Direct Conversion of Energy


    [Illustration: uncaptioned]

                         By William R. Corliss


                     U.S. ATOMIC ENERGY COMMISSION
                   Division of Technical Information


                          _ONE OF A SERIES ON
                        UNDERSTANDING THE ATOM_

  UNITED STATES ATOMIC ENERGY COMMISSION
  _Dr. Glenn T. Seaborg, Chairman_
  _James T. Ramey_
  _Dr. Gerald F. Tape_
  _Wilfrid E. Johnson_


Nuclear energy is playing a vital role in the life of every man, woman,
and child in the United States today. In the years ahead it will affect
increasingly all the peoples of the earth. It is essential that all
Americans gain an understanding of this vital force if they are to
discharge thoughtfully their responsibilities as citizens and if they
are to realize fully the myriad benefits that nuclear energy offers
them.

The United States Atomic Energy Commission provides this booklet to help
you achieve such understanding.

                                                  {Edward J. Brunenkant}
                                                    Edward J. Brunenkant
                                                                Director
                                       Division of Technical Information




                                CONTENTS


  INTRODUCTION                                                         1
  DIRECT VERSUS DYNAMIC ENERGY CONVERSION                              3
  LAWS GOVERNING ENERGY CONVERSION                                     8
  THERMOELECTRICITY                                                   12
  THERMIONIC CONVERSION                                               16
  MAGNETOHYDRODYNAMIC CONVERSION                                      19
  CHEMICAL BATTERIES                                                  22
  THE FUEL CELL: A CONTINUOUSLY FUELED BATTERY                        24
  SOLAR CELLS                                                         26
  NUCLEAR BATTERIES                                                   28
  ADVANCED CONCEPTS                                                   30
  SUGGESTED REFERENCES                                                33
  ANSWERS TO PROBLEMS                                                 34


Library of Congress Catalog Card Number: 64-61794


ABOUT THE AUTHOR

    [Illustration: William R. Corliss]

WILLIAM R. CORLISS is an atomic energy consultant and writer with 12
years of industrial experience including service as Director of Advanced
Programs for the Martin Company’s Nuclear Division. Mr. Corliss has B.S.
and M.S. Degrees in Physics from Rensselaer Polytechnic Institute and
the University of Colorado, respectively. He has taught at those two
institutions and at the University of Wisconsin. He is the author of
_Propulsion Systems for Space Flight_ (McGraw-Hill 1960), _Space Probes
and Planetary Exploration_ (Van Nostrand 1965), _Mysteries of the
Universe_ (Crowell 1967), _Scientific Satellites_ (GPO 1967), and
coauthor of _Radioisotopic Power Generation_ (Prentice-Hall 1964), as
well as numerous articles and papers for technical journals and
conferences. In this series he has written _Neutron Activation
Analysis_, _Power Reactors in Small Packages_, _SNAP—Nuclear Reactor
Power in Space_, _Computers_, _Nuclear Propulsion for Space_, _Space
Radiation_, and was coauthor of _Power from Radioisotopes_.




                              INTRODUCTION


A flashlight battery supplies electricity without moving mechanical
parts. It converts the chemical energy of its contents _directly_ into
electrical energy.

Early direct conversion devices such as Volta’s battery, developed in
1795, gave the scientists Ampere, Oersted, and Faraday their first
experimental supplies of electricity. The lessons they learned about
electrical energy and its intimate relation with magnetism spawned the
mighty turboelectric energy converters—steam and hydroelectric
turbines—which power modern civilization.

We have improved upon Volta’s batteries and have come to rely on them as
portable, usually small, power sources, but only recently has the
challenge of nuclear power and space exploration focused our attention
on new methods of direct conversion.

To supply power for use in outer space and also at remote sites on
earth, we need power sources that are reliable, light in weight, and
capable of unattended Operation for long periods of time. Nuclear power
plants using direct conversion techniques hold promise of surpassing
conventional power sources in these attributes. In addition, the
inherently silent operation of direct conversion power plants is an
important advantage for many military applications.

The Atomic Energy Commission, the Department of Defense, and the
National Aeronautics and Space Administration collectively sponsor tens
of millions of dollars worth of research and development in the area of
direct conversion each year. In particular, the Atomic Energy Commission
supports more than a dozen research and development programs in
thermoelectric and thermionic energy conversion in industry and at the
Los Alamos Scientific Laboratory, and other direct conversion research
at Argonne National Laboratory and Brookhaven National Laboratory.
Reactor and radioisotopic power plants utilizing direct conversion are
being produced under the AEC’s SNAP[1] program. Some of these units are
presently in use powering satellites, Arctic and Antarctic weather
stations, and navigational buoys.

Further applications are now being studied, but the cost of direct
conversion appears too great to permit its general use for electric
power in the near future. Direct techniques will be used first where
their special advantages outweigh higher cost.




                DIRECT VERSUS DYNAMIC ENERGY CONVERSION


Dominance of Dynamic Conversion

We live in a world of motion. A main task of the engineer is to find
better and more efficient ways of transforming the energy locked in the
sun’s rays or in fuels, such as coal and the uranium nucleus, into
energy of motion. Almost all the world’s energy is now transformed by
rotating or reciprocating machines. We couple the energy of exploding
gasoline and air to our automobile’s wheels by a reciprocating engine.
The turbogenerator at a hydroelectric plant extracts energy from falling
water and turns it into electricity. Such rotating or reciprocating
machines are called _dynamic_ converters.


A New Level of Sophistication: Direct Conversion

A revolution is in the making. We know now that we can force the
heat-and-electricity-carrying electrons residing in matter to do our
bidding without the use of shafts and pistons. This is a leading
accomplishment of modern technology: energy transformation without
moving parts. It is called _direct_ conversion.

The thermoelements shown above the turbogenerator in Figure 1 illustrate
the contrast between direct and dynamic conversion. The thermoelements
convert heat into electricity directly, without any of the intervening
machinery seen in the turbogenerator.

    [Illustration: Figure 1 _Direct conversion devices, such as the
    spokelike lead telluride thermoelectric elements inside the SNAP 3
    radioisotope generator shown above (courtesy Martin Company),
    convert heat into electricity without moving parts. In contrast, the
    SNAP 2 dynamic converter shown below SNAP 3 (courtesy Thompson Ramo
    Wooldridge, Inc.) includes a high-speed turbine, an electric
    generator, and pumps to produce electricity from heat. (NaK is a
    liquid mixture of sodium and potassium.)_]

  DIRECT VERSUS DYNAMIC CONVERSION
    SNAP 3 LESS THAN 5 WATTS
      5″
    SNAP 2 3000 WATTS
      24″
      ALTERNATOR ROTOR
      ALTERNATOR STATOR
      TURBINE ROTORS
      NaK PUMP DIFFUSER
      NaK PUMP ROTOR
      MERCURY JET BOOSTER PUMP
      MERCURY CENTRIFUGAL PUMP
      MERCURY THRUST BEARING
      MERCURY BEARING
      MERCURY BEARING


Why is Direct Conversion Desirable?

There are places where energy conversion equipment must run for years
without maintenance or breakdown. Also, there are situations where the
ultimate in reliability is required, such as on scientific satellites
and particularly on manned space flights. Direct conversion equipment
seems to offer greater reliability than dynamic conversion equipment for
these purposes.

