John Pazmino
 NYSkies Astronomy Inc
 2018 September 14initial
 2018 Novrmber 14 current

    Most home astronomers know basic physics that says matter can not 
be created or destroyed, but only commuted from one form to an other. 
For all human history this premise seemed true. Even in the case of 
combustion, where the wood 'disappears' it is conceptually possible to 
collect the ash, charred pieces, smoke and find that their mass equals 
the original wood. We merely changed it into smoke, &c. 
    Einstein in his theory of general relativity showed that mass and 
energy can be exchanged by the equation E=mc2. This equivalence ws 
demonstrated handily in atomics but it remained out of mind for 
ordinary life.
    More than the equivalence, Einstein showed that energy comes from 
mass. To generate energy we must change mass into it. It also  works 
the other way, but so far only in atomic labs for minuscule 

Awareness of E=mc2
    Perhaps the first awareness that Einstein's equation affects 
everyday life was the atom bombs of World War II. A capsule about the 
size of a large chemical bomb contained a mass of uranium or thorium 
comparable in size to a softball. It  yielded an explosion of some 15 
THOUSAND tons of TNT.  One single bomb levels an entire city and 
killed some 100,000 people in an instant. Since the War efforts were 
done to extract energy from uranium in a slow steady practical manner 
for producing electric, steam, or mechanical work. By the 1950s the 
first American atomic power plants were running. Memory of the wartime 
use of atomic power lingered, even to today, and most of the general 
public still thinks of atomic energy in terms of atomic bombs. 
    astronomers applied Einstein's formula to stars. stars apparently 
shined for ever by an unknown process of energy production. By 1950 we 
developed the the nuclear reactions that in fact do generate energy, 
radiation, in stars. A star converts a small percent of its mass of 
hydrogen into radiant energy, sufficient to last billions of years. 
The lifetime emission of starlight (of all wavelengths) consumes only 
some 7/10 percent of the star's original hydrogen mass by E=mc2. 
    Home astronomers easily relate to the stellar energy process and 
routinely work out the conversion formula for it. But it is 'far away' 
and not close to hand as an example of Einstein's physics. 
    Isn't there a earthly energy generation method that better 
illustrates the formula? 

Energy production
    We usually think of energy as something contained in a fuel. it is 
released for useful work when the fuel is consumed, typicly by a 
combustion process. Fuels are rated by their 'hearing value' or 
'energy content', based on the customary means of consuming it, like 
in a standard steam boiler or vehicle motor. 
    A device that derives its energy from a source of heat and turns 
it into work is a 'heat engine'. The source is a reservoir, like from 
continuous combustion, at a high temperature. After the work is taken 
out from the heat energy, some leftover heat is rejected at a lower 
temperature. There is no such a thing as a machine that converts all 
of the input heat energy into work. some heat always must be discarded 
    A minuscule amount of the fuel's original mass is converted into 
the released energy. The amount is too tiny to measure, leading to the 
idea that no mass was lost. Once the energy is released, the fuel is  
now waste material to discard from the combustion device. If this 
waste could be completely and thoroly collected and weighed, it would 
be a little less heavy than the original fuel. The difference turned 
into the extracted energy.u. 
    Motors and engines throw away a huge fraction of the ingredient 
energy, losing it from doing useful work. In the early days of the 
steam engine it was assumed the first models were too loosely built, 
with leaks and weak insulation. Improvements soon tempered off at some 
seeming maximum fraction of energy going to the mechanical work. There 
always was a frustrating amount of loss, being money thrown away from 
the cost of obtaining the fuel. 
    In the early 1800s we learned that there is a natural limit on the 
fraction of input heat that can be converted to work, expressed as the 
Carnot (karr-NOH) ratio. This is 

    (max fraction) = (1) - ((lo)) / (high temp)) 

where the temperatures are in Kelvin, baking off of absolute zero. 
Kelvin = Celsius + 273. As example if an engine burns fuel at 400C and 
exhausts to the open air at 150C, the maximum fraction of furl's 
energy that can perform work is 

    (max frac) = (1) - ((150 + 273) / (400 + 273)) 
               = ((673) - ((423) / (673)) 
               = (1) - (0.6285)
               = (0.3715) 
              -> ~37% 

