'

are used in mechanical heat engines. The great drawback to
steam has been that mentioned in connection with vapors as
working mediums, namely, the tremendous heat of evaporation
required to change the small volume of liquid (water) to the
large volume of vapor (steam). This is being escaped from

in the upper pressure ranges by running near the critical
temperature and pressure at which the change from water to
steam is accomplished with zero heat of evaporation. On the
other end of the Pressure scale, the back pressures and
temperatures are being reduced to as low a value as practicable
by means of condensers, etc.; but, even at low pressures, there
is a great deal of heat of evaporation left in the steam which
is rendered unavailable. The reciprocating steam—engine to
allow complete expansion of the steam would have to be of

such tremendous size and run with such great speed, with con-
sequent large floor space and cost and maximum vibration,

that the remedy is sought in the turbine, which is intrin-
sically less efficient than the engine, because of having to
make two changes in the form of the heat energy of the stean--
heat or pressure energy to kinetic energy in the steam and
from that to mechanical work on the turbine blades-~instead

of just the transformation from heat energy to work, as in

the piston engine. To get around the disadvantages of both,

a rotary engine has been long sought for, over 2200 patents
having been granted in the United States on inventions
relating to rotary engines; but the foe of efficiency and
economy in these engines has been excessive leakage, which

no one has yet been able to get around. If this trouble can

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be overcome, there seems to be considerable of an opening
for this type of heat engine.

Gas engines suffer most from excessive heating, the
combustion temperatures rising beyond the strength limit of
the metals available unless cooling is carried on with loss
of heat and otherwise available energy by the cooling medium;
that is, available energy is rendered unavailable by being
carried away in the cooling substance. At that, gas engines
show the highest efficiencies of any heat engines at the
present time.

The type of gas engine now used is the internal com-
bustion class, he old "hot-air" and similar gas engines
Operating on a medium heated by outside heat having to give
way before the higher efficiencies and greater power for the
size and weight, of the engines operating on a medium expand-
ing due to the heat of its own combustion.

In America, the gas turbine is yet regarded as purely
a theoretical possibility; but in Germany, Hans Holzworth,
chief engineer of Thyssen and Company, of Mulheim, has
' designed at least three practical gas and oil turbines and
is working on a fourth, one of 10,000 K.W. capacity at
1500 r.p.m. The thermal efficiency he obtains is low,
compared to gas engines and good steam installations; but
the cost of the plant, the maintenance, and Operating
charges are so low as compared with the other styles of
installations that the commercial efficiency is yet higher
than steam turbines or steam or gas engines, in spite of

‘the higher thermal efficiencies of the latter.

F\

-19-

QUESTIONS AND AN WERS 0N GAS TURBINES

The discussion of Gas Turbines being really a discussion
of the questions that may arise concerning their economy,
efficiency, and practicability, in this report of findings,
said findings are given as the answers t9 a tabulated list
of questions concerning the various features of design,
operation, and efficiency of gas turbines.

First are given a list of questions (and the findings
thereon) concerning which is the better of two, three, or
more choices of design or method of operation; then there is
the summation question as to whether or not the operation
of gas turbines pays under the most favorable general con—
ditions, and the findings in answer to that question and
giving the conclusions to be drawn.

The questions are numbered in order and each one is
fully stated before the report of findings is made; so there

is no doubt as to the matter being investigated and discussed.

Question I.
which is the better?

1. Explosion type turbines with consequent change in the
velocity of the impinging gases and hence lowered blade
efficiency, or
2. Constant-pressure type turbines with high and constant
temperature requiring either the addition of cooling gas or
vapor, pre-cooling of the gases, or special materials in the
turbine parts?

Answer

While the majority of designers prefer the constant-

f.

 

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pressure type, the most successful installations existing at
present, those designed by Hans Holzworth, chief engineer of
Thyssen & Company, Hulheim, Germany, are of the explosion
type.

The explosion type calls for a large amount of negative
work in cooling and scavenging the combustion chamber, but
the constant-pressure turbine demands likewise considerable
negative work in forcing the air and fuel into the chamber
against the high pressure necessary to satisfactory com-
bustion._ Of course, in the explosion-type the charge must
be compressed, too; but the compression takes place before
the explosion and therefore at a lower pressure than com-
bustion pressure.

The explosion-type offers as its chief advantage its
use of the gases without the great immediate dilution with
a cooling medium common to most constant-pressure turbines;
although the explosion-type has cooling and scavenging fluid
put through its chamber between explosions. A high prOportion
of the energy in the exploded gas is then absorbed by the
turbine rotors; and, since the jet of high temperature gas
impinges on the blades for but a small fraction of the time,
the blading does not become heated to a dangerous degree as
it would in a constant-pressure high-temperature jet. The
disadvantages of the explosion type are the variation in
the velocity of the discharged gases, making it necessary to
fall short of maximum absorption of the kinetic energy of
the jet except for very short periods just after each explo—

sion; the mechanical difficulties in getting the chamber

-21-

charged and ignited at just the preper time; the vibratory
effect; and the amount of negative work necessary to scavenge
and cool the chambers between explosions. Difficulty has
been experienced in getting the explosion at just the right
time, the ignition occasionally being delayed by causes not
yet thoroughly understood, resulting in a heavy explosion

and improper combustion, emission of smoke, etc. Holzworth's
turbines, however, have not shown much tendency towards

this defect of function; and he seems to have pretty nearly
overcome the difficulty.

The big advantage of the constant-pressure type, of
course, lies in the constant pressure and hence constant
velocity of the jet allowing the blading to be so designed
as to secure the maximum.absorpticn of the kinetic energy
of the gas stream. Theoretically, the constant high
“temperature should offer the advantage of high thermal
efficiency, according to the formula:

Effy. equals T1 - T2 ,
but the temperature of the undilutgd product of combustion,
sometimes above 5000 degrees F., is too high for constant
play upon any blading metal which is really suitable and
economical. Quartz has been used, but is brittle and
expensive; and no available metals retain any strength even
should they retain their form at such high temperatures.
From this fact arises one of the disadvantages of the constant~
pressure turbine, the necessity for cooling the product of
combustion before it can be used, thereby reducing the

m era ure 338.1158 I1 '1 rma e .L nc* 1111 81" Willc 1'16
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machine Operates. Other disadvantages are the amount of
negative work required to charge the combustion chamber
against the combustion pressure; the amount of negative
work required to add the cooling fluid-~if one is used--
against combustion pressure; the loss of heat energy by
radiation if the discharged gases from the chamber are
surface cooled; and the loss of expansive power in the
addition of a non-combustible diluent.