We should recognize that our belief in the superiority of direct
conversion is based more on intuition than proof. It is true that direct
converters will never throw piston rods or run out of lubricant. Yet,
some satellite power failures have been caused by the degradation of
solar cells under the bombardment of solar protons. The other types of
direct conversion devices described in the following pages may also
break down in ways as yet unknown. Still, today’s knowledge gives us
hope that direct conversion will be more reliable and trustworthy than
dynamic conversion. Direct conversion equipment is beginning to be
adopted for small power plants, producing less than 500 watts, designed
to operate for long periods of time in outer space and under the ocean.
Some day, large central-station power plants may use direct conversion
to improve their efficiencies and reliabilities.


How is Energy Transformed?

What is energy and how do we change it? Energy is a fundamental concept
of science involving the capacity for doing work. _Kinetic_ or
mechanical energy is the most obvious form of energy. It is defined as

                                 E = ½ mv²
  where
    E = energy (expressed in joules)
    m = mass of the moving object (in kilograms)
    v = velocity (in meters per second)

Energy can also be stored in chemical and nuclear substances or in the
water behind a dam. In these quiescent states it is called _potential_
energy. If the potential energy in a substance is abundant and easily
released, the energy-rich substance is called a _fuel_.


ENERGY CONVERSION MATRIX

    [Illustration: Figure 2 _To find how one form of energy is converted
    into another, start at the proper column and move down until the
    column intersects with the desired row. The box at the intersection
    will give typical conversion processes and examples._]

 FROM⇒            ELECTROMAGNETIC   CHEMICAL          NUCLEAR           THERMAL              KINETIC          ELECTRICAL          GRAVITATIONAL
                                                                                             (MECHANICAL)
 TO⇓

 ELECTROMAGNETIC                    Chemiluminescence Gamma reactions   Thermal radiation    Accelerating     Electromagnetic     Unknown
                                    (fireflies)       (Co⁵⁸ source)     (hot iron)           charge           radiation[2]
                                                      A-bomb                                 (cyclotron)      (TV transmitter)
                                                                                             Phosphor[2]      Electroluminescence
 CHEMICAL         Photosynthesis                      Radiation         Boiling              Dissociation by  Electrolysis        Unknown
                  (plants)                            catalysis         (water/steam)        radiolysis       (production of
                  Photochemistry                      (hydrazine plant) Dissociation                          aluminum)
                  (photographic                       Ionization                                              Battery charging
                  film)                               (cloud chamber)
 NUCLEAR          Gamma-neutron     Unknown                             Unknown              Unknown          Unknown             Unknown
                  reactions
                  (Be⁹+γ → Be⁸+n)
 THERMAL          Solar absorber    Combustion        Fission                                Friction         Resistance-heating  Unknown
                  (hot sidewalk)    (fire)            (fuel element)                         (brake shoes)    (electric stove)
                                                      Fusion
 KINETIC          Radiometer Solar  Muscle            Radioactivity     Thermal expansion                     Motors              Falling objects
                  cell[2]                             (alpha particles) (turbines)                            Electrostriction
                                                      A-bomb            Internal combustion                   (sonar transmitter)
                                                                        (engines)
 ELECTRICAL       Photoelectricity  Fuel cell[2]      Nuclear           Thermoelectricity[2] MHD[2][3]                            Unknown
                  (light meter)     Batteries[2]      battery[2]        Thermionics[2]       Conventional
                  Radio antenna                                         Thermomagnetism[2]   generator
                  Solar cell[2]                                         Ferroelectricity[2]
 GRAVITATIONAL    Unknown           Unknown           Unknown           Unknown              Rising objects   Unknown
                                                                                             (rockets)


The Energy Conversion Matrix

Forms of energy are interchangeable. When gasoline is burned in an
automobile engine, potential energy is first turned into heat. A portion
of this heat, say 25%, is then converted into mechanical motion. The
remainder of the heat is wasted and must be removed from the engine.

A multitude of processes and devices have been found which make these
transformations from one form of energy to another. Many of these are
listed in the blocks in Figure 2. Asterisks refer to direct conversion
processes, the subject matter of this booklet.

To demonstrate how this diagram is to be read, let us use it to trace
the energy transformations involved in an automobile engine. We begin
with sunlight because all coal and oil deposits (the _fossil fuels_)
received their initial charge of energy in the form of sunlight.

The first conversion, therefore, is from electromagnetic energy to
chemical energy via photosynthesis in living things. We trace the
transformation by moving down the column marked Electromagnetic Energy
until it intersects the horizontal row labeled Chemical Energy. There we
see photosynthesis listed in the block. The next conversion is from
chemical energy to thermal energy via combustion. We trace this by
moving down the Chemical Energy column to the Thermal Energy row;
combustion is listed in the appropriate block. The third and final
conversion takes place when thermal energy is transformed into
mechanical energy via the internal combustion engine.

By the repeated use of the Energy Conversion Matrix in this way, we can
chart any energy transformation.


                               Problem 1

  Continue the automobile example by going through the matrix twice more
  showing how mechanical energy is converted into stored chemical energy
  in the car’s battery.


                               Problem 2

  If 1 gram of gasoline (about a tablespoonful) yields 48,000 joules of
  thermal energy when burned with air, how fast can it make a 1000
  kilogram car go? Assume the car starts from rest and its engine is 25%
  efficient.

  Answers to problems are on page 34.




                    LAWS GOVERNING ENERGY CONVERSION


The Big Picture: Thermodynamics

To the best of our knowledge, energy and mass are always conserved
together in any transformation. This summary of experience has been made
into a keystone of science: the Law of Conservation of Energy and Mass.
It states that the total amount of mass and energy cannot be altered.
This law applies to everything we do, from driving a nail to launching a
space probe. While the conscience of the scientist insists that he
continually recheck the truth of this law, it remains a bulwark of
science.

The Law of Conservation of Energy and Mass is also called the First Law
of Thermodynamics. It is related to the Second Law of Thermodynamics,
which also governs energy transformations. The Second Law says, in
effect, that some energy will unavoidably be lost in all heat engines.
The first two laws of thermodynamics have been paraphrased as (1) You
can’t win; (2) You can’t even break even. Let us look at them further.


You Can’t Win

We used to think that energy and mass were conserved independently, and
for many practical purposes we still consider them so conserved. But
Einstein united the two with the famous equation

                                  E = mc²

  where
    E = energy (in joules)
    m = mass (in kilograms)
    c = speed of light
        (300,000,000 meters per second)

Notice the resemblance to the kinetic energy equation shown earlier.
Energy cannot appear without the disappearance of mass. When energy is
locked up in a fuel, it is stored as mass. In the gasoline combustion
problem, 1 gram of gasoline was burned with air to give 48,000 joules of
energy. Einstein’s equation says that in this case mass disappeared in
the amount

          m = E/c² = (4.8 × 10⁴)/(9 × 10¹⁶) = 5.3 × 10⁻¹³ kilogram
      (half a billionth of a gram)

But, when an H-bomb is exploded, grams and even kilograms of mass are
converted to energy.

In direct conversion processes we do not need to worry about these mass
changes, but at each point we must make sure that all energy is
accounted for. For example, in outer space all energy released from
fuels (even food) must ultimately be radiated away to empty Space.
Otherwise the vehicle temperature will keep rising until the Spaceship
melts.


You Can’t Even Break Even

Any engineer is annoyed by having to throw energy away. Why is energy
ever wasted? The Second Law of Thermodynamics guides us here. Experience
has shown that heat cannot be transformed into another form of energy
with 100% efficiency. We can’t explain Nature’s idiosyncracies, but we
have to live with them. So, we accept the fact that every engine that
starts out with heat must ultimately waste some of that energy (Figure
3).