    The other 63% of the input energy is discarded as lost energy 
unavailable for work. 
    Real machines do not perform up to the Carnot maximum, having 
internal leaks, friction, inertia, poor maintenance, &c. The realized 
efficiency may be 5-15 points LESS THAN the Carnot limit. 
    I noted the low temperature is 150C 'in open air'. This is the 
temperature of the exhaust gases leaving the machine, not the 
temperature of the surrounding air. Engine exhaust is typicly much 
hotter than the air it is rejected into. Once the gases are freeD into 
the air they no longer participate in the energy production. 
Eventually they are cooled to ambient temperature within the air. 
    There are nonthermal ways to generate energy, like chemical 
batteries water wheels, wind mills, helioelectric cells. These do not 
suffer from the Carnot limit. A water power station can extract as 
electric over 90% of the energy of the influent water. Helioelectric 
cells convert up to 45%,  of solar radiation to electric. 

Con Edison
    Commercial electric service on Earth began in 1882 when Tom 
Edison opened his electric company in Lower Manhattan. Before then, 
electric was used on-site by factories, ships, stores, street lamps, 
exhibitions, businesses, but not for open subscription from the 
public. At first he served commercial customers, there being few 
residences in Lower Manhattan. 
    Edison's electric was produced as direct current, DC, replicating 
electric provided by chemical batteries. Edison acquired electric 
companies operating in other parts of New York City, whence the modern 
name Consolidated Edison Company of New York. This is routinely 
shortened to Con Edison or Con Ed. It built more power plants on 
Manhattan and took over those of merged companies. These were 
connected together to allow flow of electric from any plant to any 
part of Con Ed's territory. 
    Con Edison ran in isolation from other power companies, a typical 
practice at that time.  All of its electric needs were supplied by its 
own power stations. 
    Con Edison in the 1920s began to purchase extra electric from 
neighboring companies via high voltage power lines. It found that DC 
was not practical  for long distance transfer of electric and it 
started a conversion to alternating current, AC. Con Ed continues the 
delivery of DC to its customers until the late 1970s. Altho today all 
electric is handled as AC, New York City has the world's largest DC 
customer load. These customers, with assistance from Con Edison, 
attach to the AC mains by an on-site rectifier. 
    In the 1990s by federal mandate, electric companies in the US had 
to become either producers or providers of electric, but not both. A 
company doing both devested one or the other function, usually by 
selling or retiring the associated assets. Con Edison released its 
power plants and kept its customers. It now buys all electric from 
companies that chose to be electric producers. 
    Electric companies horse-traded assets, creating a bizarre 
alignment of territory. For example, some companies in Maine sold 
their power plants to, uh, Florida Power & Light, at the other end of 
the East Coast. An other is Con Ed itself, taking over customers of 
companies in, uh, Massachusetts and New Hampshire. 
    Con Edison had several ancient plants from the dawn of the 20th 
century that were demolished or refurbished for other use. East River 
and Hudson Avenue stations now generate street steam.. Waterside and 
Kent Avenue were torn down. 

Good gumbo 
    In the 1980s my office worked closely with electric companies and 
collected an astounding variety of information about their operations. 
    Among the data my office gathered were the detailed workings of 
Con Edison's power stations, with the electric generated and the 
amount of fuel burned at each. In the 19880s Con Ed, along with many 
other East Coast companies, was shifting from coal to petroleum. It 
had the one nuclear station at indian Point and used minor amounts of 
natural methane. 
    The data were supplied in reports and submissions to my office for 
each year. I with my fellow engineers compiled regional statistics and 
performed studies with these data. Some times we assembled information 
and discussion for our head office or other energy-related offices. 
    From dialog then among astronomers about the Einstein mass-energy 
equation I f applied it to Con Edison. 
    I no longer have the original materials, they being transferred to 
our head office with reorganization of functions. I did have papers I 
wrote for discussion among local astronomers. They were summaries of 
the prime material, yet full enough to satisfy the reader that 
Einstein's equation doe work and that  energy extraction from burning 
fuel is patheticly inefficient. 