It will be seen that both types have their disadvan—
tages, and plenty of them. In an attempt to escape as many
of these drawbacks as possible, turbines that are rather
combinations of the two types have been designed. One
Operates on the principle of the gas first expanding on
explosion, and then contracting due to the union of the
hydrogen in the gas with the ox*gen in the air to form
water. This contraction produces a vacuum which draws a
fresh charge into the chamber which is still hot enough to
ignite the gas. Explosions occur at the rate of 3500 to
5000 per minute, giving practically continuous flow, but
the turbine as at present designed operates without comp
pression, and hence its combustion efficiency is low. But
plenty of data is on hand for work upon the gas turbine as
regards chemical, thermal, and thermodynamic possibilities,
and only mechanical obstacles appear in the way of the
devising of a turbine with a maximum of the advantages of
both the eXplosion and the constant-pressure types and a
minimum of their disadvantages. Such a turbine probably

will combine also the structural details of both types.

-23-

Question II.
. Which is better? .

1. To attempt to use the high temperatures of richly-mixed
fuel to secure a high thermal efficiency by the employmt
of heat-resisting casings and bladings, without any cooling
of the products of combustion other than by doing mechanical
work,
- 2. To attempt to use the high temperatures of the fired gem
and air to expand cooling gas or vapor (air or steam) mixed
with the products of combustion and make this expended
cooling material assist in the mechanical work of the
products of combustion by adding to the volume of said
products in the direct mixture, or _ o
3. To attempt to make the cooling gas or vapor-n-after
surface-cooling the fired gas-~dc work in an auxiliary to
the main unit that is cperated by the combustion products?

Answer. _

It is almost out of the question to attempt to build
the casing and blading of materials that can withstand a _
continuous blast of gas burned with littleor no excess air.
Such materials as would withstand temperatures sohigh
either lack therequisite strength for parts of such a V
hard-worked engine as a turbine or cost too much, or have:
both these disadvantages.

The other two methods of Operation have much its
advantages and disadvantages, and both have been used in
gas turbines that have functioned with more or less success.
or course, if one wishes to look at it that way, an explosion

-24-

type turbine is really one employing a diluent, the scavenging
air, sometimes mixed with steam, to reduce the mean temperature
of the combustion products; only in the explosion type the

exit velocity varies, as does the pressure and the composition
of the discharging fluids from the combustion chamber.

The use of a direct mixture of diluent and combustion
products necessitates a greatly increased amount of negative
work to put the increased quantity of fluid into a. chamber,
unless water is sprayed in from a nozzle or atomizer while
still in lipid form, in which case there is the resultant
high loss due to the latent heat of vaporization of water.
Unless the turbine is fitted with an exhauster or other
device for reducing the pressure below atmospheric on the
exhaust, the pressure range is _mch reduced, and the thermal
efficiency is greatly lessened. The use of the direct
mixture in a constant-pressure turbine is, however, probably
the simplest form of gas turbine capable of practical
operation. _ ..

An auxiliary unit, operated by surface radiated-and . _
conducted heat from the main gas turbine combustion chamber,
in effect Just another turbine, operating with a working
fluid heated by external means; and this auxiliary unit is
subject to the same laws as any simple turbine of the type
to which it belongs. 80 this unit usually is an ordinary
steam turbine of a typeoand design best suited to conditions
imposed by the location, size desired, and other factors
not particularly affected by the main unit itself. The
chief objection to this auxiliary unit to the gas turbine

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is that it at least doubles the complication of the engine;
and, if it is a steam unit expected to operate at near
maximum efficiency-~and a steam unit, of course, has advan- .
tages here as elsewhere over hot-air engines, mercury turbines,
etc.-, a condenser and other equipment met be added which
will increase the space required and the complicated nature
of the mechanism considerably. This naturally obviates the
consideration of this system as applied to any but large
units.
Question III.

lhich is better?
1. The doing of a large amount of negative work before
combustion by high compression before admission of the
fuel and air to the combustion chamber, .
2. Admission of air and fuel at low pressures, and Operation
by the power unit at low pressures, or
3. Admission of air and fuel at low pressures into chambers
where it can be heated to higher pressures by the heat of
combustion in adjacent chambers, by regeneration from the
hot exhaust gases, or by coming into contact with hot
fired gases just before combustion?

Answer.

leither in theory nor in practice has low-pressure
combustion proved efficient. Combustion is poor, and the
thermal efficiency is low. High-from 35 to 600 pounds per
sq. in. , depending on the fuel, etc.--pressures must be
obtained in some manner; and the simplest way is by com-
pressing the gas and air to the desired pressure before

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,mttmg 11: to the combustion chamber, although this
necessitates the doing of a large amount of negative work.
In cases where the turbine and compressor efficiencies are
both low, and a high compression pressure compared to the.
mean explosion pressure is required, the amount of negative
work may equal or exceed the‘amount of positive work, and
the turbine produce no work, or even require extra work to
enable it to Operate. , _ .

The mechanical difficulties necessary to obtain mick
heating of air compressed to a medium pressure, by surface.
contact with the walls of the adjoining combustion» chamber,
would be great, as they would obtain the heating from the
exhaust gases or from direct contact with fired gas without
seriously decreasing the pressure of the freshly-fired gas.
By a suitable arrangement of chambers and valves, the
arrangements could be made for heating in any one of the
manners suggested; but the greater problems arise in .
obtaining the heat interchange in the short time necessary
in order to keep up the supply of combus tibles, and in
doing this without affecting too web the pressure in the
combustion chambers. Ihether the cost and complication of
the extra mechanical equipment required for this raising A
the entrance pressure by preheating after medium compression
would be repaid in the increased efficiency over a simple
compressor is a problem that would have to be solved by
direct, painstaking, and well-continued experiment.

Question IV.

which is better?
1. The use of exhaust gases emerging around atmospheric

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pressures to heat gas or vapor (air or steam) for running
auxiliaries, f
2. The use of exhaust gases emerging at atmospheric pressure
to heat incoming air and fuel to produce higher pressure and
better combustion, or
3. The use of an exhauster or some other device for in some
way reducing the back pressure below atmospheric and thereby
getting greater temperature range and expansion and more
power from.the products of combustion?

Answer.