    [Illustration: Figure 3 _A typical heat engine showing heat input,
    useful power output, and the unavoidable waste heat that must be
    rejected to the environment. A pressure-volume diagram is shown
    underneath for a closed gas-turbine cycle. Circled numbers
    correspond. The energy produced is represented by the shaded area.
    Similar diagrams can be made for all heat engines as an aid in
    studying their performance._]

  A TYPICAL HEAT ENGINE
    HEAT IN
    HEAT SOURCE
      REACTOR, BOILER
    ELECTRICITY OUT
    ENERGY CONVERTER
    PUMP
    FLUID PIPE
    RADIATOR
    WASTE HEAT OUT
  PRESSURE-VOLUME DIAGRAM
    HEAT IN
    ENERGY OUT
    GAS PRESSURE
    WASTE HEAT OUT
    GAS VOLUME

Direct conversion devices are no exception. Consequently, every
thermoelectric element or thermionic converter will have to provide for
the disposition of waste heat. The designer will try, however, to make
the engine efficiency high so that the waste heat will be small. Figure
4 shows the extensive waste heat radiator on a SNAP 50 power plant
planned for deep space missions.

    [Illustration: Figure 4 _Model of SNAP 50 power plant planned for
    deep space missions showing extensive waste heat radiator. The
    system will provide 300 to 1000 kilowatts of electrical power._]


Carnot Efficiency

In 1824 Sadi Carnot, a young French engineer, conceived of an idealized
heat engine. This ideal engine had an efficiency given by

                     e = 1 - T_c/T_h = (T_h - T_c)/T_h

  where
    e = the so-called Carnot efficiency (no units)
    T_c = the temperature of the waste heat reservoir (in degrees
              Kelvin, °K[4])
    T_h = the temperature of the heat source (in °K)

Unhappily, T_c cannot be made zero (and e therefore made equal to 1,
which is 100% efficiency). Physicists have shown absolute zero to be
unattainable, although they have approached to within a hundredth of a
degree in the laboratory.

Waste heat, since it must be rejected to the surrounding atmosphere,
outer space, or water (rivers, the ocean, etc.), must be rejected at T_c
greater than 300°K. The reason for this is that these physical
reservoirs have average temperatures around 300°K (about 80°F)
themselves. The fact that T_c must be 300°K or more is a basic
limitation on the Carnot efficiency. The loss in efficiency with
increased T_c explains why a jet plane has a harder job taking off on a
hot day.

One way to improve the Carnot efficiency, which is the maximum
efficiency for any heat engine, is to raise T_h as high as possible
without melting the engine. For a coal-fired electrical power plant, T_h
= 600°K and T_c = 300°K, so that

                      e = 1 - 300/600 = 0.5 = 50%

The actual efficiency is somewhat less than this ideal value because
some power is diverted to pumps and other equipment and to unavoidable
heat losses. Later on, we shall see that magnetohydrodynamic (MHD)
generators hold prospects for increasing T_h by hundreds of degrees.

Everything that has been said about the Second Law of Thermodynamics
(You can’t even break even) applies to heat engines, where we begin with
thermal energy. Suppose instead that we start with kinetic or chemical
energy and convert it into electricity without turning it into heat
first. We can then escape the Carnot efficiency strait jacket. Chemical
batteries perform this trick. So do fuel cells, solar cells, and many
other direct conversion devices we shall discuss. Thus, we circumvent
the Carnot efficiency limitation by using processes to which it does not
apply.


                               Problem 3

  Some space power plants contemplate using the space cabin heat (T_h =
  300°K) to drive a heat engine which rejects its waste heat to the
  liquid-hydrogen rocket fuel stored at T_c = 20°K. What would be the
  Carnot efficiency of this engine?




                           THERMOELECTRICITY


After 140 Years: Seebeck Makes Good

The oldest direct conversion heat engine is the thermocouple. Take two
different materials (typically, two dissimilar metal wires), join them,
and heat the junction. A voltage, or electromotive force, can be
measured across the unheated terminals. T. J. Seebeck first noticed this
effect in 1821 in his laboratory in Berlin, but, because of a mistaken
interpretation of what was involved, he did not seek any practical
application for it. Only recently has any real progress been made in
using his discovery for power production. To use the analogy of A. F.
Joffe, the Russian pioneer in this field, thermoelectricity lay
undisturbed for over a hundred years like Sleeping Beauty. The Prince
that awoke her was the semiconductor.

As long as inefficient metal wires were used, textbook writers were
correct in asserting that thermoelectricity could never be used for
power production. The secret of practical thermoelectricity is therefore
the creation of better thermoelectric materials. (Creation is the right
word since the best materials for the purpose do not exist in nature.)
To perform this alchemy, we first have to understand the Seebeck effect.


Electrons and Holes

Let’s examine the latticework of atoms that make up any solid material.
In electrical insulators all the atoms’ outer electrons[5] are held
tightly by valence bonds to the neighboring atoms. In contrast, any
metal has many relatively loose electrons which can wander freely
through its latticework. This is what makes metals good conductors.


THERMOELECTRICITY

    [Illustration: Figure 5 _Thermoelectric couple made from p- and
    n-type semiconductors. The impurity atoms (I) are different in each
    leg and contribute an excess or deficiency of valence electrons.
    Heat drives both holes and electrons toward the cold junction._]

    T_c WASTE HEAT OUT
    ELECTRONS
    LOAD
    COLD JUNCTION
    HOLES
    ELECTRONS
    _p_ SEMICONDUCTOR
    _n_ SEMICONDUCTOR
    HOT JUNCTION
    T_h HEAT IN
  Simplified Sketch of Atomic Lattice
    HOLE
    ELECTRON
    VALENCE BONDS
    SEMICONDUCTOR LATTICES
    I = Impurity atom

Figure 5 suggests the latticework of a _semiconductor_. It is called a
semiconductor because its conductivity falls far short of that of the
metals. The few electrons available for carrying electricity are
supplied by the deliberately introduced impurity atoms, which have more
than enough electrons to satisfy the valence-bond requirements of the
neighboring atoms. Without the impurities, we would have an insulator.
With them, we have an _n_-type semiconductor. The _n_ is for the extra
_negative_ electrons.

A _p_- or _positive_-type semiconductor is also included in Figure 5.
Here the impurity atom does not have enough valence electrons to satisfy
the valence-bond needs of the surrounding lattice atoms. The lattice has
been short-changed and is, in effect, full of _positive holes_.
Strangely enough, these holes can wander through the material just like
positive charges.

The electron-hole model does not have the precision the physicist likes,
but it helps us to visualize semiconductor behavior.

The Seebeck effect is demonstrated when pieces of _p_- and _n_-type
material are joined as shown in Figure 5. Heat at the hot junction
drives the loose electrons and holes toward the cold junction. Think of
the holes and electrons as gases being driven through the latticework by
the temperature difference. A positive and a negative terminal are thus
produced, giving us a source of power. The larger the temperature
difference, the bigger the voltage difference. Note that just one
thermocouple _leg_ can produce a voltage across its length, but
_couples_ made from _p_ and _n_ legs are superior.


Practical Thermoelectric Power Generators

The first nuclear-heated thermoelectric generator was built in 1954 by
the Atomic Energy Commission’s Mound Laboratory in Miamisburg, Ohio. It
used metal-wire thermocouples. In contrast, the SNAP 3 series
thermocouples shown in Figure 1 are thick lead telluride (PbTe)
semiconductor cylinders about two inches long. In contrast to the
thermocouple wires’ efficiency of less than 1%, SNAP 3 series generators
have overall efficiencies exceeding 5%. This value is still low compared
to the 35-40% obtained in a modern steam power plant, but SNAP 3
generators can operate unattended in remote localities where steam
plants would be totally unacceptable.