Basic data 
    These are summed from CoEd's many power plants around new york 
City. Their output furnished most of the City's electric with only 
minor amounts purchased from other companies. The data are for 1987, 
merely the latest year on record when I did the original 
demonstration. In 2018 Don Edison no longer generates its electric, 
having sold or retired all of its power plants in favor of maintaining 
its customers. 1Please understand that in the 1980s the electric 
industry in the US was still running with oldstyle measures. I did not 
here try to shift them into metrics. 
    The oldstyle unit for liquid fuel is the barrel, bbl, equal to *** 
159.0 liters.
    The unit for gaseous fuel is the cubic foot, equal to 28.3 liters. 
The volume of gaseous fuel implies a pressure, not generally stated in 
the collected statistics. The gas industry nowayears  cites 
consumption in 'therm' of heat content 
    The uranium is cited in grams, already a metric measure. 
    The oldstyle unit of heat energy is the 'British thermal unit', 
virtually always abbreved to Btu. The Btu equals 1,055 joule. This is 
commonly rounded to 1,000, leading to the 'metric Btu' defined as one 
    I distinguish between boiler and other oil because the two are 
different refinements of petroleum. Power plat boilers burn a thick 
heavy oil, sometimes even raw unrefined petroleum. Other oil is that 
burned in jet engines and is a highly purified liquid. Gas, almost 
entirely methane, is burned as is in all electric facilities.. 

           boiler      other    
           oil         oil        gas         uranium     total 
 --------- ----- ----- ---------- ----- ----- ----------- -------  
 unit     barrel       barrel     K ft3       gram 
 quantity   16,621,325    490,116  84,626,616    581,428      --
 $ cost    343,230,678 12,981,570 267,508,050 32,414,636  656,224,934 
 /MBtu       93,079,476  2,744,650  84,626,616 58,724,228  239,174,970 
 Mwh         9,871,487    178,096   8,899,675  5,101,139   24,050,397 
 % Mwh       .  41.05       00.74      37.00      21.21       100.00 
 MBtu/unit       5.60        5.60       1.00     101.00       ---     
 $/unit         20.65       25.83        3.16     55.76       ---
 Btu/Mwh        9.429      15.411      10.633     13 668        9.845 
 $/Mwh         34.77        76.15      30.06       6.35        27.29 

Con Edison E = m*c2 
    Under Einstein physics all energy comes from the transmutation of 
mass, even if the energy production process does not knowingly does 
so. Ordinary combustion seems to yield energy from a store of it 
contained within the fuel, as if it was a fluid squeezed from a 
sponge. But this energy was brought to light by losing a portion of 
the fuel's mass. 
    If by some imaginary machine we could convert all of the mass of 
an input fuel into electric, how much input would Con Edison need to 
equal its actual electric production? This is found by plugging the 
electric energy into the Einstein formula and solving for mass 

    (electric energy) = 24,050,397 Mwh = 8.658e16 joule 

    mass = (elecric energy) / c^2 
         =  = (8.658e16 joule) / (3e8 meter/sec)^2 
         = 0.962 kg 

    It's important to note that the input mass is NOT a special or 
favored type of mass. it may be ANY mass, such as dung. If such a 
means of total conversion of mass into electric could ever be found, 
al of the Con Edison's electric generation, meaning almost all of the 
electric used in new York City, could be furnished by an annual 
loading of a handful of dung. 

Squander of fuel 
    An incredible feature of this table is the amount of heat thrown 
away, not turned into electric. Only about ONE-THIRD of the heat 
released from the fuel goes into electric! For most electric companies 
the rest is lost from producing useful work. Most of the los is due to 
the Carnot limit, some to mechanical deficiencies. 
    In Con Ed a good portion of the wasted heat was captured for 
making street steam, which is sold as an other energy service to 
customers in southern Manhattan. 
    We Add the Btu energy extracted from fossil fuel and Mwh produced 
by it. The uranium is omitted because it is not 'burned' as a fossil 
fuel in combustion. 

