Something around 1000 g. For 235U, the energy liberated in a fission process corresponds to a conversion in kinetic energy of 0.1% of the original mass.
1 tTNT = 4.2 · 1016 erg
1 g -> 9 · 1020 erg ~ 20 kilotons
Let us see where does this 0.1% come from. 235U can break in dozens of different ways, for instance:
[latex]
\begin{array}{rcl}
^1_0n+ ^{235}_{92}U & \to ^{236}_{92}U^*\to& ^{141}_{56}Ba+^{92}_{36}Kr+3 ^1_0n\\
^1_0n+ ^{235}_{92}U & \to ^{236}_{92}U^*\to& ^{140}_{54}Xe+^{94}_{38}Sr+2 ^1_0n\\
^1_0n+ ^{235}_{92}U & \to ^{236}_{92}U^*\to& ^{137}_{53}I+^{97}_{39}Kr+2 ^1_0n
\end{array}
[/latex]
Taking an average and including the energy:
235U -> ~135X + ~95Y + (2-3) n + 208 MeV
It is easy to understand the magnitude of the liberated energy. The nucleon bound energy in 235U is of the order of 7 MeV, while it has a value around 8 MeV in the fragments. This difference of 1 MeV per nucleon, multiplied by the approximately 200 nucleons, gives a liberated energy of 0.2 GeV. This corresponds to the conversion in kinetic energy of 0.1% of the original mass.
So, the mass converted into energy is about 1g, but the amount of uranium spent is 1000 times greater.
1 tTNT = 4.2 · 1016 erg
1 g -> 9 · 1020 erg ~ 20 kilotons
Let us see where does this 0.1% come from. 235U can break in dozens of different ways, for instance:
[latex]
\begin{array}{rcl}
^1_0n+ ^{235}_{92}U & \to ^{236}_{92}U^*\to& ^{141}_{56}Ba+^{92}_{36}Kr+3 ^1_0n\\
^1_0n+ ^{235}_{92}U & \to ^{236}_{92}U^*\to& ^{140}_{54}Xe+^{94}_{38}Sr+2 ^1_0n\\
^1_0n+ ^{235}_{92}U & \to ^{236}_{92}U^*\to& ^{137}_{53}I+^{97}_{39}Kr+2 ^1_0n
\end{array}
[/latex]
Taking an average and including the energy:
235U -> ~135X + ~95Y + (2-3) n + 208 MeV
It is easy to understand the magnitude of the liberated energy. The nucleon bound energy in 235U is of the order of 7 MeV, while it has a value around 8 MeV in the fragments. This difference of 1 MeV per nucleon, multiplied by the approximately 200 nucleons, gives a liberated energy of 0.2 GeV. This corresponds to the conversion in kinetic energy of 0.1% of the original mass.
So, the mass converted into energy is about 1g, but the amount of uranium spent is 1000 times greater.
Dave_46
Graduate Poster
Sixty - some would say positively ancient.
I think that the comments you made in the rest of your post summed up the problems nicely.
I recall one lecturer, as we were going through the transition, saying that it might make the change easier if we used another, transitional, system. We should go from foot-pound-second to bushel-furlong-fortnight to metre-kilogram-second.
Dave
epepke
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Ah, well, you're probably young. Back in the day there were these black vinyl things called "records" that had music on them, encoded as two variations in a surface at pi/4 angles to the vertical. A thing made preferably of diamond called a "stylus" pushed on them as they moved transeversely. The motion of the "stylus" moved permanent magnets in some coils and made electrical impulses that were amplified and used to drive a membrane, producing sound.
The force of the "stylus" on the "record" was measured in grams (or grammes, if you prefer). Even more confusingly, it was called "stylus pressure."
And I hope you mean the pound-mass.
epepke
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Systems of units aren't invented. They involved, and they incorporate what is known at the time. Why were the inventors of the metric system so incredibly stupid so as to measure time and distance in different units, so that c is not one? Retards. The Avoirdupois system was actually closer. A foot is about a nanosecons. I use the length of my sandal as a unit, and that's about right.
Art Vandelay
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They weren't imbeciles. They did the best with what they had.
You mean "1 kg". And for H bombs, it's about 1%.Yllanes said:
No, I meant 1000g because I was using CGS units. Perhaps I should have used SI units, to avoid throwing another system into the thread. But I didn't. If I use ergs for the energy, I must use grams for the mass.
The bomb in Hiroshima was not an H bomb, it was a fission uranium bomb.
Art Vandelay
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If you really want to avoid kilograms for some bizarre reason, then you should say "10^3 grams". "1000 grams" means "1 kg, to withing .001kg". I very much doubt that this level of precision is warranted.
No, you don't.
Yes. I meant it as further information.