Look again at the thermoelements in Figure 1 and the schematic, Figure
5. Underlying the apparent simplicity of the thermoelectric generator
are extensive development efforts. The Figure 1 thermoelectric couple,
for example, shows the fruits of thousands of experimental brazing
tests. It turns out to be uncommonly difficult to fasten thermoelectric
elements to the so-called _hot shoe_ (metal plate) at the bottom. The
joint has to be strong, must withstand high temperatures, and must have
low electrical resistance. We see also that the elements are encased in
mica sleeves to prevent chemical disturbance of the delicate balance of
impurities in the semiconductor by the surrounding gases. A further
complication is the extreme fragility of the elements, and this has yet
to be overcome.

Nuclear thermoelectric generators that provide small amounts of
electrical power have already been launched into space aboard Department
of Defense satellites (Figure 12), installed on land stations in both
polar regions, and placed under the ocean.[6] Propane-fueled
thermoelectric generators, such as shown in Figure 6, are now on the
market for use in camping equipment, in ocean buoys, and in remote spots
where only a few watts of electricity are needed. The Russians have long
manufactured a kerosene lamp with thermoelements placed in its stack for
generating power in wilderness areas.

    [Illustration: Figure 6 GENERAL PURPOSE GENERATOR
    _Commercially available thermoelectric generators using propane fuel
    can provide more than enough electrical power to operate a portable
    TV set._
                      Courtesy Minnesota Mining & Manufacturing Company.]

For the present the role of thermoelectric power appears to be one of
special uses such as those just mentioned. When higher efficiencies are
attained, thermoelectric power may, one day, supplant dynamic conversion
equipment in certain low-power applications regardless of location.




                         THERMIONIC CONVERSION


“Boiling” Electrons Out of Metals

Like the thermoelectric element, the thermionic converter is a heat
engine. In its simplest form it consists of two closely spaced metallic
plates and resembles the diode radio tube. Whereas thermoelectric
elements depend on heat to drive electrons and holes through
semiconductors to an external electricity-using device or _load_, the
salient feature of the thermionic diode is _thermionic emission_,[7] or,
simply, the boiling-off of electrons from a hot metal surface. The
thermionic converter shown in Figure 7 powers a small motor when heated
by a torch.

Metals, as we have already seen, have an abundance of loosely bound
conduction electrons roaming the atomic latticework. These electrons are
easily moved by electric fields while within the metal; but it takes
considerably more energy to boil them out of the metal into free space.
Work has to be done against the electric fields set up by the surface
layer of atoms, which have unattached valence bonds on the side facing
empty space.

The energy required to completely detach an electron from the surface is
called the metal’s _work function_. In the case of tungsten, for
example, the work function is about 4.5 electron volts[8] of energy.

    [Illustration: Figure 7 _Vacuum type thermionic converter in
    operation._
                                      Courtesy General Electric Company.]

As we raise the temperature of a metal, the conduction electrons in the
metal also get hotter and move with greater velocity. We may think of
some of the electrons in a metal as forming a kind of _electron gas_.
Some electrons will gain such high speeds that they can escape the metal
surface. This happens when their kinetic energy exceeds the metal’s work
function.

Now that we have found a way to force electrons out of the metal, we
would like to make them do useful electrical work. To do this we have to
push the electrons across the gap between the plates as well as create a
voltage difference to go with the hoped-for current flow.


Reducing the Space Charge

The emitted or boiled-off electrons between the converter plates (Figure
8) form a cloud of negative charges that will repel subsequently emitted
electrons back to the emitter plate unless counteraction is taken. To
circumvent these _space charge_ effects, we fill the space between the
plates with a gas containing positively charged particles. These mix
with the electrons and neutralize their charge. The mixture of
positively and negatively charged particles is called a _plasma_.

The presence of the plasma makes the gas a good conductor. The emitted
electrons can now move easily across it to the collector where, to
continue the gas analogy, they condense on the cooler surface.

    [Illustration: Figure 8 THERMIONIC CONVERSION
    _Thermionic converters may be flat-plate types or cylindrical types.
    The cylindrical converter (a) is an experimental type for ultimate
    use in nuclear reactors._
                              Courtesy Los Alamos Scientific Laboratory.]

  a
    INSULATOR
    COOLED COLLECTOR
    INCANDESCENT URANIUM
    FUEL ELEMENT
    CESIUM PLASMA
    CIRCULATING COOLANT
    VACUUM INSULATOR
    CESIUM POOL
  b
    WASTE HEAT OUT
    LOAD
    ELECTRONS
    LOW WORK FUNCTION COLLECTOR
    T_c
    CESIUM ION
    PLASMA FILLED GAP
    BOILED OFF ELECTRONS
    HIGH WORK FUNCTION EMITTER
    T_c
    HEAT IN


Result: A Plasma Thermocouple

Unless a voltage difference exists across the plates, no external work
can be done. In the thermocouple the voltage difference was caused by
the different electrical properties of the _p_ and _n_ semiconductors.
Both the emitter and collector in the thermionic converter are good
metallic conductors rather than semiconductors, so a different tack must
be taken.

The key is the use of an emitter and a collector with different work
functions. If it takes 4.5 electron volts to force an electron from a
tungsten surface and if it regains only 3.5 electron volts when it
condenses on a collector with a lower work function, then a voltage drop
of 1 volt exists between the emitter and collector.

To summarize, then, the thermionic emission of electrons creates the
potentiality of current flow. The difference in work functions makes the
thermionic converter a power producer.

There is an interesting comparison that helps describe this phenomenon.
Consider the emitter to be the ocean surface and the collector a
mountain lake. The atmospheric heat engine vaporizes ocean water and
carries it to the cooler mountain elevations, where it condenses as rain
which collects in lakes. The lake water as it runs back toward sea level
then can be made to drive a hydroelectric plant with the gravitational
energy it has gained in the transit. The thermionic converter is similar
in behavior: hot emitter (corresponding to the sun-heated ocean); cooler
collector (lake); electron gas (water); different electrical voltages
(gravity). Without gravity the river would not flow, and the production
of electricity would be impossible.


Thermionic Power in Outer Space

Thermionic converters for use in outer space may be heated by the sun,
by decaying radioisotopes, or by a fission reactor. Thermionic
converters can also be made into concentric cylindrical shells (Figure
8a) and wrapped around the uranium fuel elements in nuclear reactors.
The waste heat in this case would be carried out of the reactor to a
separate radiator[9] by a stream of liquid metal. Since thermionic
converters can operate at much higher temperatures than thermoelectric
couples or dynamic power plants, the radiator temperature, T_c, will
also be higher. Consequently, space power plants using thermionic
converters will have small radiators. Once thermionic converters are
developed which have high reliability and long life, they will provide
the basis for a new series of lighter, more efficient space power
plants.




                     MAGNETOHYDRODYNAMIC CONVERSION


Big Word, Simple Concept

Magnetohydrodynamic (MHD) conversion is very unlike thermoelectric or
thermionic conversion. The MHD generators use high-velocity electrically
conducting gases to produce power and are generically closer to dynamic
conversion concepts. The only concept they carry forward from the
preceding conversion ideas is that of the _plasma_, the electrically
conducting gas. Yet they are commonly classified as _direct_ because
they replace the rotating turbogenerator of the dynamic systems with a
stationary pipe or _duct_.

