The Numbers Don’t Work

by James R. Barrante, Ph.D.

The major idea driving the greenhouse gas effect originates with the observation from the late 1800’s that planet Earth is warmer than similar planets of the same size and distance from their star.  The reason given by a number of scientists, including the physical chemist Svante Arrhenius, was that it was because Earth had an atmosphere containing specific gases that could absorb a portion of the infrared light radiated by the planet and return it to the planet.  The Earth receives light from the sun that warms the planet.  In turn, in order to maintain a constant temperature, Earth must radiate a portion of the light back to space.  The wavelengths of light radiated by the planet fall in a band in the infrared region of the light spectrum, controlled by the Earth’s temperature.  Any interference in this process, such as the absorption of this infrared radiation by atmospheric gases,  will upset the energy balance of the planet.

The two major gases able to intercept wavelengths of infrared light radiated by the planet are water vapor (its level varies with climate, so let us assume an average level of about 2%), and carbon dioxide (about 0.04%).  These two gases are known as “greenhouse gases.”  Just from the concentration difference alone, we can see that water vapor is the major player here.  Moreover, water vapor is able to absorb a much wider band of infrared light than is CO2.  Most scientists agree that of the total radiation absorbed, water vapor absorbs about 90%.

Based on calculations made by assuming the planet was a blackbody radiator, it was found that the planet was 33ºC warmer than it should be, supposedly caused by our atmosphere.  Assuming that the two major greenhouse gases are water vapor and carbon dioxide, carbon dioxide would be responsible for 10%, or 3.3ºC, of that warming.  That is, increasing the CO2 in the atmosphere from 0 ppmv (parts per million by volume) to the 1850’s value of 280 ppmv should have raised the temperature of the planet by 3.3ºC.  It is well known that the absorption of light by matter is not linear with concentration, but falls off exponentially or logarithmically.  In the late 19th century, Arrhenius suggested a simple equation to relate the amount of warming by a greenhouse gas to its level in the atmosphere to be

ΔT = T2 – T1  =  ln (C2/C1)

where k is an experimentally determined constant and ln is the natural logarithm.  We can see that this equation is problematic, if the concentration C1 is equal to zero.  So let us modify the equation by choosing some very small level of CO2 to represent zero concentration.  (It turns out that this choice is quite arbitrary, as long as it is very small).  The new equation becomes


Using the original premise that the presence of CO2 in the atmosphere raised the temperature of the globe by 3.3 degrees, we can determine the constant k.

3.3  =  ln (280/1 × 10¯¹º)

k  =  0.115ºC

We are now able to see how global temperature changes with increasing concentration of CO2.  It is clear that if you double the concentration of CO2 in the atmosphere, global temperature will increase by a whopping 0.08°C.  So, increasing the CO2 level from 0 ppmv to 100 ppmv, raised global temperature by 3.2°C; further increasing the level from 100 ppmv to 200 ppmv raised global temperature by 0.08ºC; and further raising the level from 200 ppmv to 300 ppmv raised global temperature by 0.05ºC.

A number of years ago climate scientists announced that the increase in CO2 level from its 1850’s value of 280 ppmv to the present value of about 380 ppmv raised global temperature by 0.8ºC.  Let’s see how that squares with our modified Arrhenius equation.

ΔT  =  0.115 ln (380/280)  =  0.035ºC

Not very good, is it!  Something obviously is wrong!  Whatever the case, it is apparent that associating a 0.8ºC temperature increase in global temperature with an increase in the CO2 level from 280 ppmv to 380 ppmv is not at all consistent with the CO2 and water vapor’s warming the planet by 33ºC as described by the climate-change crowd.  The numbers do not work!




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Ocean Acidification and its Effects on Corals III. Temperature

by James R. Barrante, Ph.D.


In OA I and OA II we considered the ocean chemistry of the carbonic acid system at constant temperature.  Under these circumstances, it is apparent that if the partial pressure of carbon dioxide in the atmosphere increases, the pH of a buffered ocean must drop.  We were able to show in OAII that increasing the partial pressure from 280 ppmv to 380 ppmv will decrease ocean pH from a values of approximately 8.2 to 8.1. pH units.  In OAIII we shall consider the effect of temperature on these equilibria.  Since we are working with activities rather than concentrations, it is not necessary to consider ocean salinity here.  A significant amount of research has been done concerning the temperature dependence of the equilibrium constants.  This data can be found online.  A typical set of equations are:

ln K1 =  – 1596.1/T  –  9.2597

ln K2 =  – 2174.5/T  – 16.467

ln kH =  – 2400/T  +  11.431

ln Ksp =  2388.9/T  – 27.213

where K1 is the first dissociation constant of H2CO3, K2 is the second dissociation constant of H2CO3, kH is the Henry’s Law constant, and Ksp is the average solubility constant of CaCO3.