All threc;gf these systems have been used in practice
with more or 1.5. success. a steam turbine run from steam
heated by exhaust gases may, under favorable efficiencies
of turbine and compressor and low ratios of negative to
positive work, generate enough power to run the compressor.

‘Regenerative heating or pressure-raising by:means of
the exhaust gases gives about the same added efficiency as
the use of an exhaust heated steam-driven auxiliary; and may,
in most cases, require a less complicated mechanism. On an
explosion type turbine, though, the use of the auxiliary may
be preferable to heating regeneratively, when there is a
cooling blast of air or steam.to be passed through the same
path as the fuel mixture travels, as in that case the heat
is wasted on the cooling fluid and the efficiency of the
cooling material is decreased accordingly.

in exhauster, usually, consumes as much.power as it
adds, unless the gas is cooled by'being used for regeneration
before passing through the exhauster, in which case its

lessened volume permits of the exhauster doing less work

1.

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~29-

than is done by the greater expansion of the gas in the
turbine. The exhauster and regenerator, then, combined in
the manner described, work well together in increasing
power and efficiency. The exhauster and auxiliary do not
work very well together, however, as the auxiliary makes
the function at the exhauster merely that of a pump for
the fluid heating the steam or other working medium of
the auxiliary, and any method of inducing a flow of the
exhaust gases over the boiler will do practically as well
as an exhauster, without requiring probably as large an
expenditure of negative work. There is not usually heat
enough left in the exhaust gases after regeneration to
satisfactorily operate an auxiliary power unit.

Since the gases found in the exhaust of a gas turbine
or engine do not liquefy until nearly at a temperature of
absolute zero, they are not capable of being condensed for
practical purposes; and therefore a condenser analogous to
a steam condenser can not be used on a gas turbine. To
actually condense (liquefy) a very small portion of the
exhaust gas of a gas engine or turbine would require
cumbersome apparatus and an outlay of money that would
make the power cost prohibitive. The only practicable form
of pressure reducer at present apparent is the cooler and
exhauster type mentioned before in the discussion of
regeneration.

Question V.

Which is better?

1. Large units, necessarily stationary or marine, developing

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power for factories, lighting plants, ship-propulsion, etc. , or

2. Small units, which may be portable or tractice, developing

power for automobiles and small portable power applications?
Answer. .

Large units-«4500 H.P. and up, especially up to 5,000-
10,000 kilowatts--are found to be the only practicable units
at present; although, of course, the laboratory machines
of Zoelly, Warner, and others are made in smaller sizes.

But when results are desired on a dollars and cents basis,
the little laboratory machine is found impracticable. Some
smaller units, comparatively smaller, are installed on
torpedo boats, etc. On airplanes intended for flying at
high altitudes, the exhaust from the regular piston and
crank gas engine is used to drive a gas turbine running the
supercharger. Torpedoes are also sometimes equipped with
small, very high-speed gas turbines, Operating at constant
. pressure as the result of the combustion of compressed air
and fuel. But the object of using a turbine in large gas
installations is to cut down the tremendous size as much am
possible, which would not be done by making the turbine
merely an auxiliary to the main unit, as it is on the
airplane engine. While another use could be found for the
power besides running a supercharger--running a compressor
for instance, which corresponds at atmospheric pressure" to
a supercharger at the pressure found five miles above sea
level-~the exhaust from the main unit would have to be just
so much higher to allow a turbine to Operate with atmospheric
exhaust; and there would be more likely a loss instead of a

I.

IV

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gain in efficiency through taking the power out of the. gas
_ in two engines rather than one, and there certainly would
be an increase in cost. The airplane engine, designed to
operate with varying back pressures, could dispense with
theturbine at atmospheric pressure and use it with advan-
tage at high altitudes; but an engine Operating at a
constant back pressure would have no use for such an
auxiliary unit. The aviation motors, anyway, are designed
more for maximum H.P. per unit of weight than for economy
or thermal efficiency; .which case is directly apposite that
of the large gas power unit. Likewise the torpedo motor
makes but one run in its brief career before it is blown
up, and high economy and thermal efficiency and long life
to the casing and bladings are of little consequence as
long as it has the speed and power to direct its charge
fast, far, and accurately while it lasts.

The application of the turbine principle to the small
gas motor, such as the automobile engine or the portable
farm engine, faces such competition that it seems unlikely
to be brought about for many, many years, if at all. The
small plant is 5 very efficient developer of power for its
size; and the small turbine, like the small steam turbine
compared to the small reciprocating engine, is at a
disadvantage. The auxiliaries, such as compressor, re-
generator, etc. , required by a gas turbine make it too
complicated and cumbersome to compete with the reciprocating
gas engine, especially since the advantage in therml
efficiency is with the reciprocating engine.

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Question VI.

which is, better?

1. The impulse type of gas turbine with all the energy removed
in one or two velocity stages,
2. The reaction type with a slight pressure drOp per stage and
many stages, or
5. Some combination of the two, as is sometimes used in steam
turbine design?

Answer.

All practical gas turbines at present used or designed,
from the little highpspeed torpedo motor to the 10,000 kilowatt
Holsworth turbine now'being built in Germany, are of the
impulse type with usually two velocity stages. The impulse
type takes the energy out of the gas quickly before the‘blading
gets hot; and, with two velocity stages, keeps the peripheral
velocity down within safe limits. lith.the reaction type, the
first sets of blades and nozzles are exposed to intense heat;
and the gas has to be throttled down or otherwise reduced in
velocity‘because of the lower peripheral speed of the rotor.
Therostically, the reaction type with cooled gas should
eperate just as efficiently as the impulse type, but practical '
designers, such as Holzworth, Arinengaud and Lemale, and
Pelterie, find that the impulse turbine suits them best.

Question VII,
‘lhich is better?
1. A fuel already in the gaseous form,
2. A form of easily volatilised liquid fuel, such as gasoline,

naphtha, benzene, kerosene, etc., or

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3. A fuel in the form of heavy oils volatilizing only at high
temperatures, such as fuel oil, etc.?
Answer.

The choice of fuel depends largely on the locality,
relative cheapness, etc.; but gas turbines work best on fuels
suited to their particular types. Holzwarth's large turbines
operate on natural or producer gas--although his 300 Km.
unit eperated on fuel oil--, Iarren demonstrated the chamber
and nozzle efficiency of gasoline used in a small unit, and
in between these extremes are many designers whose turbines
eperate, or are supposed to eperate on fuel oil, gasoline,
kerosene, etc. It soon that the gas turbine uses best about
the same kind offuel as does. a reciprocating gas engine of
equal power and corresponding size; gasoline, benzine, kero-
sene, etc. for the smaller sizes; and fuel'oil, natural gas
and producer gas for the larger units.