    [Illustration: Figure 9 _In the MHD duct (a), the electrons in the
    hot plasma move to the right under influence of force F in the
    magnetic field B. The electrons collected by the right-hand side of
    the duct are carried to the load. In a wire in the armature of a
    conventional generator (b) the electrons are forced to the right by
    the magnetic field._]

  a
    MHD Duct
    HOT PLASMA IN
    COOL GAS OUT TO RADIATOR
    Magnetic Field
    LOAD
    ELECTRONS
  b
    CONVENTIONAL GENERATOR
    SHAFT
    LOAD
    Magnetic Field
    ARMATURE WIRE
    ELECTRONS

In the conventional dynamic generator, an electromotive force is created
in a wire that cuts through magnetic lines of force, as shown in Figure
9b. It may be helpful to visualize the conduction electrons as leaving
one end of the wire and moving to the other under the influence of the
magnetic field.

The force on the electrons in the wire is given by

                                  F = qvB

  where
    F = the force (in newtons[10])
    q = the charge on the electron (1.6 × 10⁻¹⁹ coulomb)
    v = the wire’s velocity (in meters per second)
    B = the magnetic field strength (in webers per square meter[10])

The surge of electrons along the length of the wire sets up a voltage
difference across the ends of the wire. A generator uses this difference
to convert the kinetic energy of the moving wire or armature into
electrical energy. The wire is kept spinning by the shaft which is
connected to a turbine driven by steam or water.

Let us try to eliminate the moving part, the generator armature. What we
need is a moving conductor that has no shaft, no bearings, no wearing
parts. The substance that meets these requirements is the plasma.
Examine Figure 9a. The MHD generator substitutes a moving, conducting
gas for the wires. Under the influence of an external magnetic field,
the conduction electrons move through the plasma to one side of the duct
which carries electrical power away to the load.

The MHD generator gets its energy from an expanding, hot gas; but,
unlike the turbogenerator, the heat engine and generator are united in
the static duct. The gradual widening of the duct shown in Figure 9a
reflects the lower pressure, cooler plasma at the duct’s end. Some of
the plasma’s thermal energy content has been tapped off by the duct’s
electrodes as electrical power.


The Fourth State of Matter

Plasma can be created by temperatures over 2000°K. At this temperature
many high-velocity gas atoms collide with enough energy to knock
electrons off each other and thus become ionized. The material thus
created, shown as a glowing gas in Figure 10, does not behave
consistently as any of the three familiar states of matter: solid,
liquid, or gas. Plasma has been called a _fourth state of matter_. Since
we have difficulty in containing such high temperatures on earth, we
adopt the strategy of _seeding_. In this technique gases that are
ordinarily difficult to ionize, like helium, are made conducting by
adding a fraction of a percent of an alkali metal such as potassium.
Alkali metal atoms have loosely bound outer electrons and quickly become
ionized at temperatures well below 2000°K.

    [Illustration: Figure 10 _Glowing plasma in experimental device at
    General Atomic’s John Jay Hopkins Laboratory, San Diego. T-shaped
    plasma gun provides data for research in thermonuclear fusion._
                       Courtesy Texas Atomic Energy Research Foundation.]

A helium-potassium mixture is a good enough conductor for use in an MHD
generator. In this plasma the electrons move rapidly under the influence
of the applied fields, though not as well as in metals. The positive
ions move in the opposite direction from the electrons, but the
electrons are much lighter and move thousands of times faster thus
carrying the bulk of the electrical current.


MHD Power Prospects

The MHD duct is not a complete power plant in itself because, after
leaving the duct, the stream of gas must be compressed, heated, and
returned to the duct. Very high temperature materials and components
must be developed for this kind of service. Moreover, while the duct is
simple in concept, it must operate at very high temperatures in the
presence of the corrosive alkali metals. This presents us with difficult
materials problems. When the problems are solved, probably within the
next decade, MHD power plants should be able to provide reliable power
with high efficiency. They may then serve in large space power plants,
and, most important, they may provide cheaper electricity for general
use through their higher temperatures and greater efficiencies.




                           CHEMICAL BATTERIES


Electricity from the Chemical Bond

If you vigorously knead a lemon to free the juices and then stick a
strip of zinc in one end and a copper strip in the other, you can
measure a voltage across the strips. Electrons will flow through the
load without the inconvenience of having to supply heat. You have made
yourself a chemical battery.

The chemical battery was the first direct conversion device. Two hundred
years ago it was the scientists’ only continuous source of electricity.

Since the chemical battery does not need heat for its operation, it is
logical to ask what makes the current flow. Where does the energy come
from?

The battery has no semiconductors, but, like the thermoelectric couple
and the thermionic diode, it uses dissimilar materials for its
electrodes. A conducting fluid or solid is also present to provide for
the passage of current between the electrodes. In the example of the
lemon, the copper and zinc are the dissimilar electrodes, and the lemon
juice is the conducting fluid or _electrolyte_ that supplies positive
and negative ions. The battery derives its energy from its complement of
chemical fuel. The voltage difference arises because of the different
strengths of the chemical bonds. The chemical bond is basically an
electrostatic one; some atoms have stronger electrical affinities than
others.


Chemical Reactions Used in Batteries and Fuel Cells

Consider the following chemical reactions of common batteries together
with some fuel cell reactions which will be discussed further in the
next section.

  Battery Reactions
    Pb + PbO₂ + 2H₂SO₄ ⇔ 2PbSO₄ + 2H₂O
    Fe + NiO₂ ⇔ FeO + NiO
    Zn + AgO + H₂O ⇔ Ag + Zn(OH)₂
    Pb + Ag₂O ⇔ PbO + 2Ag
  Fuel Cell Reactions
    2LiH ⇔ 2Li + H₂
    2CuBr₂ ⇔ 2CuBr + Br₂
    2H₂ + O₂ ⇔ 2H₂O (Bacon cell)
    PbI₂ ⇔ Pb + I₂

In principle all these reactions are the same as those going on inside
the lemon, although each type of cell produces a slightly different
voltage because of the varying chemical affinities of the atoms and
molecules involved. There are literally hundreds of materials which can
be used for electrolytes and electrodes.

No heat needs to be added as the electrostatic chemical bonds are broken
and remade in a battery to generate electrical power. The chemical
reaction energy is transferred to the electrical load with almost 100%
efficiency. The Carnot cycle is no limitation here; only “cold”
electrostatic forces are in action. The reactions cannot go on forever,
however, because the battery supplies the energy converter with a very
limited supply of fuel. Eventually the fuel is consumed and the voltage
drops to zero. This deficiency is remedied by the fuel cell in which
fuel is supplied continuously.


An Old Standby in Outer Space

Almost every satellite and space vehicle has a chemical battery aboard.
It is not there so much for continuous power production but as a
rechargeable electrical accumulator or reservoir to provide electricity
during peak loads. The battery is also needed to store energy for use
during the periods when solar cells are in the earth’s shadow and
therefore inoperative. In this capacity the dependable old battery
serves the most modern science very well indeed.




              THE FUEL CELL: A CONTINUOUSLY FUELED BATTERY


Potential Fuels

The battery has a very close relative, the fuel cell. Unlike the battery
the fuel cell has a continuous supply of fuel.

