Zen and the Second Law of Thermodynamics

The Clausius expression of the Second Law of Thermodynamics:

No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.

This is unequivocal, so how does the "Greenhouse Effect" in the atmosphere raise the temperature of the Earth's surface? The atmosphere is cooler than the surface, so the flow of heat must be from the surface to the atmosphere, and so it is. Yet a number of people claim that this is proof that the "Greenhouse Effect" does not exist; "A cooler body cannot heat a warmer body" they proclaim, while in fact no-one has even suggested that this is the case. Some even go so far as to claim the so-called "back radiation" from the atmosphere to the surface doesn't exist.

Such claims have no basis whatsoever. Atmospheric longwave infrared "back radiation" has been measured, and its spectrum plotted, routinely since the 1950s. A simple web search can reveal summaries of some of the hundreds of scientific papers on the topic. It is part of the fabric of atmospheric physics. To ignore or dispute the existence of the phenomenon can only be termed denialism. However, disputing the effect(s) of this radiation in detail is another matter entirely. Such arguments can be examined for scientific logic and therefore veracity.

A Question of Scale (3) - Latent Heat

Latent (hidden) heat plays an important role in climate and weather, but its importance is often overlooked or misunderstood. Heat is simply the energy of vibration of atoms or molecules in solids, liquids and gases. Heat is motion; motion is heat. More motion equals more heat - hotter. Less motion equals less heat - colder.

In a solid such as ice, water molecules are fixed relative to one another. They can move a small amount relative to their neighbours, but can't move freely through the solid; it's as if they were inter-connected by springs or stiff elastic. These notional "springs" are the strong attractive force which operates at the relatively short distance between the molecules.

In a liquid, molecules vibrate much more, and are free to move about, like table-tennis balls in a bucket. Shake the bucket, and the balls move about. Shake it more; balls from the bottom can move to the top, and vice-versa. They collide with one another, thus transferring energy of motion (kinetic energy). More vigorous shaking may result in a ball leaping above the others - it may even leap out of the bucket. This is a simple illustration of evaporation - balls moving through the air have effectively become a gas.

In a gas, the molecules have much greater energy of motion, and are free to move in all directions like the balls that escaped from the bucket. They collide one with another, transferring and sharing their kinetic energy. As a consequence they are much farther apart than molecules in a liquid or solid.

To transform a solid into a liquid, enough heat has to be added for the kinetic energy of the atoms or molecules to overcome the strong attraction between them. The amount of heat per unit of mass of the solid is termed the latent heat of fusion for that solid. It is many times greater than the specific heat, which is the amount of heat per unit of mass to raise its temperature by one degree Celsius (or Kelvin). Why is this important? It takes far more heat to melt ice than it does to warm ice to its melting point.

The specific heat of ice is 2.108 kJ/kgK (thousand joules per kilogram per degree Kelvin); the latent heat of fusion of ice is 334 kJ/kg. It takes 158 times as much heat to melt a given mass of ice as to raise its temperature by one degree. It appears to me that it's a common misconception that once ice is raised to its melting point it will melt rapidly. It would take 158 times longer to melt ice than to raise its temperature the last degree to the melting point, given the same rate of heat input.

We use this property of ice almost daily. A couple of ice cubes in a glass of juice or spirit lowers the temperature rapidly, but that cooling reduces the heat available for the ice to melt, which must then come from the surroundings - the sun, the air or a warm hand. A large ice-floe or iceberg can drift for months before disappearing completely. Some of the much larger ones can endure for years. The ice that does melt removes a lot of heat from the surrounding air and water, reducing the temperature difference and slowing the transfer of heat and therefore the melting rate.

Enough about ice - I can see the bottom of my glass. Conversion of a liquid into a gas, as in water to water vapour (or steam) requires an even greater input of heat energy as does melting. The figure of 334 kJ/kg for ice to water compares with 2,270 kJ/kg for water to vapour - nearly 7 times as much. This is important because it's the mechanism by which vast quantities of heat energy are transported aloft from the surface of the Earth into the atmosphere. It's a major factor in climate - some would argue (including myself) that it's the major factor.

Evaporation of water cools land and more importantly ocean surfaces, the resulting upward convection drives surface winds, and the water vapour condenses to forms clouds which block sunlight from reaching the surface. The condensation into clouds releases the latent heat into the upper atmosphere, where it's better placed to finally radiate into space and balance the incoming dynamo of the climate; energy from the sun. Water and its latent heat therefore has a major impact in cooling the Earth's surface, a direct result of its unusual properties compared with other common substances.