Question VIII.

Ihich is better?

1. Both carburetion and vaporization of the fuel before it
enters the combustion chamber,
2. Carburetion outside and vaporization inside the combustion
chamber, or
3. Both carburetion and vaporization within the combustion
chamber?

Answer.

Carburetion and vaporization of the fuel, complete mixing
with air and preheating to a gaseous state if liquid fuel is.
used, should both be accomplished before the mixture is
ignited to secure maxim results as regards combustion; and

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the point where this complete carburetion is secured or should
be reached, depends on the type of turbine and the nature of
fuel used. With gaseous fuel there is, of course, no further
vaporization required, and the mixing of the gas and air is
all there is to look after. This should be accomplished
before ignition. In any explosion type turbine it can be
accomplished just as well within the chamber before ignition
as not. In a constant-pressure turbine, the mixture should
take place in the nozzle or injecting apparatus, so that, as
the gas issues at the point of ignition, it would be thoroughly
mixsd‘ready to burn perfectly.

Liquid fuels should be both carburetted and vaporized
before ignition. If the turbine is of the explosion type,
this may be done quite readily in the combustion chamber, or
if the flow is such in a constant pressure type that com-
bustion occurs only at the far end, giving the gas and air a
chance 'to become thoroughly vaporized before ignition. But,
with liquid fuels in a constant-pressure turbine, it is
probably best to have the carburetion take place before the
air and fuels get into the combustion chamber. They can then
be volatilized as they enter and be ignited imediately upon
entering. Liquids occupying less volume than gases, there is
less negative work to be done, if the fuel is made to enter
the combustion chamber against a given pressure in a liquid
rather than in a gaseous state. But unless vaporization is
complete, this gain in power is more than offset by the loss
due to incomplete combustion.

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~34-
Question 11.
lhat are the comparative thermal efficiencies and
commercial efficiencies of gas turbines, gas engines, and

steam turbines on power installations?
Answer

1
The thermal efficiency of the best gas turbine is about
equal to that of the best steam turbine and much inferior
to that of a reciprocating gas engine of the same power.
There is little analogy between steam and gas turbines. Steam
turbines owe their superiority in economy and efficiency over
recip rocating engines to their ability to make use of greater
expansions and lower vacuums than the engines, due to size
limitations, can cover. Between the same conditions of
temperature and pressure, steam turbines, especially in
medium large sizes, are outclassed by piston steam engines.
The turbine makes a double transformation of energy;~' from
pressure energy to kinetic energy in the steam and from
this kinetic energy of the steam to the mechanical energy
of the rotor: while the engine makes but the one change
directly from pressure energy to mechanical energy, and
therefore has less chance of wasted energy being lost as
heat during transformation from one form to another. The
gas turbine, as well as the steam turbine is up against
this fact, and is still a long ways from getting around it,
as far as therml efficiency is concerned.
In the smaller sizes the gas turbine, at present, has
no chance at all against the gas or steam engine; but in the
larger units other considerations besides thermal efficiency

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have great weight. The gas turbine occupies mneh.less space
and weighs and costs:mueh.less than a reciprocating gas
engine of equal power or than a steam turbine with.all the
equipment, boilers, condensers, feed-water pumps, etc. that
are necessary to the operation of‘a modern steam plant, ‘
although the actual turbine is mueh.smaller for steam.than
for gas. Also the operating cost is less for the gas turbine
than for either of the other two. '

Figuring cost of fuel, of operation, of interest on
investment, of depreciation charges, of lubrication, etc.
the large (HolsIarth) gas turbine costs roughly about half
as much as a gas engine and about .8 as much as a steam
turbine per unit of work (Kilowatt-hour) produced. So that,
as far as what may be called "commercial” or dollars-and-
cents efficiencyis concerned, the gas turbine has the
edge on its rivals. .

Question X.

After assuming the most favorable individual conditions
grouped together or the most favorable combination of
individual conditions affecting gas turbine design, whiehp
ever will produce the maximum.thermal and commercial
efficiencies, is the gas turbine able to compete with the
gas engine and steam.turbine; and, if so, under that con-
ditions and in what forms?

Answer. A
is Just pointed out, the Holssarth turbine is able to
hold its own against steam turbines and gas engines as

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regards actual cost of power produced. It seems unlikely
that the gas turbine will soon match in thermal efficiency
the gas engine; and, with higher pressures being used and
greater superheats and more nearly complete vacuums in
steam installations, the gas turbine is going to be hard
but to match the thermal efficiency of steam. So, should
the price of fuel rise considerably, compared to the rental of
floor space, the cost of manufacture, etc. , the gas turbine
would be rendered impractical; but this seems unlikely in
the very near future.

The Holzwarth is an explosion-type turbine with the
exhaust gases divided, part to do regenerative heating,
and part to run steam-driven auxiliaries. Several experi-
ments have been or are being made with constant-pressure
type turbines, and when a blading has been devised that
will stand high temperatures and certain other minor
mechanical difficulties are overcome a constant-pressure
turbine latching in efficiency the Holzwarth can be expected.
lost theorists favor the constant-pres sure type and are
working on that kind of turbine, while Professor Rateau
has found that tungsten tool-steel blading will stand
temperatures up to 1200 degrees P.; so the day of the

successful constant-pressure type seems near.

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Chapter III.

As we follow the subject of thermodynamics up from the
simpler and more obvious manifestations of the relation
between heat and work as shown in Joule's Law in Elementary
Physics, through the more and more complex forms of the
mechanical application of this la: and mechanical principles
in Engineering Thermodynamics, to the highly technical and
elaborately complicated and mathematical treatment of
Thermochemistry, we see the subject broadening to take in
the whole field of the sciences dealing with non-living
matter and even to some extent entering into, and being
entered into by, the biological sciences. Finally we reach
the science or scientific study in which all the physical
sciences are united, Physical Chemistry, in which first
causes and primary manifestations are sought out. And, when
we reach this study of basic physical characteristics and
manifestations, we find that already a great many limits to
the fundamental commonplace conceptions of space, time, and
matter, and their relations with each other, have been proved,
or postulated with a lack of proof of the contrary, by
physicists, engineers, and chemists, in these comparatively
elementary sciences and applications; and we also find that
Physical Chemistry sets up further limits; and, finally, we
may see where a comparison and correlation of these various
facts and postulates will lead to still further limits being
hypothesized, at the very least, in an attempt to get yet
closer to fundamental truth.