    [Illustration: Figure 11 _This diagram shows how a hydrogen-oxygen
    fuel cell works. The chemical battery works in the same way, except
    that the chemicals are different and are not continuously supplied
    from outside the cell. The water produced by the H-O cell shown can
    be used for drinking on spaceships._]

  ANODE H₂ IN
  CATHODE O₂ IN
  ELECTRONS
  LOAD
  KOH ELECTROLYTE
  K⁺ ION
  OH⁻ ION
  NEGATIVE ION FLOW
  40H⁻ + 2H₂ ⇒ 4H₂O + 4e
  O₂ + 2H₂O + 4e ⇒ 40H⁻

The hydrogen-oxygen cell of Figure 11 is typical of all fuel cells. It
essentially burns hydrogen and oxygen to form water. If the hydrogen and
oxygen can be supplied continuously and the excess water drained off, we
can greatly extend the life of the battery. The fuel cell accomplishes
this. Fueled _electrical_ cell would be more descriptive since the
physical principles are identical with those of the battery.

Perhaps the most challenging task contemplated for the fuel cell is to
bring about the consumption of raw or slightly processed coal, gas, and
oil fuels with atmospheric oxygen. If fuel cells can be made to use
these abundant fuels, then the high natural conversion efficiency of the
fuel cells will make them economically superior to the lower efficiency
steam-electric plants now in commercial service.

So far we have dwelt on the fuel cell as a cold energy conversion device
that is _not_ limited by the Carnot efficiency. A variation on this
theme is possible. Take a hydrogen iodide (HI) cell, and heat the HI to
2000°K. Some of the HI molecules will collide at high velocities and
dissociate into hydrogen and iodine: 2HI = H₂ + I₂; the higher the
temperature, the more the dissociation. By separating the hydrogen and
iodine gases and returning them for recycling to the fuel cell where
they are recombined, we have eliminated the fuel supply problem and
created a _regenerative_ fuel cell. We have, however, also reintroduced
the heat engine and the Carnot cycle efficiency. The thermally
regenerative fuel cell is a true heat engine using a dissociating gas as
the working fluid.


Scheme for Project Apollo

Most of the impetus for developing the fuel cell as a practical device
comes from the space program. The cell has admirable properties for
space missions that are less than a few months in duration. It is a
clean, quiet, vibrationless source of energy. Like the battery it has a
high electrical overload capacity for supplying power peaks and is
easily controlled. It can even provide potable water for a crew if the
Bacon H - O cell is used. For short missions where large fuel supplies
are not needed, it is also among the lightest power plants available.

These compelling advantages have led the National Aeronautics and Space
Administration to choose the fuel cell for some of the first manned
space ventures. Project Apollo, the manned lunar landing mission, is the
most notable example. Here the fuel cell will be not only an energy
source, but also part of the ecological cycle which keeps the crew
alive.


                               Problem 4

  A manned space vehicle requires an average of 2 electrical kilowatts.
  A nuclear reactor thermoelectric plant having a mass of 1000
  kilograms, including shielding, can supply this power for 10,000
  hours. The basic fuel cell has a mass of 50 kilograms and consumes ½
  kilogram of chemicals per hour. The chemical containers weigh 25
  kilograms. What is the longest mission where the total weight of the
  fuel cell will be less than the weight of the nuclear power plant?




                              SOLAR CELLS


Photons as Energy Carriers

All our fossil fuels, such as coal and oil, owe their existence to the
solar energy stream that has engulfed the earth for billions of years.
The power in this stream amounts to about 1400 watts per square meter at
the earth, nearly enough to supply an average home if all the energy
were converted to electricity. The problem is to get the sun’s rays to
yield up their energy with high efficiency.

The sun’s visible surface has a temperature around 6000°K. Any object
heated to this temperature will radiate visible light mostly in the
yellow-green portion of the spectrum (5500 A[11]). Our energy conversion
device should be tuned to this wavelength.

The energy packets arriving from the sun are called photons. They
travel, of course, at the speed of light, and each carries an amount of
energy given by

                               E = hf = hc/λ

  where
    E = energy (in joules)
    h = Planck’s constant (6.62 × 10⁻³⁴ joule-second)
    f = the light’s frequency (in cycles per second = c/λ)
    c = the velocity of light (300,000,000 meters per second)
    λ = the wavelength (in meters)

Using the fact that an angstrom unit is 10⁻¹⁰ meter, the energy of a
5500 A photon could be calculated as

         E = hf = hc/λ = (6.62 × 10⁻³⁴ × 3.00 × 10⁸)/(5.50 × 10⁻⁷)
                 = 3.61 × 10⁻¹⁹ joule = 2.2 electron volts

Comparing this result, 2.2 electron volts, with the energies required to
cause atomic ionization or molecular dissociation (an electron volt or
so), we see that it is in the right range to actuate direct conversion
devices based on such phenomena.


Harnessing the Sun’s Energy

Historically, the sun’s energy has most often been used by concentrating
it with a lens or mirror and then converting it to heat. We could do
this and run a heat engine, but a more direct avenue is open.

About a decade ago it was found that the junction between _p_ and _n_
semiconductors would generate electricity if illuminated. This discovery
led to the development of the _solar cell_, a thin, lopsided sandwich of
silicon semiconductors. As shown in Figure 12, the top semiconductor
layer exposed to the sun is extremely thin, only 2.5 microns. Solar
photons can readily penetrate this layer and reach the junction
separating it from the thick main body of the solar cell.

    [Illustration: Figure 12 THE SOLAR CELL
    _The photograph shows the solar cell in use on a satellite. The
    spherical, radioisotope, thermoelectric generator at the bottom of
    the satellite is used to supplement the solar cells. In the solar
    cell, hole-electron pairs are created by solar photons in the
    vicinity of a p-n junction._
             Courtesy U. S. Air Force and National Aeronautics and Space
                                                         Administration.]

  _p_ SILICON
  _n_ SILICON
  ELECTRON-MOLE PAIRS
  JUNCTION
  PHOTONS FROM SUN OR RADIOISOTOPE
  ELECTRONS
  ENERGY OUT

Whenever _p-_ and _n-_type semiconductors are sandwiched together a
voltage difference is created across the junction. The separated holes
and electrons in the two semiconductor regions establish this electric
field across the junction. Unfortunately, there are usually no current
carriers in the immediate vicinity of the junction so that no power is
produced.

The absorption of solar photons in the vicinity of the junction will
create current carriers, as the photons’ energy is transformed into the
potential energy of the hole-electron pairs. These pairs would quickly
recombine and give up their newly acquired potential energy if the
electric field existing across the junction did not whisk them away to
an external load.

The solar cell produces electricity when hole-electron pairs are formed.
Any other phenomenon that creates such pairs will also generate
electricity. The source of energy is irrelevant so long as the current
carriers are formed near the junction. Thus, particles emitted by
radioactive atoms can also produce electricity from solar cells,
although too much bombardment by such particles can damage the cell’s
atomic structure and reduce its output.

The solar cell is not a heat engine. Yet it loses enough energy so that
the sun’s energy is converted at less than 15% efficiency. Losses
commonly occur because of the recombination of the hole-electron pairs
before they can produce current, the absorption of photons too far from
the junction, and the reflection of incident photons from the top
surface of the cell. Despite these losses solar cells are now the
mainstay of nonpropulsive space power.




                           NUCLEAR BATTERIES


Energy from Nuclear Particles

As we have seen, solar cells are able to convert the kinetic energy of
charged nuclear particles directly into electricity, but a simpler and
more straightforward way of doing this exists. This involves direct use
of the flow of charged particles as current.

