torsdag 18 november 2010

My stance on GHG taxes

Updated and expanded on 2011-04-18

Emitting fossil fuels is generally recognized to cause a net external cost, a large part of which occurs in the future. In a perfect world the costs and benefits of greenhouse gas emissions could be objectively determinable at no cost with great accuracy and precision; money would then change hands to account for these costs and benefits in order to cancel them out.

The real world is not at all like that. As best we are able to determine it appears that adaption is misery and triage and it will be a great; some countries will benefit, but most won't and its expected to be a great net cost to the world. Many of the costs are subjective; what's the cost of the loss of some species? If the maldives shrink and eventually disappear, there's an objective cost of moving people around, but there's also a subjective cost to the inhabitants.

The purpose of a greenhouse gas tax is to do a half-assed job of internalizing future external costs into the current price of a good or service, under the theory that doing a half-assed job is better than doing none at all.

Fossil fuels, meat production and biofuels are provided with quite enormous subsidies in many places; before bothering to do something rather more difficult, stop that. This is an easy to rectify harm.

Whether government needs to be bigger or smaller is an issue entirely separate from GHG taxes. In order to offset the additional taxes collected on GHGs it would be necessary to ramp down VAT, sales tax, employment taxes, income tax or other taxes to cancel it out. If you don't do this the battle becomes over whether government should grow or shrink rather than whether GHGs should be taxed or not.

It does not make sense to only tax carbon dioxide and not the other major greenhouse gases. On the one hand you want to be fair and not give an undue advantage to some technology like biofuels(N2O) or natural gas(if ~2-3% of natural gas leaks out it is no better than coal over the next 100 year period); on the other hand you don't want the unnescessary complexity of worrying about unimportant greenhouse gases.

The cost of regulation should be insignificant compared to the tax collected; otherwise you are introducing a huge dead-weight loss.

If you introduced a tax only on domestic GHG emissions, this would give domestic companies a competitive disadvantage compared to foreign companies not burdened by such a tax. You make a lot of politically powerful enemies this way. This isn't likely to ever be implemented anywhere.

If you try to establish some type of world government body that applies a uniform tax on GHG everywhere you would solve this problem but you would create several problems which are even harder to solve. This extraordinary degree of political cooperation would be hugely unpopular, incredibly difficult to achieve, it would undermine national sovereignty, the political body that administers it would be remote and unaccountable. You're opening yourself up to all kinds of mischief. It may be used as a political club by the powerful nations to beat up the less powerful ones. It may, as in the case of the EU, suffer from galloping mission creep. The EU was was sold as a free-trade and currency union; the currency union was designed to fail, forcing a crisis that can be used as a stepping stone towards a political union. Unwanted by almost everyone, it is fast becomming a united states of Europe. World government is a plain awful idea on every level and neither can, will or should happen. Trying to create world government will waste a lot of time and effort; it will give the paranoiacs who believe GHGs to be some kind of socialist or government conspiracy a huge shot in the arm.

From the above, the solution I would like to see is a GHG tax that is not applied to any exports; nor is it applied at any stage in the production. My GHG tax would be applied as a sales tax, at the point of consumption for finished consumer goods and services. This would replace the arbitrary sales tax we have today and would possibly have to eat into VAT and other taxes to remain revenue neutral.

This has several advantages. It does not disadvantage domestic producers; you don't piss them off so much as to create new political enemies. Implemented properly, if two regions adopt this policy it should not cause double taxation or loop holes that allow evasion of the taxation on goods that flow between them; the tax occurs only at the end point.

The beauty of this is that you can adopt such a carbon tax unilaterally; you can have different rates in different countries without introducing too many new opportunities for arbitrage(the only one I can think of is end consumers who live near a border to a low carbon tax country, who may choose to cross that border to buy a particularly carbon intensive item).

As usual, the devil is in the details. You don't want undue invasion of privacy and obstruction of business activity. For business who refuse to properly account for GHGs or cannot account for the GHG emissions of an imported good, you can give the option of simply assume the worst-in-class GHG emissions for the offending item. It must be worst-in-class, otherwise businesses would choose not to disclose GHG emissions whenever they exceed the standard rate. This is simplification and cost-reduction measure; for low volume production boutique items and minor ingredients the worst-in-class GHG tax would be much smaller than the cost of figuring out the actual GHG emissions when not explicitly given by the manufacturer.

There are some ugly corner cases that would need to be sorted out. E.g. grocery stores take in more perishable goods than they need because it costs them more to leave a customer's needs unfulfilled than it does to throw away significant volumes of expired goods.

It's clear that it would be a significant expense to switch over; but the switch is a one-time cost and it is not unprecedented(e.g. the introduction of VAT or sales tax were also expensive one-time costs).

fredag 5 november 2010

The curve of binding energy.

Credit: User fastfission on wikipedia, image is in public domain.

Now, what is so remarkable about this graph that tells you how tightly bound different elements are? It makes sense of a great many interesting things about the Universe that we live in.

The strong nuclear force that binds nuclei together is very strong, but it is also very short range. In small nuclei every additional nucleon you add is attracted with the strong force to every other nucleon, but in big nuclei it only interacts strongly with the nucleons in its vicinity at any given moment. In contrast, the electric force is a much longer range force, it falls off only as the inverse square of distance between the charges. Each additional proton you add repels all other protons in the nucleus. This is a gross simplification, but it gives an intuitive feel for why there is an optimum size of nuclei that is most tightly bound.

Amongst other things you can see that merging toghether light elements is energetically favourable all the way up to iron and nickel. This process is known as fusion and is what powers stars.