To begin with ordinary Physics, we find the postulate

of the Conservation of latter sets a maximm limit to the

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quantity of matter. "The amount of matter in space is fixed.
latter can be neither created nor destroyed.“ A corollary to
this is the law of Conservation of Energy. ”The total amount
of energy in all creation is a constant. Energy can be
neither created nor destroyed." A special application of the
latter law is the doctrine of the Conservation of Electricity,
"The quantity of Electricity in space is fixed. Electricity
can be neither created nor destroyed." These postulates, of
course, say nothing about the fact that matter, electricity,
and energy in general, have varied and varying distributions
and forms or manifestations. Taking this for granted, the
postulates--or at least the first two-are accepted as laws
in the light of lack of proof to any contrary, by engineers
and physicists in general everywhere.

Physics, of course, does not go beyond the molecule in
the direction of the infinitesimal, as the molecule is the
smallest amount of any physical element or substance
existing as such an element or substance; but it does tell
us of an indivisible minim unit of static electric charge,
the value of which has been determined to be 4.774 x 10'3“-
Electrostatic Units. (An Electrostatic Units is that charge
possessed by each of two poles one centimeter apart and
repelling each other with a force 6: one fine). The intensity
factors in Physical functions, such as temperature in heat,
pressure in work, and force in energy, are postulated as
varying or variable from Absolute Zero to Infinity, except
perhaps in the case of the temperature and pressure of very

large masses of matter, such as some of the huge nebular

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masses observed by astronomers in far-off space, in which the
pressure that would be produced by the tremendous gravitational
effect of the huge quantity of matter may be limited by the
extreme molecular activity or heat produced towards and in the
central portion of the mass by the external pressure, at some
figure that would have no conceivable meaning for us in term
of tons per square inch; and in which also the temperature may
be limited by the light pressure of the incandescent center
repellim the in-pressing masses outlying so that the density
and temperature of the total never reaches and never may reach
the maximum it would otherwise attain. Light pressure is one
of the smallest forces measurable, at present, in the laboratory;
but, as it increases as the square of the temperature, it may
prove yet to be one of the greatest forces in the huge uncom-
pressed nebular masses of space, where the external temperature-
as determined by spectroseOpic readings--is probably between
20,000 and 30,000 degrees Centigrade. At any rate, this
hypothesis of tremendous light pressure explains, as no other
theory does, the fact that no masses in space, of more than a
certain size, appear in a solid or compressed form, and the
further fact that external temperatures above those mentioned
have not been detected in any bodies so far studied. Internal
temperatures are limited only by the room allowed for molecular
vibration. In the line of physical research, though very
highly advanced, Professor Einstein's Theory of Relativity,
which seems, in some aspects at least, fairly well substan-
tiated, hypothesizes an upper limit to space itself, that the
extent of space is a tremendous but finite quantity. The

~40-

maxim velocity possible is also fixed, by the relativity
theory, as the speed of light in a vacuum, 186,337 miles per
second. lichaelson's latest value for the velocity of light
is some 140 miles per second less than the older accepted
figure.

Engineering Thermodynamics does not treat of exact
physical limits, although it does consider that the heat
form of energy is the form towards which all other forms are
evolving, and that the temperature factor, or measure of
available energy, is constantly decreasing in value, while
the entropy factor, the measure of unavailable energy, is
constantly increasing. In other words, engineering theory
and practice at present holds that mechanical, chemical,
electrical, and the other high-grade forms of energy, are
being slowly transformed into the lower grade heat torn, and
that that heat form is becoming less and less available for
doing work. This is the law of the Degradation of Energy,
otherwise known as the Second Law of Thermodynamics--the
First Law of Thermodynamics being a special case of the
general Law of the Conservation of Energy. The First Law
states that whenever work is transformed into heat, the
heat produced is preportional to the work expended, or,
when heat energy is made to do work, there is a constant
ratio between the heat transformed and the work done. The
Second Law states that heat can not pass from a colder to a
warmer body without some compensating action taking place.
It is impossible by means of a self-acting machine unaided
by any external agency to convey heat from one body to

another at higher temperature. No change in a system of

rd

I.

-41-

bodies that can take place of itself can increase the avail-
able energy ef the system»

Further than these laws, the limits imposed by or upon
Engineering or lechanical Thermodynamics are those of mechanical
practice and working ability, as, for instance, the maximum
pressure under uhich a steam boiler will operate efficiently,
or the maximum temperature that the‘blading of a gas turbine
can stand. .

In Theme-chemistry a law (the First Law of Thermo-
Chemistry) is met with.which, like the First Law of Thermo-
dynamics, is a special form.of the Law of the Conservation of
Energy. This thorns-chemical law states that the amount of
heat required to decompose a chemical compound into its
elements is equal to the heat evolved when the elements
combine to form.the compound.

But in Chemistry we meet with a number of limits of
smallness, among which are the molecule-~the smallest portion
of a compound that can exist as that compound substance, and
already mentioned in connection with.Physics-§, the ion-~the
smallest amount of a radical that has still the preperties of
that radical--, and the atone-the smallest amount of a
chemical element having still the qualities of that element.

A feature of chemical compounds of interest from.a
thermo-chemical viewpoint is that endothermic compounds, or
those in which.heat is absorbed in the formation of the comp
pound, are comparatively unstable and will readily decompose,
sometimes violently; while exothermic compounds, or those

which give off heat as the compound is formed and which

include most compounds, are usually quite stable.

[I

”W

,i

y.)

-42-

Physical Chemistry offers perhaps the most interesting
and certainly some of the most involved ideas concerning limits
and characteristics of the fundamental concepts. The Electron
Theory begins where Chemistry leaves off and divides the atoms
of all substances or elements into just two kinds of substance--
protons, or minute indivisible bits of positive electricity;
and electrons, the smallest and electrons, the smallest and
indivisible quantities of negative electricity. The different
elements are formed from these two basic substances by varying
numbers and arrangements. The general arrangement is, however,
the same in all elements; the center or nucleus of the atom
is made up of one or more protons, while the electrons rotate
at a very high.velocity about this nucleus of protons as the I
planets do about the sun. Usually the numbers of protons and
of electrons are equal, but it is possible for an electron to
become detached from.one atom and attached to another, leaving
the first with an excess of negative electricity or a negative
charge. This brings us down to the ultimate limit of divisi-
bility of matter, and also leads us, by the aid of the
relativity theory, to consider the transformation of one of
these smallest possible particles of matter--the electrons--
into pure energy radiating out, in the form of added turbulence
in the surrounding atoms, from the electron thus transformed.

