E=MC2 AT CON EDISON ----------------- John Pazmino NYSkies Astronomy Inc www.nyskies.org firstname.lastname@example.org 2018 September 14initial 2018 Novrmber 14 current Introduction ---------- 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 quantities. 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 kilohoule. 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.. -------------------------------------------- FUEL AND ENERGY DATA FOR CON EDISON FOR 1987 ------------------------------------------- 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 -> ONE KILOGRAM OF ANY KIND OF MASS 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 heat. 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 temperatures. 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 yields. 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 particles 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 e+ p / \ / D2 / \ p \ He3 / \ / \ p p \ / \ / / e+ he4 --energy p / / \ \ / / \ D2 / p / \ / p \ / He3 / / 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. Conclusion -------- 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 horsepower. 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..