"I think this would shift the burden from states currently funding the government, those with finance, biotech, to the states with assembly, agricultural, and extraction industries."

I don't know why this would make any difference to be honest. The principle is the same as that forming the basis for the House of Representatives: that if a funding bill must originate from the House of the People, then the People ought to be responsible for paying their own individual share of those burdens - regardless their industry or occupation. As a side effect, this would also make those States who artificially prop themselves up with immigrant labor have to pay more as a result.

"I think a better solution is the minimal central government the founders of the country created, but it a small central gov't been long forgotten. In my fantasy, ..."

I echo your dream. My fantasy world similarly consists of an almost imperceptible government where the President has a cabinet of only two or three people and private enterprise runs the nation - not the lobbyists. And all because from grade school days children are taught and grow up under principles of self-government and responsibility rather than self-entitlement and victimhood.

Thanks - It's not so much a validation of Henry's Law, but an example of it. Henry's constants are calculated by my program along with other intermediate results. The following is the top header of the program source listing, with a description of the methods:
PROGRAM SOUR
C ============
C
C
C FOR THE AMMONIA-CARBON DIOXIDE-WATER SYSTEM USING THE EDWARDS,
C MAURER, NEWMAN AND PRAUSNITZ PITZER ACTIVITY COEFFICIENT
C CALCULATION METHOD AND THE NAKAMURA ET AL. METHOD TO CALCULATE
C FUGACITY COEFFICIENTS. THE SYSTEM HAS THIRTEEN UNKNOWNS:
C MOLES OF WATER, SIX IONIC MOLALITIES, TWO AQUEOUS MOLECULE
C MOLALITIES, THREE VAPOR MOLE FRACTIONS AND TOTAL MOLES OF VAPOR.
C

If CO2 increases, this should be beneficial to plant life. We also know from ice core samples that in the distant past, CO2 in the atmosphere was as high as 4,000 ppm (from Wikipedia), and probably not because the dinosaurs were driving too many SUVs. I still think natural variations are the first-order effects, and man-made contributions are 2nd or 3rd-order at most. Environmental modeling is extremely complicated, unless you introduce a lot of simplifying assumptions. I haven't heard anything about the energy source from Ni, but any energy that's released has to be stored there in the first place. Different crystal lattice configurations can have different energy states, with energy either stored or released with certain phase changes. But, there is still the First (conservation of energy) and Second (entropy, and no thermal process can ever be 100% efficient) Laws of Thermodynamics. Interesting stuff!

I haven't thought about Newton's Method for over 20 years. It's cool you have a chance to work on it.

This chemistry is outside my area too, but my impression is chemical reactions involving CO2 predominate in the Earth's atmosphere over physical reactions, e.g. the equilibria between the atmospheric pressure and CO2 dissolved in water. I suspect the equilibrium between plant life consuming CO2 and aerobic respiration producing CO2 predominates. Human activities releasing carbon + energy that was stored over hundreds of millions of years of sun shining is tipping the balance, causing atmospheric CO2 concentrations to be in the low 400 ppm instead being in the 300 ppm range. I don't understand the details of how this fits into the cycle of glacial maxima and minima, but I accept the science that human activities are big part of the increase and that it will likely have costly effects.

BTW, the periphery of our areas overlap. I encountered CO2 measurement when I was working on a project that measured the ratio of isotopes of C in CO2 for medical purposes. The mechanics of isotopes is probably more your area.

It reminds me of a talk I heard on LENR, where they said there may be processes that release energy from moving between of non-radioactive isotopes Ni. It sounds too go to be true.

KevinSch. . looks good, is this a validation of Henry's Law?

In the computer output, it looks like there are four different forms of carbon-bearing species present in the liquid phase: CO2_aqueous (0.01286 Molal), CO3_ion (1.984 Molal), HCO3_ion (4.933 Molal), and NH2CO2_ion (0.352 Molal). So, CO2_aqueous is the lowest concentration of the four species. Also note that the vapor phase is mostly CO2 (mole fraction = 0.786). As I mentioned in my original post, the computer program I'm using defines chemical equilibrium constants for all the relevant reactions that describes the system, including CO2 reacting with the other species present (also note that H2O dissociation into H+ and OH- is also captured, and that the pH of the system is -log10([H+]) = 7.87, so the solution is close to neutral but is slightly basic (pH>7). I'm not actually a chemist (I'm a nuclear engineer), but my strongest background is in numerical methods (modeling and simulation). My "chemist friend" who I originally wrote the solver for supplied most of the code, and I'm pretty much "taking on faith" the chemistry behind it. The "solver" I wrote for the program uses a multi-variable form of Newton-Raphson iteration to find an approximate solution to the 13 nonlinear equations. Newton iteration for one function of a single variable looks like:
x(i+1) = x(i) - f(x(i)) / f'(x(i)), where "i" is the iteration index and f' is the first-order derivative of the function, f. In multi-variable form, the unknown "x" and the function "f" become vectors, and instead of dividing by the derivative, you multiply the inverse of the Jacobian matrix by the "f" vector (so it is a matrix inversion problem for each iteration). The Jacobian matrix elements are the partial derivatives of each of the functions with respect to each of the "x" variables, so J(i,j) = df(i)/dx(j).