Professor Planck has then hypothesized a minimum amount
or quantity of motion or energy, the quantum, which amounts to
6.55 x 10’27 ergs x seconds, developed thus:

“N

‘\

vu

’Qr

’7

-45~

Velocity equals Length x time'l.
Energy " Kass x velocityz
" [ass 3: lengch x time'z.
Quanta " Energy 3: time
‘ " lass x length2 x time’2 x time
" lass x length2 x time‘l.
Since the erg is the smallest unit of work or energy

and the second the smallest general unit of time, the value
of the quantum is given in terms of these two constants; or
1 quantum equals 6.55 x 10'27 erg: seconds. The general rule
for the use of quanta is that if a system vibrates with a
certain frequency it can exchange energy with other systems
only in amounts which are exact multiples of the product of
this vibration rate multiplied by the value of one quantum,
as given. Planck has modified this theory twice, first to say
that energycould be emitted continuously by a system, but
could be absorbed only in multiples of the product mentioned;
and later to reverse this stand and maintain that emission
'occurred only when the energy to be emitted reached a value
an exact multiple of the product spoken of, while absorption
of energy could occur continuously. Either of these views
explains quite satisfactorily many puzzling phenomena; while
neither of them, by itself, accounts satisfactorily for some
other phenomena observed by scientific investigators, and mat
be supplemented by other, and probably less well supported,
hypotheses. Of course, to the layman, and even to the average
professional man dealing as engineer or physicist with the
different forms of energy, the quantum theory makes little

4“

, '0

1"

~44-

difference; but, when further develOped, there is no telling
what difference it may make.

Now we have seen that science has given us indivisible
limits of mass and energy, and maximum limits of space and
velocity, while the very recent researches of Professor
Hilliken seem to indicate another step taken towards the
discovery of the least amount of movement in the amplitude
of vibration of his recently discovered "penetrating rays"
which have a higher frequency, as well as a much more penetra-
tive effect--going through 6 to 17 feet of solid lead, to 1/2
inch for the ”hardest" x-rays--than the ordinary x-rays,

What all this seems to be leading to is that there is,
similarly and necessarily, a minimum and indivisible unit of
time, a period of least change of position of mass or of
least change of form of energy, which would seem to be, before
being mathematically worked out, a decimal multiple of 10'20

'30 seconds .

or even 10
With this idea in mind, and also considering the present
theory of the relativity of space and mass and energy, we can
finally discuss all our fundamental, or what were yesterday
called fundamental, concepts in terms of one basic concept,
which, for lack of a better term, we shall herein refer to
as “Inertia.” This becomes evident in two forms or phases
and in various and varying degrees of balance between, and
forms of, these two phases, the static and the kinetic, from
the minutest bit of matter and amount of energy to the vast

reaches of interstellar space and the complicated processes of

the human mind itself. If the basic concept is inertia, and

,‘I

1‘!

-45-

its basic phases are static and kinetic, then the two
supposedly'most fundamental concepts, mass and energy, that
are considered in the relativity theory as related and inter-
dependent, probably furnish the best and ohiefest examples

of the two phases; so mass may be considered as static inertia,
and energy, pure energy, as kinetic inertia. Other fundamental
concepts are definable likewise in terms of this basic concept.
Space becomes the extension of inertia, and time the number

of least changes in distribution, and balance between the
phases of inertia, when time is measured by the minimum unit
heretofore hypothesized.

A rather philosophical definition of space is ”the range
of experience.” This, of course, is but the expression "the
extension of inertia," brought down to ordinary experiences.
Time has been defined as "the duration of experience," or the
duration of being, measured by the process of happening,"
which means the same as "the measurement, numerically, of
changes of inertia forms, phases, and distributions," or
"the comparison of the continuity of one phase of inertia with
the discontinuity of another phase," matching the definition
of space as ”the range or degree of extension of change of
condition of inertia.”

Considering time in terms of number of least changes and
other physical concepts as varying in multiples of these
least changes, it can be seen where mathematics becomes not
only one of the most useful, as it is new, but also one of
the most real and concrete, of the sciences, THE SCIENCE. As
our limits, one by one, become fixed scientifically at the

,Q

{‘I

(O

/l

[l

,3

-46-

lower end of the scale, the term ”derivative” as used in
Calculus takes on a more and more definite meaning and
absolute value, depending, of course, on the variables and
numbers considered. There appears, just now, to be no good
reason for assuming that space is infinitely divisible; in
fact, as before stated, recent researches tend to establish
that indivisible unit of space corresponding to that reached
in so many other physical concepts. It my even be possible
that there is a least change of direction, although there
seems to be no necessity as yet for such a hypothesis.

From these basic hypotheses, then, it should be possible
to define all other physical terms as relationships of the
static and kinetic manifestations of inertia with a numerical
value of least changes in form, arrangement, and distribution
of inertia. The only obstacle to a complete mathematical
demonstration of these relationships is the lack of knowledge
of the value of the basic unit of time. Attempts have been
made to derive this value mathematically by trying to find a
comon factor to the periods of infra-red and x-ray vibrations,
but this method gave no factors that were common and irreducible.
It may be hoped that, when complete data on lilliken's
penetrating” rays are available, that the vibration period of
these rays will lead us a step nearer the ultimate division of
time. lathematical examinations of the penetrating effects of
infra-red and waves of even higher frequency have thus far

offered no sight of the more or less exact value of the

0111-8179 unit, Curves drawn on both rectangular and logarithmic

graph paper showed very little direct correlation between

frequency and penetration. In this connection, Dr. George K.

("O

Ir‘1

-4'7-

Burgess, Director Of the Bureau Of Standards, has the following
to say:

1. "For long electromagnetic waves, including radio waves,
electrical conductors such as metals absorb the waves, while
insulators are in general transparent; though insulators
differ in marked degree in their transmission for the higher
frequencies. '

2. As we approach frequencies Of infra-red and visible
light, no simple generality can be made except that metals
are in general Opaque. Gold, however, in the thinnest films
transmits green light appreciably. In the near ultra-violet
nearly all solids and liquids become Opaque. later is Opaque
for wavelengths less than 1800 AU (Angstrom unit equals
10'"8 cm). From 1000 to 5 AU is a region where all materials
are almost completely Opaque. From 5 tO .05 AU (the region
of ordinary xi-rays) all substances increase enormously in
transparency, and roughly speaking the transmission depends
only on the density Of the substance.