    (heat energy) = 180,450,442 MBtu = 1.903e17 joule 

    (electric energy) = 18,943,258 Mwh = 6.820e16 joule 

    (electric/heat) = (6.820e16 joule) / (1.903e17 joule)  
                    = 0.3583 
                   -> 36%
    The ratio electric/heat is barely 36%! The other 64% of the heat 
extracted from the fuel is thrown away. It really sinks in when 
viewing the City from a high window or terrace. Think of all the 
electric in use at the moment for lighting, process heat, computers, 
telcomms, ventilation, air-condition, factory machines, elevators, 
cooking, transit, &c. Now imagine TWICE that amount whisked into the 
air and water (from exhaust gases and condensing spent steam) as waste 
    I can not compare this fraction of useful work with the Carnot 
limit because the high and low temperatures are indeterminate. Con Ed 
had dozens of boilers and engines, all with their own high & low 
    This squander of fuel energy is not only for Con Ed. All fuel 
burning power plants suffer comparable low efficiency. Other 
industries based on generating useful work from heat suffer similar 
    As at the early  21st century humankind hasn't yet found a 
practical safe economical method of getting useful work, such as 
electric, from fossil fuel. The combustion process, as refined as it 
evolved into today, is altogether a hideous squander of the world's 
stock of fossil fuel. 

Mass loss in nuclear power
    I no longer have the operating procedure for Con Ed's Indian Point 
station. in 1987 it worked one unit of the original three, unit 
#2.(Unit #1 was retired and unit #3 was sold to NY Power Authority 
before 1987. 
    Indian Point burned uranium with 4%-5% U235, the isotope that 
splits, fissions, under neutron impact.  The event releases energy 
from the loss of mass between the ingredient U235 and egredient 
fragment nuclei. This energy, from all the nuclei undergoing fission 
heat circulating water into steam for egenrating electric. 
    Native uranium contains about 0.7% U235. The rest, for both fuel 
and native uranium, is the stable isotope U238.
    It may surprise some readers that uranium as a chemical element 
was discovered in the , uh, 1790s, whence its single-letter chemical 
symbol.  It was routinely used as decorative plating and coatings, 
like for dinnerware. In the 20th century native uranium was included 
in certain optical glass to modify  its spectral transmission. 
    The nuclear fuel refinery boosts the U235 content of the fuel by 
remoing excess U238. The greater percent of U235 increases the chance 
of neutrons hitting a fissile nucleus. 
    Without the original documents I give here a typical uranium 
reaction ons among many exploited in nuclear power plants. 

    U325 + n -> Kr92 + Ba141 + (3 * n) + energy 
         +--> U236 
    Of all the U235 nuclei hit by neutrons about 89% do split into 
krypton, barium, and more neutrons. The other 11% absorb the incident 
neutron to create U236, a 'did' isotope that can not fission in the 
nuclear reactor. During the reactor operation the fuel stock fills 
with U236 and other products of radiodecay to. Eventually the fuel 
becomes too 'cold' for making steam.The fuel is removed from the 
reactor and replaced by new stock from the fuel refinery. Indian Point 
exchanged fuel every two years. 
    The mass number, sum of protons and neutrons in the nucleus, of 
the krypton and barium  vary in each instance of U235 fission. The 
mass number of each must be for a valid isotope and the sum of both 
mass numbers must be 233. The remaining 3 mass units, to equal the 
ingredient 236 units, come from the three neutrons from the fission. 
    We examine the mass, in kilograms, of the ingredient and egredient 

 1u = 1.660539r-275kg 

    We look at the mass of the ingredients and egredients 

    (ingredient mass) = (U235) + (neutron) 
                      = (390.2996.e-27kg) + (1.6749e-27kg) 
                      = 391.9745e-27kg 

    (egrediant mass) = (Kr92) + (Ba141) + 3 * (neutron)) 
                     = (152.6470e-27kg) + (233.9939e-27kg) 
                      + ((3) * (1.6749e-27kg)) 
                     = 391.61299e-27kg 

    (mass loss) = (ingredient) - (egredient) 
                = (391.9115e-27kg) - (391.7419e-27kg_ 
                = 0.3616e-27kg 
               -> 0.0923% of ingredient mass 
This seems like an awfully tiny mass loss! The energy released by this 
mass loss is 

    (energy ) = (mass) * (c^2) 
              = (0.3616e-27kg) * **3e8m/s( ^ 2) 
 )            = 3.2544e-11 joule 

which also seems like an awfully tiny energy conversion. In fact, 
this, scaled to one kilogram is, uh, 2-1/2 MILLION times the energy 
extracted from coal by the best of combustion processes. 