The equation relating the pH of ocean water to the partial pressure of atmospheric CO2 at temperature  is


This equation was derived in OAII.  There are obviously a number of variables in this equation that could be changing at the same time.  It might be interesting to approach the problem as one does with PVT data and look at a surface graph.  First note that because the concentration of calcium ion in the oceans is so large, we can assume that the activity is constant at 0.00123.

It is well-known that pH is a sensitive function of temperature.  Consequently, to assume that the pH of our oceans depends only on the concentration of dissolved CO2 is a sophomoric definition of the boundaries of the system.  To express the data graphically, it is necessary to do so on a surface.  Slices of the three-dimensional graph are easily seen by following isotherms or CO2 isobars.  Note that the change in pH with temperature is not insignificant.  It has been noted that the pH of the oceans has dropped about 0.1 pH units in 150 years.  This normally is incorrectly attributed to the absorption of atmospheric CO2, and while atmospheric CO2 does come into play here, one should note that as little as a 2-degree C increase in ocean temperature can decrease ocean pH by as much as 0.05 pH units.  Moreover, assuming that the concentration of dissolved CO2 increases in a solution in which its temperature increases is not consistent with Henry’s Law.

Below is the P-pH-T representation of ocean pH.  Keep in mind that the system is highly buffered.  For clarity, the pH at various intersections of the curves is given.  Because of the three-dimensional nature of the graph, to find temperatures and pressures, be sure to follow the intersections along lines to their respective axes.  The temperature range was taken to represent global SST in zones from the equator at 303K to Antarctica at 273K.  Note the variation in ocean pH between these two temperatures on any isobar.  At today’s value of 400 ppmv, the pH changes from 8.30 to 8.00.  This would suggest that describing an average ocean pH has no physical meaning.  I would imagine that a similar effect occurs going from surface temperature to deep-water temperature.  It’s clear that using a secondary school chemistry course definition of pH in this complex system serves no useful purpose and leads one to the wrong conclusions about ocean acidification.


    P-pH-T Data for Ocean pH.

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Applied Mathematics for Physical Chemistry


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January 26, 2016 · 9:31 am

Scientific Folly of Averages

by James R. Barrante, Ph.D.


There is a misunderstanding among many scientists that using average values to do science is acceptable under any condition.  This is actually not the case.  To understand this, we must look at Error Theory.  Scientists are generally interested in two types of errors:  random error and systematic error in their measurements.  Random error is related to inherent errors in measuring devices, particularly when these measuring devices are being used near their limitations.  This type of error is associated with the precision of the measurement, how close individual measurements of the same parameter are to each other.  Systematic error is related to experimental design.  This type of error is associated with the accuracy of the measurement; that is, how close individual measurements of the same parameter are to the “true” value.   The precision of a measuring device can be increased by making the measurement more than once and taking an average only if the following is true:  the measurement must be made using the same measuring device on exactly the same sample over and again thousands of times.  Thus, the precision of the average or mean value will be greater than the precision of a single measured value.

No statistical analysis will affect the systematic error.  The average will be no more accurate than a single measurement.  What, then, is the advantage of measuring a sample several times and taking an average.  The reason is to insure that no systematic error was made in the measurement, a possibility if the measurement was made a single time.  For example, if you were determining the mass of an object, to insure that you did not misread the balance, you might take three consecutive readings, each one after zeroing the balance.  If they are all within the random error of the balance (generally supplied by the manufacturer), you can be sure that no error was made reading the scale of the balance.  Does this mean that the average of the three is accurate.  Not in the least.  If the balance had not been calibrated, the average could be precise (e.g., 24.55; 24.52; 24.54), but not accurate.  For example, the true weight could be 16.24.  Calibrating the balance is necessary to minimize systematic error.  It’s part of experimental design.

When do averages have no scientific meaning?  The study of climate change is a perfect example.  The idea of an average global temperature as it relates to an average global atmospheric CO2 level has about as much scientific meaning as the average diameter of a football has to its shape.  Knowing that the average diameter of a standard football is 9.00 inches tells you nothing about its shape.  In fact, the average presented as a single number would suggest that the football is spherical.  The average value of some measured parameter of a system (like pressure or temperature) is scientifically significant only if 1) the system is very small; 2) its boundaries are well-defined; and 3) measurements are made with the same measuring device on various points over the system where these measuring points have the same environment.  The globe satisfies none of these requirements.

You can certainly determine the temperature of the globe at various points around the globe and obtain an average that is valid as an average temperature.  But you cannot do anything scientifically meaningful with that number.  For example, suppose we wish to determine how atmospheric CO2 level affects that average.  For this to be scientifically meaningful, it would have to be true that only CO2 level could affect the temperature at every single measuring point over the entire system.  When the Soviet Union fell, a number of temperature measuring stations in Siberia were closed.  The average global temperature suddenly increased.  Climate change theory would have you believe that a sudden increase in CO2 level caused the sudden increase in average global temperature.  Another example, the average atmospheric CO2 level is found to suddenly increase.  It is assumed that this sudden increase in CO2 level was caused by an increase in burning fossil fuels.  In actuality, the opening of a coal-burning power plant occurred at one measuring point, while a volcanic eruption occurred at another measuring point.  Different causes, same effect.