5. An approximate rule applicable to all chemical elements
at the shorter wavelengths is that the absorption is prepor-
tional to the number Of atoms per unit volume times the fourth
power Of the atomic number times the cube Of the wave length.
Water will be relatively transparent, steel intermediate, and
both lead and gold very Opaque. In the 100 fold range Of wave-
length Of x-rays, the absorption Of any one substance will vary
a’million fold.”

This approximate rule put in the shape Of a formula may

be expresses by A equals K 3(nu)4 (lamvda)3, but its

’x

-48-

extreme approximation makes it of little value for careful
comparisons .

Another method that has been investigated is that of
determining the velocity Of impulse transmission in solids.
From results Of such determinations as applied to and derived
from very small bodies, very small time intervals may be
computed. Devices for testing out this speed Of impulse trans-
mission, by noting the time interval required for the far end
Of a rod to get in motion after the nearer end has been struck
a sharp blow, have been designed; but have not as yet been
constructed or tried out. One such device Operates as follows:

A fairly long rod equipped at each end with a marking
needle, pointer, or pencil, rests on guide rollers as nearly
frictionless as possible. Rotatable discs are mounted on a
shaft parallel to the bar, sO that the pencils are each the
same distance from the nearest disc as the other. The shaft
carrying the discs has a slow translatory motion at right
angles to its axis and in the plane or its axis and the bar,
as well as a rapid rotatory motion. A gravity or spring
actuated hammer strikes one end Of the bar and sets it in
motion longitudinally. The discs are rotated at high speed
by a drive pulley midway between them. The pencils at either '
end Of the forced bar record on the discs the exact time the
particular end of the bar moves; the motion Of the shaft with
its bearings towards or away from the bar prevents the pencils
from simply making circles in which the beginning is indis-
tinguishable, but causes them to produce instead a spiral.
Checking up to make sure that the discs zero all right at high
speeds is done by another apparatus which causes two other

,0

~49-

pencils to strike simltaneously one on each disc. The discs
must be driven at constant speed; and friction must be
eliminated as far as possible, while all connections are still
made to allow a minimum Of play. Different cross-sections, and
cross-sectional areas should be used for bars Of the same
material, and different materials Of identical mass, volume,

or section should be tried out; while the apparatus should be
used in at least the four cardinal directions'of the compass
find the four intermediate directions, to eliminate magnetic,
electromagnetic and other effects that might have a bearing on
the results Obtained. Of course the length Of the bar and the
angular velocity Of the discs are readily secured, and the
develOpment Of the velocity with which the movement Of the bar
is transmitted is then a matter Of comparatively simple
arithmetic. However, mechanical difficulties make the Operation
Of the apparatus less simple than the general principles here
outlined would indicate, and a successful construction would
result only from‘long, patient, and painstaking labor.

After abandoning the experimental method for the time
being, recourse was had to pure theory by which a formula was
develOped for the time it should take for an impulse tO travel
the length of any certain bar. It is to be understood that the
impulse is one Of translatory motion and not Of compressional
vibration (sound) for which the theoretical formula is
V equals the Square root Of e/d, which checks out most
accurately in experimental work. (V equals velocity; e equals
coefficient Of elasticity; and d equals density in the sound
velocity formula). -

Several assumptions must necessarilv be made in anv

,1

14

theoretical develOpment; and we have no exception in this case.
' The problem may be stated: A rod lying horizontally on a
frictionless table is struck on one end by a hammer moving
axially with the rod. How long is it before the far end of
the rod moves?

We assume first that the resultant final velocity of the
rod compared to that Of the striking hammer is governed
strictly by the lawslof elastic impact and conservation Of
momentum. Next we assume that the farther end of the rod
'remains fixed at first and that the rod is simply compressed
by the force of the blow; therend struck remains fixed and
far end Of rod is moved‘by expansion Of the rod. Also since
force Of rod in expanding equals force required to compress it,
and mass moved in expansion equals mass moved in compression;
therefore acceleration, space, velocity, and time Of expansion
equals same Of compression.

Finally we assume that the kinetic energy disappearing in
the collision is all used to produce compression in the rod.

These many postulates naturally make the formula entirely
theoretical; but evidently they will hold increasingly well ‘
with.amaller and smaller rods and consequent shortened time
intervals, which are the cases in which.we are most interested.
In develOping this formula, we will use symbols for physical

characteristics as follows:

Rod Symbolism Hammer
L Length 1

, A Cross-sectional area a
E Coefficient of elasticity e
M Mass 1::

-51-

Rod Symbolism ' Hammer
0 Amount Of Compression c

v equals velocity Of hammer before impact
V " \ ” ” " and rod after impact

mv " (111 plus 10V. V equalsmv

m plus M
Kinetic energy of hammer before impact equals K-El

 

 

 

K-E equals “"2
l 23
Kinetic Energy Of hammer after impact equals K-Ez.
K-Ez equala 2‘72 equals m (WLZ equals
8 28
3 2
m v

 

2g (:11 plus M2
Kinetic Energy Of rod after impact equals K-Es

K-Es equals W2 equals WE equals
Knew”

y “P “1
K-E‘ equals K-E: plus K-E:5 equals m plus ll "2 equals
- 23 '
1:: plus 11 (mV )2

?g m pIus H

 

K-E equals 1112‘!2

4 f(m plus Y)
Energy used up in producing compression equals
2
K-E - K-E equals mV2 - mZV equals mV2
1 ”"24 EE- 7g(m plus 117 53- (1 m H)
equalsmv ( 1 _ V)
28
Force rXquired to produce compression C equals 10: . E
equals CE .
II
Average force during compression equals 1/2 g .
Work done in compression Of rod equals 0.4;: g equals

iCZE equals K-E - K-E4 equals mv2
II 8

Action and reaction being equal, compression in

hammer will be equal but Opposite tO that in rOd and may be

1 (1-3
V

neglected in considering effect on rod. * (If hammer area or

-52-

elasticity is large compared to that Of rod).

 

 

 

2 .
C E equals sz m. equals
EI g ( 1 ' M plus m. )
mv2(Mplusm-m
g M'plus m
GEE equals sz ( M )
I1— g leusm
M lus m. ‘g 02E equals v2
2 E ' m.’ II—

v equals 20: C, (I: equals negative acceleration of hammer.