Classical E=mc2 
    The enduring favorite example of Einstein's formula for home 
astronomers is the energy production inside stars. Stars for most of 
their life burn hydrogen into helium. The released energy is the light 
and other radiation emitted by the star.
    The details were worked out in the 1950s using the newly 
declassified literature from the atom bomb project of world War II and 
the newly invented electronic computers. 
    The basic process is the proton-proton cycle since a hydrogen 
nucleus is a proton. The 'cycle' idea comes rom te use of the output 
particles to go into new rounds of hydrogen burning. diagrams can be a 
bit misleading to show only a single loop of activity rather than a 
roman orgy of action among ambient hydrogen nuclei.
    There are many ways to diagram the proton-proton reaction, One is 
    p     / 
     \  / 
     /  \         
    p    \     
         /     \ 
       /         \               p 
     p             \           / 
                     \      / 
         /   e+        he4 --energy 
    p      /           /    \ 
     \   /           /        \ 
      D2           /           p 
     /  \        / 
    p    \     / 

The reaction flows left to right, arrows being too clumsy to depict in 
ASCII text. 
    Note that in this version SIX protons enter the reaction, but two 
leave it. The net reaction is four protons making one helium nucleus 
with energy release. The output protons go into an other cycle with 
adjacent cycle. Some authors show these protons returning to the left 
side of the diagram as if they enter the same reaction all over again. 
    The deuteron, D2, is also written H2, being 'heavy hydrogen' with 
one proton and one neutron. the proton, p, is also H1,  the hydrogen 
nucleus.  The positron,e+, emitted to make H2, is the antielectron, 
with the electron symbol 'e' with a plus charge. 
    The mass-loss  equation becomes 

    *ingredient mass) = ((4) * (proton))
                      = ((4) * (1.673e-27kg) 
                      =  6.692e-27kg 

    (egredient mass) = (helium4) 
                     = 6.645e-27kg 

    9mass loss) = (ingredient mass) - (egredient mass) 
                = (6.692e-27kg) - (6.645e-27kg) 
                = 0.047e-27kg     = 0.047e-27kg 
              -> 0.702% of ingredient mass 

    The energy from this mass loss is,

    *energy) = (mass loss) * (c^2) 
             = (0.047e-27kg) * ((3e8m/s) ^ 2)
             = 4.230e-12 joule

Spin-off features 
    The home astronomer can move further with the E=mc2 topic by 
working with the radiation of the Sun. Can this tiny amount of energy 
per reaction be enough to make the Sun shine as he does? 
    By good fate the Sun is in a stage of steady stable radiation. He 
is not a pulsating or erupting star.  What is generated in the core by 
the hydrogen burning is sent into space from the photosphere. yes, it 
does take a hundred thousand years for the radiation, passed from core 
to surface, to escape but this is a tiny part of the Sun's full 
lifetime. The observed radiation fro the Sun equals that produced 
within him. 
    From ground measurements, improved with helopphysics satellites, 
the total radiopower of the Sun is 3.96e26 joule/sec. By proportion, 
we have 

    (Sun mass loss) = (Sun energy) * (react loss) / (react energy) 
                    = (3.96E26J/s) * (0.047e-27kg) / (1.230e-12J) 
                    = 4.308e9kg/s 
                  -> 4.3 million tons per second 

    Until 2018 this was treated as a nitid maths result, way beyond 
human detection. For one factor the motions of the planets in solar 
orbit seemed stable, with no change due to weaker solar gravity, for 
as long as we confidently calculate into the past. 
    in the past several years we fielded the MESSENGER probe in orbit 
at Mercury. its position and motion measurements of Mercury by far  
exceded the precision of previous astrometry. 
    MESSENGER found that Mercury's orbit is enlarging due to slackened 
solar gravity answering to, yep, a solar mass loss of quite 4 million 
tons per second. 
    An other spin-off feature is the estimate of the Sun's lifetime, 
and that of other stars. First we note that the historical measure of 
star radiopower covered only the visual wavelengths, which we cited as 
'luminosity' in solar units. By happy fortune stars radiate pretty 
much as blackbody radiators with the bulk of their output as light. To 
a reasonable level of approximation, luminosity is equal to total 
energy output. 
    Among well-behaved stars like the Sun the energy represented by 
luminosity is equal to the mass loss converted into that radiation. 
    An other factor is that the Sun consists of some 75% hydrogen, the 
rest being almost all inert helium. Of this 75% he burns only some 
10%.. The remaining hydrogen is outside of the core, where conditions 
van not support fusion reactions. Of this 10^ only 0.7% is actually 
converted into energy. 
    The lifetime of the Sun is the total loss of hydrogen divided by 
the rate of mass loss. We have 