I don't know what your problem with grams is:
1 erg = 1 g·cm2·s-2
1 J = 1 kg·m2·s-2
I normally use Gaussian units, when I am not using geometrised or some other kind of natural units. The Gaussian system is based on the CGS system, which uses grams for mass. If I put grams and cm/s into E = mc2 I get ergs. If I use kg and m/s I get joules. And if I use kg and cm/s I get neither ergs nor joules...
As for the 1000 - 103 issue... 1000 is ambiguous, it isn't clear whether the writer is meaning 4 significant figures or 1, but in a discussion like this it is clear that we are talking about orders of magnitude and it works as a shortand for the more cumbersome to write 103. If you really want to indicate 4 significant figures, you won't use 1000, but 1.000 · 103. Anyway, if using 1000 to mean 'a thousand' is going to confuse people I won't do it anymore.
ponderingturtle
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Why should such arbitrary factors constantly need to be inserted into your work? You are making some things easier and some things harder, so if it made what you where doing harder by introducing more constants into the equations why would you want it?
Take say analysis of a structure. If you measure the mass of everything in lbs you do not need to pull out gravity to figure out how much force things need to be able to take. You are just moving where you put the factors of g not doing anything else.
ponderingturtle
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Exactly properly you should pick the units that make your work more convienient.
Dr Adequate
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The wonderful thing is that having foisted on Americans the stupidest system of measurements ever devised, my country immediately went metric.
It's the subtlest ever form of economic warfare.
BWAHAHAHA!
OK, that wasn't subtle, but no-one's going to believe you.
It's the subtlest ever form of economic warfare.
BWAHAHAHA!
OK, that wasn't subtle, but no-one's going to believe you.
Rat
Not bored. Never bored.,
Almost nobody in the UK uses kilometres to express distance. We are metric for most things, but distances are miles, beer and milk come in pints (though other liquids are metric), and people are weighed in stones and pounds (though everything else is usually weighed as metric).
The whole switch to metric for all goods sold made for some odd anomalies. A beer could still be sold in pints, but soft drinks couldn't be. There was some agonizing in the tabloids about how a shandy (half beer, half lemonade) could be sold.
Cheers,
Rat.
Art Vandelay
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And of course, you can't buy pound cake anymore. You have to buy 454 gram cake.
I've never managed to have this discussion with non-scientists without it getting bogged down in silly disputes about whether miles are better than Km in measuring driving distances, or inches vs cm in woodwork etc. Most people seem not to understand the importance of standardisation, and of having a system that's suitable for science and engineering.
First, it is unsatisfactory that different systems of units are used for different purposes in science, engineering and everyday measurement; or for reasons of chance, whim or history. The resulting problems for science, industry and commerce are immense, and the situation absolutely has to be rectified. I should have thought this was self-evident (it's been recognised for centuries), but it seems from this thread that we are not agreed even on that.
Apart from the ridiculous FPS 'system', I'm surprised to see people using non-SI metric units that I thought were defunct (ergs etc.). The only possible choice is SI, as it's less flawed and far more widely accepted than its rivals (though imperfect).
As has been mentioned, the roots of the problem are ancient. For each of the independent dimensions in mechanics, mass, length and time, rival units co-existed for millennia with ill-defined conversions (for example, to cover various size ranges). As technology developed, the need for standardisation and precision became more pressing, and at the same time the problems increased because of compound quantities in science and engineering, which tended to acquire their own independent units rather than being derived from existing fundamental units.
Serious attempts to define an international system suitable for science and engineering began in the 18th century, but unfortunately several rival systems were proposed. Two approaches were tried:
1) (wrong) Keep most or all of the existing measurements; define them precisely with exact conversion constants.
2) (right) For each dimension, scrap all existing units and define a new one, or keep just one. Have no conversion constants other than powers of 10 specified by standard prefixes. Define no compound units; derive them from the base units.
British scientists began using metric units in the mid to late 19th century. I'm not sure why it took so long for a metric system to be fully accepted even in science, but I strongly suspect national pride and anti-French sentiment.
A couple of people have missed my point that there should be no numerical conversion constants within a system.
You absolutely should not have to remember to multiply (or divide) by (for example) the number 32 to make the units come out right. If gravity is involved then you should have to use gravitational acceleration explicitly in the calculation (else the confusion between mass and weight is reinforced). If it isn't, then 32 shouldn't come into the calculation at all.
Several people have suggested that there isn't a problem; you simply use pounds (mass) and poundals. Or slugs and pounds (force). Unfortunately their simple solutions are incompatible; in well over 100 years there's been no progress in agreeing a single FPS system. And it's incorrect to claim that the pound is a unit of force. Certainly it is in one particular version of FPS (possibly the one learned by most Americans), but in other FPS systems (and in everyday measurement) it's a unit of mass. There's no way to resolve the confusion brought about by generations of obstinate scientists and bungling committees other than to scrap all non-SI systems (that's only one of many reasons).