Where cause and effect is meaningful is when the system is small with well-defined boundaries.  A small cylinder holding a gas is heated from 300 K to 400 K.  A pressure gauge on the cylinder measuring average pressure increases from 1.0 bar to 1.3 bar.  The average pressure change is consistent with the average temperature change, because the cylinder is a system that satisfies the three conditions mentioned above.  This is the nature of the natural sciences and it cannot be changed within the realm of the scientific method.  Unfortunately, many climate scientists do not seem to understand this.

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Demise of Dinosaurs

by James R. Barrante, Ph.D.

It is well-known that dinosaurs disappeared from the planet over a relatively short period time (on a geological time scale).  Many theories have been floated as to what caused their rapid demise.  The latest is that an asteroid struck the planet about 60 million years ago and did them in.  But there is another possible and perhaps more plausible explanation.  It is pretty clear that large animals like dinosaurs required a tremendous amount of food.  Atmospheric levels of CO2 during the era of the dinosaurs is estimated to be around 3000 to 4000 ppmv, ten times what it is today.  It is very unlikely that dinosaurs could have survived at CO2 levels of 400 ppmv or less, a fact that seemed to be overlooked in recent movies describing the Jurassic period.

If one looks over the history of atmospheric CO2 (you can find papers online), you will find that during a period from about 100 million years ago to about 60 million years ago, the period estimated to be when dinosaurs went extinct, atmospheric CO2 levels fell from about 3000 ppmv to 250 ppmv.  If that is, in fact, the case, an asteroid hit would not have been necessary to get rid of all these large animals on the planet.  We know from experience that pre-industrial levels of 280 ppmv CO2 caused mass famine to Earth’s populations in the 1700’s and 1800’s, when these populations began to grow.  It is highly probable that dinosaurs simply starved to extinction, the large vegetarians going first, then large meat-eaters, and finally smaller species.  Moreover, along with this, a reasonable explanation for the cause of this large drop in CO2 level would have been a “rapid”  (remember, on a geological time scale a million years would be “rapid”)  drop in ocean temperature, causing the excess CO2 to dissolve in the oceans.  We see the reverse happening today.  The temperature of the oceans is increasing and atmospheric CO2 levels are also increasing accordingly, lagging behind by about 400 years.

In any case, a rapid cooling globe would have made it difficult for large, cold-blooded animals to survive, thus insuring the repopulation of the globe by small, furry, warm-blooded mammals.  This scenario most likely will occur again.  Experts predict that in order for humans to make it through the 21st century, food supplies will have to double.  There is no way this is going to happen at atmospheric levels of 400 ppmv.  For large animals to survive through the 21st century, atmospheric CO2 levels would have to increase to 700 or 800 ppmv.  Will governments allow that to happen?  Not if the rank and file continue to believe that our source of food on the planet is changing the climate and this is going to be devastating.  Actually, what will be devastating will be the attempts by misguided (I am being kind) individuals to lower atmospheric levels of CO2 , which will destroy food supplies for most large animals, including humans, on the planet.  Insects probably will survive.  To quote the newspaper comic strip character Pogo, “I have seen the enemy and it is us!”

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Filed under Basic Science, Carbon Dioxide Properties, Solubility of CO2 in Water

The Real Greenhouse Gas Effect

by James R. Barrante, Ph.D.

Have you ever wondered why carbon dioxide and water vapor are called “greenhouse gases?”  They have nothing to do with greenhouses.  The major gases operating in a greenhouse are oxygen gas and nitrogen gas (air).  In physical chemistry, we refer to gases like carbon dioxide, water vapor, methane, etc. as infrared active gases.  An infrared active gas is, as it suggests, a gas that is capable of absorbing infrared light (I’m using the term “light” here rather than the more correct “radiation,” just to remind the reader that these gases are absorbing light and not heat).  All gases absorb heat, but certain gases, such as N2 and O2, are not able to absorb infrared light.  Also, as a reminder, the infrared light that CO2 absorbs at 15 microns cannot pass through glass, so its behavior in a greenhouse, aside from the fact that its concentration is 0.04%, is irrelevant.  One might argue that the surfaces in the greenhouse are radiating infrared light at 15 microns and CO2 would absorb that radiation.  That certainly may be true, but so what!  That energy is going nowhere.  The surfaces would in turn be cooling.  The radiation at 15 microns is not going to pass out of the glass windows of the greenhouse, except to be absorbed by the glass and eventually make it out as heat along with any other heat energy, but that process will be slow.