The _nuclear battery_ shown in Figure 13 performs this trick. A central
rod is coated with an electron-emitting radioisotope (a beta-emitter;
say, strontium-90). The high-velocity electrons emitted by the
radioisotope cross the gap between the cylinders and are collected by a
simple metallic sleeve and sent to the load. Simple, but why don’t space
charge effects prevent the electrons from crossing the gap as they do in
the thermionic converter? The answer lies in the fact that the nuclear
electrons have a million times more kinetic energy than those boiled off
the thermionic converter’s emitter surface. Consequently, they are too
powerful to be stopped by any space charge in the narrow gap.

Nuclear batteries are simple and rugged. They generate only microamperes
of current at 10,000 to 100,000 volts.

    [Illustration: Figure 13 A NUCLEAR BATTERY
    _The nuclear battery depends upon the emission of charged particles
    from a surface coated with a radioisotope. The particles are
    collected on another surface._]

  ENERGY OUT
  INSULATOR
  LAYER OF BETA-EMITTING RADIOISOTOPE
  VACUUM


Double Conversion

In the earlier description of the energy conversion matrix, we saw that
we could go through the energy transformation process repeatedly until
we obtained the kind of energy we wanted. This is exemplified in a type
of nuclear battery which uses the so-called _double conversion_
approach. First, the high-velocity nuclear particles are absorbed in a
phosphor which emits visible light. The photons thus produced are then
absorbed in a group of strategically placed solar cells, which deliver
electrical power to the load. Although efficiency is lost at each energy
transformation, the double conversion technique still ends up with an
overall efficiency of from 1 to 5%, an acceptable value for power
supplies in the watt and milliwatt ranges.




                           ADVANCED CONCEPTS


Ferroelectric and thermomagnetic conversion are subtle concepts which
depend upon the gross alteration of a material’s physical properties by
the application of heat. Devices employing such concepts are true heat
engines. Instead of the gaseous and electronic working fluids used in
the other direct conversion concepts, the ferroelectric and
thermomagnetic concepts employ patterns of atoms and molecules that are
actually rearranged periodically by heat.


Ferroelectric Conversion

Ferroelectric conversion makes use of the peculiar properties of
_dielectric_[12] materials. Barium titanate, for example, has good
dielectric properties at low temperatures, but, when its temperature is
raised to more than 120°C, the properties get worse rapidly. We cannot
discuss dielectric behavior thoroughly in this booklet; suffice it to
say that in this process heat is absorbed in a realignment of molecules
within the barium titanate latticework.

If we now place a slab of barium titanate between the two plates of an
electrical condenser and charge the condenser, as shown in Figure 14, we
have a unique way of converting heat into electricity directly. When the
barium titanate is heated above its _Curie point_[13] of 120°C, the
condenser’s capacitance is radically reduced as the dielectric constant
falls. The condenser is forced to discharge and move electrons through
an external circuit consisting of the load and the original source of
charge. Useful electrical energy is delivered during this step. Figure
14 shows the process schematically and mathematically. When the
dielectric is cooled, waste heat is given up by the barium titanate, and
the cycle is complete.

    [Illustration: Figure 14 FERROELECTRIC ENERGY CONVERSION
    _The ferroelectric converter is really an electrical capacitor whose
    capacitance is changed by temperature. When heat is added,
    capacitance drops, voltage rises, and the capacitor is made to
    discharge through the load. CYCLE: ① Switch #1 closed, #2 open.
    Condenser charges from battery to charge Q₂ at voltage V₁ with
    capacity C₁. ② All switches open. Heat added, capacity changes from
    C₁ to C₂, charge remains constant, so voltage changes from V₁ to V₂.
    ③ Switch #2 closed, #1 open. Condenser discharges through load and
    battery to charge Q₁ at voltage V₁ with capacity C₂. ④ All switches
    open. Heat rejected, capacity changes from C₂ to C₁, charge remains
    constant, so voltage changes from V₁ to V₀. CYCLE THEN REPEATS.
    Energy supplied from battery each cycle is E₁. Energy delivered to
    load and battery each cycle is E₂. Net energy converted is then
    E₂ - E₁, the difference in the shaded areas._]

  (a) CIRCUIT
    HEAT IN
    BARIUM TITANATE DIELECTRIC
    WASTE HEAT OUT
    SWITCH #2
    LOAD
    SWITCH #1
    BATTERY
  (b) CYCLE DIAGRAM
    charge
    volts
    Q₂, Q₁, E₁, E₂, V₀ V₁  V₂
    GENERAL INFORMATION:
      C₂ < C₁
      V = Q/C


Thermomagnetic Conversion

The _analog_[14] of ferroelectricity is ferromagnetism. A converter
employing similar principles to those in ferroelectricity can be made
using an electrical _inductance_ with a ferromagnetic core. When the
temperature of the ferromagnetic material is raised above its Curie
point, its magnetic _permeability_ drops quickly, causing the magnetic
field to collapse partially. Energy may be delivered to an external load
during this change. Instead of energy being stored in an electrostatic
field, it is stored in a magnetic field.

Ferroelectric and thermomagnetic conversion both represent a class of
energy transformations which involve internal molecular or crystalline
rearrangements of solids. There is no change of phase as in a steam
engine, but the energy changes are there nevertheless. In thermodynamics
such internal geometrical changes are called _second-order_ transitions,
as opposed to the _first-order_ transitions observed with heat engines
using two-phase working fluids like water/steam.


On the Frontier

Other potential energy conversion schemes are being investigated by
scientists and engineers. Those listed in the Energy Conversion Matrix
(Figure 2) only scratch the surface.

In particular, we are just learning how to manipulate photons. There are
photochemical, photoelectric, and even photomechanical transformations.
These have hardly been tapped.

Consider the reaction when an electron and its antimatter equivalent,
the positron, meet. They mutually annihilate each other in a burst of
energy! This energy will be harnessed someday.

What energy conversion device are we going to use to completely convert
mass into energy? The energy requirements for interstellar exploration
are so great that these voyages will be impossible unless a new device
is found that can completely transform mass into energy.

Then again, we haven’t the faintest idea of how to control gravitational
energy, but we may learn.

The panorama is endless.


                               Problem 5

  A 1,000,000-kilogram spaceship takes off for Alpha Centauri, our
  nearest star, 4.3 light years away. If it accelerates to nine-tenths
  the velocity of light, what is its kinetic energy? How much fuel mass
  will have to be completely converted to energy to acquire this
  velocity?




                          SUGGESTED REFERENCES


Articles

Fuel Cells, Leonard G. Austin, _Scientific American_, 201: 72 (October
      1959). A survey of the different types.

Nuclear Power in Outer Space, William R. Corliss, _Nucleonics_, 18: 58
      (August 1960). A review of all nuclear space power plants.

Fuel Cells for Space Vehicles, M. G. Del Duca, _Astronautics_, 5: 36
      (March 1960).

Fuel Cells, E. Gorin and H. L. Recht, _Chemical Engineering Progress_,
      55: 51 (August 1959).

Thermionic Converters, Karl G. Hernqvist, _Nucleonics_, 17: 49 (July
      1959).

The Revival of Thermoelectricity, Abram F. Joffe, _Scientific American_,
      199: 31 (November 1958). Excellent historical and technical
      review.

The Photovoltaic Effect and Its Utilization, P. Rappaport, _RCA Review_,
      20: 373 (September 1959). Recommended for advanced students.

The Prospects of MHD Power Generation, Leo Steg and George W. Sutton,
      _Astronautics_, 5: 22 (August 1960).

Conversion of Heat to Electricity by Thermionic Emission, Volney C.
      Wilson, _Journal of Applied Physics_, 30: 475 (April 1959).
      Recommended for advanced students.