"Now, another thing I have thought of is that the individual states should be apportioned a share of the total bill according to the total number of representatives they have serving in Congress (a minimum of three: two Senators + one Congressman). "
I think this would shift the burden from states currently funding the government, those with finance, biotech, to the states with assembly, agricultural, and extraction industries. I can't imagine the latter accepting more of the tax burden. They are more receptive to promises of more government benefits and simplistic narratives that blame their problems on people who are different and the industries paying the taxes funding their benefits. They pay zero income taxes, except for payroll taxes, but they somehow imagine they are paying taxes.

Sometimes I wish the finance and tech areas were separate from the rest of the country and each could do its own thing. I think a better solution is the minimal central government the founders of the country created, but it a small central gov't been long forgotten. In my fantasy, urban and rural teenagers would train together in well-regulated militia with weapons and tools they keep and own personally. They don't have to agree on anything except the broad principles in the Constitution.

"In this model, is some CO2 and some NH3 in the liquid phase?"
"Yes,"
It must be in the gaseous phase but in solution with water. CO2 doesn't exist in the liquid phase at standard pressure. In solution its equilibrium point has it mostly bubbling out into normal air at sea level.

"I also think the amount you pay should increase the very next week after a new policy initiative."

That's an interesting idea, but it would be chaos to implement. It's hard enough for the government to get the tax tables right one time per year - trying to constantly adjust them after major policy adjustments would be nuts.


Now, another thing I have thought of is that the individual states should be apportioned a share of the total bill according to the total number of representatives they have serving in Congress (a minimum of three: two Senators + one Congressman). The House must originate all spending bills and often is controlled by the most populous states. So let them be responsible for forking out the most money to pay for the bills they pass! And tie the apportionment directly to the actual spending which took place during the year - not what they "budget".

I'm also in favor of a Constitutional Amendment which would put the costs of all Representatives' salaries and benefits (and that of their staffers) back on the States whom they represent. I really could care less if a Senator from California makes a million per year while a Senator from Idaho makes $50K - as long as their own states are paying the bills. It would also mean that their books are subject to audit by their State authorities. I think that the elected branch of government should be paid for by the people they represent rather than out of coffers they directly control.

Yes, I input the total number of moles. In my example, the number of moles of CO2 in the vapor phase was 0.54 (for the 60 C case). The number of moles in the liquid phase is therefore 7.0 - 0.54 = 6.46 moles. The program does output the various ionic forms in the liquid phase. Instead of me retyping in the output here, I'll just copy and paste the "tail-end" of the output file:

Liquid Phase Molalities and Activity Coefficients:

Ionic strength = 0.112365E+02 molal
H2O 0.492487E+02 AW 0.918976E+00
Hion 0.134369E-07 AH 0.977538E+00
OHion 0.723011E-05 AOH 0.915178E+00
NH3aq 0.514195E+00 ANH3 0.891992E+00
NH4ion 0.925273E+01 ANH4 0.126924E+00
CO2aq 0.128607E-01 ACO2 0.997687E+00
CO3ion 0.198375E+01 ACO3 0.130500E-02
HCO3ion 0.493293E+01 AHCO3 0.951841E-01
NH2CO2ion 0.352293E+00 ANH2CO2 0.729538E+00

Vapor Phase Mole Fractions and Fugacity Coefficients:
yH2O 0.181711E+00 fH2O 0.992995E+00
yNH3 0.323162E-01 fNH3 0.996795E+00
yCO2 0.785973E+00 fCO2 0.996863E+00

Total vapor 0.68644 moles


Note: The spacing didn't reproduce very well from the original (ASCII format) output file - in the original output file, the above table is nicely laid out. But, you should be able to still read it.

In this model, is some CO2 and some NH3 in the liquid phase?

Okay, sample problem: Assume a basis of 55.51 moles of water (1 kg, or 1 liter), 7.0 moles CO2, and 9.0 moles of ammonia. At 1 atmosphere pressure and 60 degrees C, the amount of CO2 in the vapor phase is 0.54 moles (total number of moles in vapor phase = 0.686). If I increase temperature to 65 degrees C, the number of moles of CO2 in the vapor phase increases to 0.85 moles (with total number of moles in vapor phase = 1.192). Now, these conditions are admittedly far from Earth's atmospheric conditions, but the base case (60 C) was the original test case for this problem, and the program sets up initial estimates for the concentrations internal to the program (they're hard-wired in the source code). I tried several times to get "more Earth-like" conditions to converge, but ran into numerical stability problems and the program kept crashing. To get this problem to run, I would have to go back into the source code and re-hard-wire more realistic initial estimates (and its been probably 10 years since I've looked at the source code) and then recompile the program. Sorry I couldn't give you a better sample problem - have you got a charge code for billable hours? :-) Anyway, this does show the trends. It's very unlikely nature would reverse the sign of the perturbation at lower temperatures and lower CO2 (and ammonia) concentrations. I hope this helps... (you're lucky I found the code after all these years!)