The major confusion here is a gross misunderstanding of the concept of temperature.  There are at least two ways to raise the temperature of a system, and one has nothing to do with heat.  The temperature of a system is a measure of specific types of energy associated with the wiggling, spinning, and movement through space of the atoms and molecules making up a system.  It is a property of matter.  This energy is transferred between quantities of matter, when they come into physical contact with each other (collide), and this type of transfer is what we define as “heat.”  It requires the presence of matter to take place and cannot take place in a vacuum.  We get no heat from the sun; nor does the Earth radiate heat to space.  The energy we receive from the sun comes to us in the form of light.  When you are standing out in sunlight, you are not feeling the sun’s heat, you are feeling its light.

Now the temperature of a system also can be raised by doing work on the system.  There is no heating unit in a microwave oven.  The light radiation in a microwave oven causes water molecules in food to spin faster.  This rotational energy is transferred to the food as heat. Likewise, when infrared light strikes an infrared active gas, its temperature increases, not because it has absorbed heat, but because the electromagnetic energy of light interacts with the electromagnetic properties of matter causing, in this case, the atoms making up the gas to jiggle faster.  If a gas, like O2 or N2, has no way for the electromagnetic energy of light to affect it, it is infrared inactive and basically is transparent to this type of light.

The idea that a greenhouse effect operates in our atmosphere came about from the observation that a planet with an atmosphere is warmer than a planet without an atmosphere.  But is this really an infrared active gas effect?  Would a planet with an atmosphere of pure O2 and N2 or pure argon, for example, be warmer than a planet with no atmosphere?  It seems logical that is would.

Let’s look at the operation of a real greenhouse.  What makes a greenhouse work has nothing to do with the atmosphere inside the greenhouse.  Any gas or mixture of gases would do the job.  The most important features of a greenhouse are the glass (or suitable substitute) windows.  Sunlight, mainly in the visible-uv region of the spectrum passes through the glass windows and strikes the solid surfaces in the greenhouse raising their temperature (remember, no heat is involved here).  The sunlight is doing work on the atoms and molecules making up those surfaces, just like in a microwave oven.  Nitrogen and oxygen gas molecules collide with the solid surfaces and absorb thermal energy.  This is a process involving heat.  If you are in doubt as to how much thermal energy is absorbed by these gases, sit in your car with the windows up in July in direct sunlight.  That hot air you feel is not CO2.  Because these gases cannot pass through the glass, the greenhouse warms.  As we described above, the warmed solid surfaces of the greenhouse do radiate a large amount of infrared light, some wavelengths of which will pass through glass, exiting the greenhouse.  If you believe that it’s the water vapor doing the warming, remember that over a desert, there basically is no water in the atmosphere.  It is hard to believe that the collision of nitrogen and oxygen gases with the hot desert sand is not the major contributor of the hot, desert winds.   Nitrogen and oxygen gases are truly the major greenhouse gases in Earth’s atmosphere.

Does the planet operate this way?  Of course it does.  We all have experienced it.  During daylight hours, sunlight strikes the planet’s surface and raises its temperature.  Again, no heat is involved in the process.  Touch the pavement on a hot, summer’s day.  Nitrogen and oxygen gases collide with the warmed surfaces and absorb some of this energy.  This is a heat process.  Since these gases are not infrared active, they cannot radiate this energy as light.  This heat energy is truly “trapped” in primarily the translational motion of the molecules in the atmosphere.  All nitrogen and oxygen can do is to spread the energy around to other air molecules as they rise from the surface by colliding with their neighbors.  During the night, the gases near the surface pass the energy back to the surface by colliding with it, which, in turn, can radiate it to space.  But keep in mind that the Second Law of Thermodynamics operates here.  The atmosphere can pass the energy back to the surface as heat only if the surface is cooler than the air.  Generally, in summer, this might not be the case, since solids hold on to heat energy more efficiently than do gases.

Does the “infrared active gas effect” involving CO2 and water vapor (what climate scientists refer to as the greenhouse effect) come into play here?  Absolutely, but since these gases can radiate heat energy as light, it would seem logical that these do not hold this energy but either pass it on to N2 and O2 or radiate it to surroundings  Interestingly, the Second Law does not operate here, as it does with N2 and O2.  The irradiated photons do not go looking for a receiver that is cooler than the emitter. That light energy can be absorbed by substances that may be at a higher temperature than the emitter.  Moreover, unlike thermal energy transfer which is agonizingly slow, light energy transfer (radiation) takes place at the speed of light.  How about that?

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Let’s Do P-Chem Homework!

by James R. Barrante

From the author of “Applied Mathematics for Physical Chemistry,” 3rd ed., a new textbook on solving physical chemistry problems in the iBook Store.  Only $9.99.  See it today.


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