     (Sun lifetime) = (total mass loss) / (rate of mass loss) 
                    = (1.99e30kg) * (0.75) * (0.10) * (0.007))
                     / (4.3e9kg/s) 
 =                  = 2.4307e17 seconds 
                   -> 7.699e9 years 

    This is a bit under the generally accepted 8-1/2 billion years, 
yet it is close as a first approximation. 
    If the usual normal specs given for stars in general included 
their consumible hydrogen and mass loss we could calculate the 
lifetime of stars, just as we did for the Dun. The specs do not have 
this information. We can get an estimate of star lifetime by 
substituting what parameters we have to hand. 
    By allowing that the portion of a star's mass that's consumed is 
the same as for the Sun, we can use the star's full mass as a ratio of 
the Sun's, in solar units. For the rate of mass loss we can use the 
star's luminosity, also in solar units. This is a looser fit because 
luminosity covers only the visual wavelengths and not the whole 
spectrum. By good luck for most stars the luminosity contains the bulk 
of a star's radiopower, with minor amounts of radiation beyond the red 
and violet ends of the spectrum. 
    With the caution of thee two approximations, we can ratio a star's 
lifetime against the Sun as 

    (star lifetime) = (8.2e9 year) * (mass) / (luminosity) 

For a star of 5 solar mass and 10 solar luminosity, we have 

    (star lifetime) = (8.2 billion year) * (5 Sun) / (10 Sun)   

    Stricta mente the estimate is valid for the star's residence on 
the Main Sequence. That's when hydrogen burning provides the star's 
ennergy output. After the hydrogen fuel gives out the star leaves the 
Main Sequence and goes into other fusion reactions as a redgiant for 
some 10% longer duration of life. For the Sun this would make his full 
lifetime more like 9.02 billion years. For back-of-envelope work this 
is commonly rounded to 10 billion years. The simple tule above no 
longer applies. 
    For example Sitius has luminosity of 25 and mass of 5.0, both in 
solar units. bear in mind that references differ in cite values for 
star parameters , sometimes by large tolerances. For Sirius, a main 
Sequence star, we have

    (Sirius lifetime) = (8.2 billion year) * (2.0 Sun) / (25 sun) 
                       = 0.656 billion year 
                      -> 656 million year

    We can either apply the fluff factor of 10% to get the entire 
lifetime of 75.2 million years. or we can use in the formula 9.0 -- or 
10 -- billion years for the full lifetime of the Sun.
    Large errors occur for stars off of the Main Sequence, those with 
luminosity class other than 'V' in their spectral type That's because 
we're applying a wrong method of energy production for these stars. 

    I do alloW that I was in a favored career to routinely collect 
statistics and data from Con Edison, and other electric companies in  
my office's territory. It may be frustrating for readers to acquire 
data about their own electric company. In case you ask, no, I have 
NOTHING saved from any other company. I saved as souvenirs ONLY some 
material for Con Edison. 
    Many companies publish yearbooks or operating digests, available 
on request. In some cases their data are posted in the company web. 
    The state agency that oversees electric companies may collect 
operating data for public use.  
    A parallel analysis could be carried out for an other industry, 
perhaps a large mill or factory. The 'useful work' may be tricky to 
quantify in energy terms. One suggestion is a delivery or taxi 
service. The input is the motor fuel and the output work is the 
runnage of vehicles. Estimates may be needed for vehicle mass and 
    The example of a real energy production, electric power here, 
makes the Carnot maximum-wok and Einstein mass-energy equation more  
appreciable. It shows it works in daily life, They are not just some 
peculiar theory or science application..