"It just boggles the mind."
Yes. I can't get my mind around it. Maybe some of them can't understand why I don't eat healthful and go easier on some of my other unhealthful habits.

I think they're undisciplined with money, and the will have money problems no matter what. A change in the withholding tables is not their core problem.

"I think people would change their tunes dramatically if they had to write out one big check to the government every year"
Yes. Any way that the money could touch their hands in cash form and then get handed over would be good. Numbers on a paystub aren't enough.

I also think the amount you pay should increase the very next week after a new policy initiative. Whether it's intervening in Syria, a new program to help children, a law for longer prison sentences for criminals, more research for cancer, people would start paying immediately.

"Because [global warming] is an invented calamity."
This is simply making stuff up, making up stuff that we wish were true. It has no basis in reality. We might has well be discussing whether the world is only a few thousand years old. It's making stuff up from whole cloth.

"When you solve the system, sure enough, as the temperature increases (for a constant pressure), the CO2 tends to shift from the liquid phase to the vapor phase."
At what temperature and pressure is this phase change occurring?

I need warmer weather...just got my third in a row $900+ electricity bill. All electric home. Not a good idea. My Generac is natural gas powered.

It looks to me as if some people just hate industry, and are trying to come up with patronizing (and self-righteous) excuses to destroy it. But let's not let them.

Very nice explanation! Thank you!

I think its even more insidious than that. First, there is a priori physics (physical chemistry, actually) which supports the assertion that CO2 concentration in the Earth's atmosphere is a consequence of global warming, not a driving function. Yes, increased CO2 levels can trap more of the sun's incoming radiation, but the argument is that that is a second-order affect. Water vapor is also a "greenhouse gas" in that it serves to trap incoming solar radiation, and is more effective than CO2 (for one thing, its concentration is much higher). The truth is that CO2 is also in equilibrium with dissolved CO2 in the world's oceans. To quantify this, I once helped a chemist friend of mine with a problem he had. He had found a Fortran program that defined all 13 nonlinear equations in 13 unknowns for the ammonia/CO2/water system, but the source code lacked a numerical routine that actually solved the system. I wrote him one as a subroutine. The 13 equations defined the equilibrium concentrations of the three components in both vapor and liquid phases, for a given temperature and pressure and given the moles of each component present. The program contained a pretty rigorous treatment of activity coefficients for the liquid phase along with vapor phase fugacities. When you solve the system, sure enough, as the temperature increases (for a constant pressure), the CO2 tends to shift from the liquid phase to the vapor phase. So, if the Earth's global average temperature is increasing (due to, say, increasing solar output, tied to sunspot cycles, etc.), you would EXPECT the world's oceans to release more CO2 (and the converse is also true). So, increasing temperature causes more CO2 in the air, because of the shift in the equilibria between vapor and liquid phases. On the other hand, increased CO2 production by man, would be mitigated by these same equilibria relationships forcing more CO2 back into the oceans. (Le Chatelier's Principle in chemistry states that whenever there is a change in the equilibrium state of a system, there will tend to be mechanisms that will mitigate the change.)

Shining the light of Truth on a leftist is like turning the kitchen lights on at 2:00 am and watching all the cockroaches scurry away for cover.

You mean they might have something against burst water pipes, and general freezing to death? Sorry, I know its a serious situation. But, when the wind doesn't blow, there is no wind power, and there is no solar power at night. Batteries (for leveling power from wind and solar) have to be charged before they can dispatch power to the grid, and if there is a long period of time when the wind doesn't blow, those batteries can discharge and you have nothing. Even coal plants can go down in the winter under certain conditions. Coal plants require such large quantities of coal that coal input is by conveyor belts feeding the burners from large piles of coal outside (generally, in most coal plants I know of). When it gets cold enough for a long enough time, those conveyor belts can freeze up. That happened not too many years ago in the Northeast. Fortunately, the region had ample nuclear stations to keep the power on.

I have solar panels that heat my pool, and very effectively compared with a pool heater which I rarely use actually. The sun is quite powerful here in las vegas, and would do a good job heating my house if they were deployed in such a way to do that. The heat output is impressive, and free !

Good points term but It is the sun. The sun does what it does and it has a regular cycle. The heat in my home comes from my furnace.

We hate lies leftists hate the truth.