(1‘: equals V2
56

Time of acceleration equals t.
V equals 00 t. t equals gr equals 2 equals 39
v

equals 5g times the square root Of LAMm
(M plus MEE

t equals 2 times the square root Of LAMm
(1's plus M)gE.

t equals time Of compression equals time Of expansion.

 

Time Of transmission equals T equals 2t.

T equals 4 times the square root Of LAMm
(mTflus M)gE

 

equals 4 times the square root Of LAMV
A v

This formula applied to bodies of atomic size should give
very small time intervals. For instance, if an electron, the
smallest possible hammer, travelling with any velocity, were
to hit the outside (orbit Of the electron in the atom) Of a
hydrogen atom, which is probably the smallest body having a

(postulated) finite coefficient of elasticity, how long would
it take the impulse tO travel the radius of the hydrogen atom?

In the formula T equals 4 times the square root of LAMm
(m plus WEE.
modern physical chemistry gives us the following values:

 

9-55-
L equals radius Of orbit Of Hydrogen atom equals
'5 x 10'"9 cm. A
A equals cross-sectional area Of Hydrogen atom equals
(5 x 10'9)2 pi one.

M equals mass of Hydrogen atom equals 1 grams.

m equals mass of electron equals H equal: $01 10“"?8 grams.

g equals acceleration due to gravfizyvequals 980 cm per sec.2.
It is thus seen that we have everything but E, the coefficient
Of elasticity Of the atom, which has not been determined as yet.
Born and others have computed the coefficient Of elasticity
as between atoms in molecules of various salts; but this case
requires the interior coefficient Of elasticity Of the atom
prOper, rather than the measure Of the elastic effect “as
between atoms or molecules Of the element hydrogen.

Hy some means, however, this minimum _time unit will be
evaluated; and scientists will have another final division to
work with, in considering energy transfers and transformations.
The rather unfortunate thing about these“ energy transformations
is that, while life and other conditions on the earth are not
exactly dependent upon a certain quantity Of other forms of
energy--a wide variation in the amount of electrical, chemical,
or mechanical energy existing in a given system being per-
missible, sometimes from practically zero to very large amounts--
the demand Of most organisms and systems for an amount Of heat

energy with a comparatively high intensity factor or temperature...

compared to the absolute zero Of temperaturem-makes it necessary
to waste large amounts Of heat energy, because Of this high

temperature below which the heat energy is unavailable. Also

the other forms Of energy seem tO have a tendency to change to

-54-

this more wasteful heat form. Perhaps further research with
these least units Of matter, energy, and time will tell why.

Hilliken believes the very high frequency rays he has
' found in existence are caused by the formation Of atoms Of
the elements as we know them, from the basic protons and
electrons somewhere out in space, some Of this matter being
changed to energy as manifested by the short wave-length
electromagnetic vibrations. SO the constant tendency noted
in terrestrial practice for energy to become slower in its
vibration rate and more and more unavailable my mean a
raturn from the kinetic phase of inertia to the static phase,
or, in other words, the retransformation Of energy back into
matter, taking place so gradually and steadily and over sO
large a portion Of our range of experience that it has hardly
been noticed as such. This .completion Of the cycle Of changes
Of phases or manifestations Of inertia is satisfying from a
philosOphical standpoint, anyway, even though we have not as
yet sufficient scientific evidence tO more than hint at its
proof.

All forms of energy are finally considered as more or
less mechanical; and thermodynamics treats Of the relation
between heat energy and mechanical energy; while it has
generally been held that all other forms Of energy tend to
degenerate into heat energy and Of the lowest grade in which
the temperature, or measure Of the kinetic molecular energy,
tended towards a minimum, and the entrcpy, or measure of un-
available energy, tended towards a maximum. ‘ SO we see, that,-
broadly speaking, thermodynamics covers practically the whole
field Of energy, and certainly every phase Of the study Of

BIBLIOGRAPHY

Books
A System.of Physical Chemistry, Vol. III, Lewis.
An Advanced Course of Instruction in Chemical Principles, Noyes.
Applied XHRays, Clark.
Audel's Gas Engine Ianual
College Physics, Kimball
Dictionary Of Applied Physics, Vols. 1; III, IV, and V, G1az6broOk.
Encyclopedia Brittanica, 11th.Edition.
Elements Of Physical Chemistry, Jones.
Experimental Engineering, Carpenter and Diederichs.
Elementary Physical Chemistry, Taylor.
Engineering Thermodynamics, Lucke.
Gas Turbines, Marks and Danilov.
General Physics, Ferry.
General Physics for Colleges,‘Webster, Farwell, and Drew.
Guldner's Internal Combustion Engines, Diederichs.
Handbook Of Chemistry and Physics, Hodgman and Lange.
Hydraulics, Hughes and Safford.
Internal Combustion Engines, Carpenter and Diederichs.
Introduction to Contemporary Physics, Darrow.
Kinetic Theory Of Gases, Loeb.
Mechanical Engineer's Handbook, larks and Loewenstein.
Physics for Colleges, Sheldon, Kent, Paton, and killer.
Physics for College Students, Knowltcn.
Physical Chemistry, Ewell.
Physical Chemistry, Lincoln.
Physical Chemistry in the Service Of the Sciences, van't Hoff
and Smith.
Practical Thermodynamics, Cardullo.
Problems of Hodern Physics, Lorentg.
Proceedings Of the American Chemical Society for 1913, January,
Lewis.
Reflections on the letive Power of Heat, Carnot and Thurston.
Service Chemistry, Lewis.
Steam.and Gas Turbines, StOdOla and Loewenstein
(also Dampf und Gas Turbinen, Stodola).
Steam.Turbines, Hoyer.
Technical Thermodynamics, Zeuner.
Text-Book Of ledern Physics,‘We1d and Palmer.
Thermochemistry, Thomson,
Thermodynamics, Emswiler.
Thermodynamics and the Free Energy Of Chemical Substances, Lewis.
Thermodynamics and Chemistry, Duhem and Burgess.
Thermodynamics and Chemistry, Nernst.
Thermodynamics Of Technical Gas-Reactions, Haber and Lamb.
The Scientific Papers of J. Willard Gibbs, Vol. I.
XrRays and Electrons, Compton.

Magazines
Automotive Industries
Electrician
Engineer
Engineering
L'Illustration
Mechanical Engineering"
Harine Engineering and Shipping Age
Power

Power Plant Engineering
Scientific American

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