It is apparent that helium-4 is a remarkably stable nuclei for such a light element. Elements with electrons arranged into complete shells are very unreactive; they're known as noble gases. Like the shell model that you learned about in chemistry class, there is a corresponding model for nuclides. Nuclides with a certain number of either protons or neutrons are especially stable because they have a complete outer shell. The numbers 2, 8, 20, 28, 50, 82 or 126 are called "magic numbers"; atoms with this many neutrons or protons are called "magic" and they are extra stable. Helium-4 has 2 neutrons and 2 protons; it is "double magic".

The slope of the binding curve gradually flattens before reaching its peak at nickel-62. In less massive stars like the sun the fusion process stops at carbon and oxygen; slightly heavier stars can fuse carbon and the process stops at oxygen, neon and magnesium. Massive stars can fuse everything up to iron.

Harnessing fusion power on Earth is difficult to achieve because it involves smashing toghether two positively charged particles that strongly repel each other. Only if they get very close can the strong nuclear force overpower the coulomb repulsion.

It is also energetically favourable for heavy elements to be split appart into smaller nuclei. The most common way for heavy elements to do this is to eject a helium-4 nucleus, which repelled by the coulomb repulsion will have a very large amount of kinetic energy. This is known as alpha decay. The curious stability of helium-4 is why alpha decay involves the tossing out of a helium-4 nuclei and not a proton, deuteron or lithium-7 nucleus.

The heaviest nuclide that is completely stable as far as anyone is aware is lead-208; a "double magic" nuclide(82 protons, 126 neutrons). Bismuth-209 was believed to be stable until recently, when it was discovered that Bismuth-209 has a half-life of 19 ×1018 years.

The heaviest elements that exist in measurable abundance in nature are actinides(IUPAC: actinoids); named after actinium, the first element in the actinide series. These elements can perform a new trick, they can split apart into bigger chunks than helium-4.

Uranium-235 in particular can be induced to split by pelting it with neutrons. If one of these neutrons get close enough it can be captured by the uranium nucleus, forming an excited nucleus of uranium-236. ~82% of the time this excited nucleus will split apart into two unequal halves, known as fission products. The rest of the ~18% of the time the excited nucleus returns to ground state by emitting a gamma ray. When this nucleus fissions, it releases more neutrons that can be used to continue the process.

However not all of these neutrons are released promptly; a small fraction are released by the decay of fission products, known as delayed neutrons. This is why both nuclear bombs and nuclear reactors are practical. There are enough prompt neutrons to create a very fast, run-away reaction under the right conditions; a bomb.

There are also enough delayed neutrons that it is possible to create a reactor that is not self-sustaining on prompt neutrons alone('prompt critical'). The delayed neutrons are thereby necessary to sustain the reaction, and since it takes time for them to emerge the power output of the reactor can be made to increase very slowly and controlably; slowly enough for self-regulation to occur. There are many mechanisms that can do this kind of self-regulation as the reactor heats up, such as thermal expansion and resonance broadening of the neutron capture resonance in U-238. Therefor, if the reactor operator injects only a little bit of positive reactivity into a properly designed reactor, the power level will rise a bit, the temperature will increase and then stabilize at a new, higher level.

Some reactors can handle even a huge insertion of reactivity with ease. Below is an example of such a reactor; a small research reactor at Penn State. What you see here is a control rod being rapidly ejected from a TRIGA core using compressed gas. The power-outout increase rapidly and peaks at about a gigawatt thermal. As the core heats up the reactivity drops to such an extent that it becomes negative and the reaction slows; the power goes down and eventually homes in towards some level where reactivity approaches 0(i.e. no change in power output).

Essentially all elements except hydrogen, helium and lithium that we see around us were once made in a star. But if stars can't fuse iron, why are there heavier elements than iron around? While there is some argument about the relative importances of the different processes, it is generally agreed that they are produced by the s-process, p-process and r-process. The s-process is the slow process of successive capture of neutrons that may occur in some heavy stars(believed to be mostly occuring in asymptotic giant branch). The r-process is the rapid process of neutron capture that occurs during a super nova. The p-process is photodisintegration, which can strip a neutron or an alpha particle from a heavy nuclide; this is responsible for producing some heavy, proton rich elements.

To a romantic, we are made of star-dust; risen from the ashes of a dying star. A cynic would point out that another word for "star-dust" is nuclear waste from a giant reactor exploded so violently that it surely must have killed everything within light-years, if there was anything there to kill.

The mole

Apparently it is difficult for some school children to comprehend what a mole is. I don't see why this should be the case, since a mole is just a numerical amount of atoms, molecules or formula units of a substance. That number, avogadros constant, is chosen in a way that makes the numbers involved easier to work with. Perhaps it is because teachers are too clever by half in explaining the concept?

Avogadros number is chosen to be the number of atoms which has a mass in grams with the same numerical value as the molecular mass of it's constituent molecules in atomic mass units. If the molecular mass of a molecule is 18.02 u, it's molar mass is 18.02 g/mole.

It would have been eminently possible to never introduce the concept of unified atomic mass units and moles; you could simply have tables that list the mass in kilograms of an average atom of an element, or specific isotopes. You could express the number of molecules as a unitless, numerical value; the actual number of molecules.

The problem with doing things this way is that any amount of substance visible to the naked eye consists of great big thundering hordes of molecules, and the mass of any molecule you're interested in will be incredibly tiny.

The choice of the unified atomic mass unit is also quite clever. It is 1/12th the mass of an atom of carbon-12. There is a slight variation in binding energy per nucleon between different atoms, and neutrons are slightly heavier than protons, but the mass of an isotope in atomic mass units is to within about 1% simply the sum of the number of protons and neutrons.

Thus U-238 should have an isotopic mass of about 238 u(actual: 238.051 u). Fe-56 should have an isotopic mass of about 56 u(actual 55.934 u). Hydrogen-1 should have an isotopic mass around 1(actual 1.0078 u).