One thing I have learned (by heart) from this thread: the value of g in FPS.
First, it is unsatisfactory that different systems of units are used for different purposes in science, engineering and everyday measurement; or for reasons of chance, whim or history. The resulting problems for science, industry and commerce are immense, and the situation absolutely has to be rectified. I should have thought this was self-evident (it's been recognised for centuries), but it seems from this thread that we are not agreed even on that.
Apart from the ridiculous FPS 'system', I'm surprised to see people using non-SI metric units that I thought were defunct (ergs etc.). The only possible choice is SI, as it's less flawed and far more widely accepted than its rivals (though imperfect).
As has been mentioned, the roots of the problem are ancient. For each of the independent dimensions in mechanics, mass, length and time, rival units co-existed for millennia with ill-defined conversions (for example, to cover various size ranges). As technology developed, the need for standardisation and precision became more pressing, and at the same time the problems increased because of compound quantities in science and engineering, which tended to acquire their own independent units rather than being derived from existing fundamental units.
Serious attempts to define an international system suitable for science and engineering began in the 18th century, but unfortunately several rival systems were proposed. Two approaches were tried:
1) (wrong) Keep most or all of the existing measurements; define them precisely with exact conversion constants.
2) (right) For each dimension, scrap all existing units and define a new one, or keep just one. Have no conversion constants other than powers of 10 specified by standard prefixes. Define no compound units; derive them from the base units.
British scientists began using metric units in the mid to late 19th century. I'm not sure why it took so long for a metric system to be fully accepted even in science, but I strongly suspect national pride and anti-French sentiment.
A couple of people have missed my point that there should be no numerical conversion constants within a system.
Numerical conversion constants within a system is a completely different issue from whether some natural constant or quantity has a value of 1 in the system. That's of negligible benefit (in fact it's better if there aren't any such quantities, because it encourages both sloppy thinking and the practice of using different systems for different purposes; and in any case the value won't stay at exactly 1 as measurements or definitions of units are refined).
You absolutely should not have to remember to multiply (or divide) by (for example) the number 32 to make the units come out right. If gravity is involved then you should have to use gravitational acceleration explicitly in the calculation (else the confusion between mass and weight is reinforced). If it isn't, then 32 shouldn't come into the calculation at all.
Several people have suggested that there isn't a problem; you simply use pounds (mass) and poundals. Or slugs and pounds (force). Unfortunately their simple solutions are incompatible; in well over 100 years there's been no progress in agreeing a single FPS system. And it's incorrect to claim that the pound is a unit of force. Certainly it is in one particular version of FPS (possibly the one learned by most Americans), but in other FPS systems (and in everyday measurement) it's a unit of mass. There's no way to resolve the confusion brought about by generations of obstinate scientists and bungling committees other than to scrap all non-SI systems (that's only one of many reasons).
One thing I have learned (by heart) from this thread: the value of g in FPS.
ponderingturtle
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And of course, you can't buy pound cake anymore. You have to buy 454 gram cake.
But pound cake comes from the ingredients
a pound of butter
a pound of flour
a pound of eggs
a pound of sugar
That is what I have heard anyway..
ponderingturtle
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The problem is that actual scientists and engeneers to not do what you say they should do. They use what units are convienient for what they are doing.
For example, should c=300,000,000 m/s or should c=1? Well alot of things get easier with c=1 so such a system is used when it is convient, but useing such a system in every day life would be a pain so a different system is used.
Standardization is helpful, but what sorts of problems are you going to make the forced standard unit suited for? And what do you do when you are going things that the units are not well suited for?
Most physics textbooks (outside freshman texts) are in the Gaussian system. Some of them are 'bilingual' or only recently starting to adopt the SI. The CGS system is just as sensible as the MKS (on which the SI is based). Most fundamental physicists use CGS (with electrostatic or electromagnetic units, depending on the situation), because it is much more convenient. In electromagnetism instead of having as fundamental constant epsilon_0, it has the speed of light. The fields E, D, B, and H have all the same dimensions, so countless formulas are simplified or look much nicer. Even texts like Jackson's Classical Electrodynamics, which converted to SI in 1999 (3rd edition) to sell more books, keep Gaussian units in those chapters related with relativity (classical theory of fields, radiation, moving charges in general). Other books, like Kittel's Introduction to Solid State Physics, have all the formulas in both systems in their latest editions. And most of the rest of famous physics books are not in the SI. An example from both disciplines mentioned above: in electrodynamics Landau & Lifshitz's Classical Theory of Fields (and all their course in theoretical physics); and in condensed matter Ashcroft & Mermin. In quantum mechanics, the SI is rarely used. Most handbooks are also in CGS units. So it's going to be a while until it becomes the usual system in fundamental physics.