Improved Solar Cells Planned for IMP-D, R. D. Hibben, _Aviation Week &
      Space Technology_, 83: 53 (July 26, 1965).

Thin-film Solar Cells Boost Output Ratio, P. J. Klass, _Aviation Week &
      Space Technology_, 83: 67 (November 29, 1965).


Books

_Direct Conversion of Heat to Electricity_, Joseph Kaye and John A.
      Welsh, John Wiley & Sons, Inc., New York 10016, 1960, 387 pp.,
      $11.50. Recommended for advanced students.

_Selected Papers on New Techniques for Energy Conversion_, Sumner N.
      Levine, (Ed.), Dover Publications, Inc., New York 10014, 1961,
      444 pp., $3.00. A reprinting of many classical papers on direct
      conversion.

_Energy Conversion for Space Power_, Nathan W. Snyder, (Ed.), Academic
      Press, Inc., New York 10003, 1961, 779 pp., $8.50. A collection of
      American Rocket Society papers.

_Man and Energy_, Alfred Rene Ubbelohde, George Braziller, New York
      10016, 1955, 247 pp., $5.00 (hardback); $1.25 (paperback), from
      Penguin Books, Inc., Baltimore, Maryland 21211. A popular
      treatment of energy and power.


Motion Pictures

The following films are produced by Educational Services, Inc., and are
available from Modern Learning Aids, A Division of Modern Talking
Picture Service, Inc., 3 East 54th St., New York 22, New York.

  _Energy and Work_, 0311, 29 minutes, $150.
  _Mechanical Energy and Thermal Energy_, 0312, 27 minutes, $120.
  _Conservation of Energy_, 0313, 27 minutes, $150.
  _Photo-Electric Effect_, 0417, 28 minutes, $220.




                          ANSWERS TO PROBLEMS


First, mechanical energy drives the car’s electric generator. Second,
the electrical energy is converted into chemical energy when the battery
is recharged.


                       *   *   *   *   *   *   *

From the kinetic energy equation we get

                              v = √(2 E/m)

Since the engine is 25% efficient, the energy available to propel the
car is 48,000 × 0.25 or 12,000 joules. So

           v = √(24,000/1,000) = 2√6 = 4.9 meters per second


                       *   *   *   *   *   *   *

                e = (300 - 20)/300 = 14/15 = 0.93 = 93%

The crossover point, t, in hours is found by equating the nuclear power
plant mass and that of the fuel cell with its associated fuel. The
equation is

                          1000 = 50 + 25 + ½t
                        t = 1850 hours = 77 days


                       *   *   *   *   *   *   *

        E = ½ mv² = (10⁶(0.9 × 3 × 10⁸)²)/2 = 3.6 × 10²² joules

The ship will use the same amount of energy to decelerate at its
destination. Note that this calculation assumes a perfect efficiency in
converting the energy of matter annihilation into the kinetic energy of
the space ship. The mass consumed is

           m = E/c² = (3.6 × 10²²)/(9 × 10¹⁶) = 4.0 × 10⁵ kg

almost half the spaceship mass.




                               Footnotes


[1]Systems for Nuclear Auxiliary Power.

[2]Described in this booklet.

[3]Magnetohydrodynamics.

[4]The Kelvin temperature scale starts with zero at absolute zero
    instead of at the freezing point of water. Therefore, °K = °C + 273;
    °K = ⁵/₉ (°F + 460).

[5]Termed _valence_ or _conduction_ electrons, these are responsible for
    chemical properties, bonds with other atoms, and the conduction of
    electricity.

[6]See the companion Understanding the Atom booklet, _Power from
    Radioisotopes_.

[7]Discovered by Thomas Edison in 1883.

[8]An electron volt is equal to the kinetic energy acquired by an
    electron accelerated through a potential difference of 1 volt. It is
    equal to 1.6 × 10⁻¹⁹ joule.

[9]In outer space, waste heat must be radiated away. The rate at which
    heat is radiated is proportional to the fourth power of T_c
    (Stefan-Boltzmann law).

[10]The newton and the weber are mks (meter-kilogram-second) units.

[11]An angstrom unit (A) is a unit of distance measurement equal to
    10⁻¹⁰ meter.

[12]Dielectric materials are nonconductors such as are those used
    between the plates of a condenser to increase its electrical
    capacity.

[13]The Curie point is the temperature at which a material’s crystalline
    structure radically changes and becomes less orderly.

[14]Ferroelectricity and ferromagnetism are very similar. The equations
    describing these phenomena are almost identical except that
    capacitance is replaced by its magnetic analog, inductance, and so
    on.


This booklet is one of the “Understanding the Atom” Series. Comments are
invited on this booklet and others in the series; please send them to
the Division of Technical Information, U. S. Atomic Energy Commission,
Washington, D. C. 20545.

Published as part of the AEC’s educational assistance program, the
series includes these titles:

  _Accelerators_
  _Animals in Atomic Research_
  _Atomic Fuel_
  _Atomic Power Safety_
  _Atoms at the Science Fair_
  _Atoms in Agriculture_
  _Atoms, Nature, and Man_
  _Careers in Atomic Energy_
  _Computers_
  _Controlled Nuclear Fusion_
  _Cryogenics, The Uncommon Cold_
  _Direct Conversion of Energy_
  _Fallout From Nuclear Tests_
  _Food Preservation by Irradiation_
  _Genetic Effects of Radiation_
  _Index to the UAS Series_
  _Lasers_
  _Microstructure of Matter_
  _Neutron Activation Analysis_
  _Nondestructive Testing_
  _Nuclear Clocks_
  _Nuclear Energy for Desalting_
  _Nuclear Power and Merchant Shipping_
  _Nuclear Power Plants_
  _Nuclear Propulsion for Space_
  _Nuclear Reactors_
  _Nuclear Terms, A Brief Glossary_
  _Our Atomic World_
  _Plowshare_
  _Plutonium_
  _Power from Radioisotopes_
  _Power Reactors in Small Packages_
  _Radioactive Wastes_
  _Radioisotopes and Life Processes_
  _Radioisotopes in Industry_
  _Radioisotopes in Medicine_
  _Rare Earths_
  _Reading Resources in Atomic Energy_
  _Research Reactors_
  _SNAP, Nuclear Space Reactors_
  _Sources of Nuclear Fuel_
  _Synthetic Transuranium Elements_
  _The Atom and the Ocean_
  _The Chemistry of the Noble Gases_
  _The First Reactor_
  _Whole Body Counters_
  _Your Body and Radiation_

A single copy of any one booklet, or of no more than three different
booklets, may be obtained free by writing to:

            USAEC, P. O. BOX 62, OAK RIDGE, TENNESSEE 37830

Complete sets of the series are available to school and public
librarians, and to teachers who can make them available for reference or
for use by groups. Requests should be made on school or library
letterheads and indicate the proposed use.

Students and teachers who need other material on specific aspects of
nuclear science, or references to other reading material, may also write
to the Oak Ridge address. Requests should state the topic of interest
exactly, and the use intended.

In all requests, include “Zip Code” in return address.

                Printed in the United States of America
USAEC Division of Technical Information Extension, Oak Ridge, Tennessee
                                May 1968




                          Transcriber’s Notes


—Silently corrected a few typos.

—Modified some image references to reflect the pageless flowable eBook
  format.

—Retained publication information from the printed edition: this eBook
  is public-domain in the country of publication.

—In the text versions only, text in italics is delimited by
  _underscores_.