See this page for the properties of dihydrogen monoxide (or hydroxyl acid - it's nasty stuff, thousands of people die because of it, or a lack of it, or in it, every year).

A Question of Scale (2)

The atmosphere is, as I have previously said, very large. It extends tens of kilometres above the Earth's surface, though because of rapidly decreasing density, half the total mass is contained in the first 5 km. Ocean volume is less, almost exactly half of the "normalised" (1 atmosphere pressure) atmosphere. A good illustration can be seen here, which shows the relative size of the Earth and spheres representing ocean and atmosphere.

However, while the atmosphere has a larger volume, it has a much smaller mass; the atmosphere is a mixture of gases, and the ocean is liquid water with small amounts of dissolved solids. Normal atmospheric pressure at the Earth's surface can balance a column of mercury (which is a very dense liquid metal) 760 mm high (just over 3/4 metre); this equates to a column of water 10.33 metres high. Another way to envisage this is to consider that the atmosphere exerts a pressure equal to the weight of the column of air above a given area. The pressure is 1.03325 kilograms per square centimetre; the height of a column of water weighing 1.033 kg, and therefore exerting the same pressure on 1 sq.cm is 1033 cm or 10.33 metres. The mass of the atmosphere is equivalent to a depth of just 10.33 metres of sea water. When the ocean area is taken into account (71% of the earth's surface), this equates to 14.5 metres depth of ocean.

When heat content or capacity is considered, the disparity is even larger. The specific heat (amount of heat needed to heat one gram of a substance one degree Celsius) of sea water is 3.93, the specific heat of dry air is 1.006.

So what does all this mean? It means that the heat capacity of the atmosphere is equivalent to just 14.5 x 1.006/3.93 or just 3.7 metres of ocean depth. The ocean's heat capacity is hundreds of times greater than that of the atmosphere. When he was explaining about the logic of lighter electrons orbiting the relatively massive atomic nucleus (rather than the opposite as had been claimed by some), Ernest Rutherford said “When you’ve got an elephant and a flea, you assume it’s the flea that jumps.”

When considering the internal driving factors in Earth's climate, the atmosphere is the flea, and the ocean the elephant.

A Question of Scale

In considering physical systems I find it essential to have a concept of the relative size of things and quantities. For example, the carbon dioxide (CO2) concentration I referred to in my last (and first) post is usually quoted in parts per million (ppm) - actually measured by volume, so more accurately ppmv. Strictly, ppm refers to concentration by weight. The currently accepted concentration is 390 ppmv, which sounds a lot, until it's expressed as a percentage; 0.039% or just under four-hundredths of one percent. As a fraction it's 1/2564.

However, the atmosphere is very large, and that 0.039% represents about 2,500 gigatonnes (billion tonnes) of CO2. That seems pretty big, until it's compared with CO2 dissolved in the world's oceans - about 50 times as much, carbon in the biosphere (all living things, including bacteria and plants) - several hundred times as much, and in carbonate rocks in the earth's crust - several thousand times as much. For comparison, the amount of CO2 emitted annually as a result of mankind's activities is estimated to be about 32 gigatonnes.

So is that 0.039% important, or at all significant? Of course it is - the question though, is how significant. Despite contrary assertions, there is strong disagreement about the relative importance of that (increasing) amount on Earth's climate and ecology. Someone once said "There's what we know about the climate, there's what we don't know about the climate, and there's what we don't know we don't know about the climate. Of these three, the last is by far the largest". I would suggest that applies to every area of scientific theory and research, though perhaps in different proportions.

A Personal Viewpoint

Sometime in 2003, I developed an interest in the subject of Global Warming. Newspaper articles discussed the perils of a warming world, the forthcoming global food crisis, and the touted culprit was carbon, or to be more precise carbon dioxide, which is much different. I was supposed to be concerned about my "carbon footprint", be doing more to use "sustainable" foods, fuels and products, and to be seen to be doing "my bit" to "save the planet".

Always having subscribed to the motto "take no-one's word for it", I decided to do a little research on the internet. I was surprised to find myself in an enclosed sphere of blogs and websites, many of which seemed to me to have a rather shrill background tone, and much of the analysis seemed to be unquestioning and authoritative. There was very little on the actual science of this "Global Warming", such as references to research papers or articles written by actual scientists. Blog discussions were almost entirely between comment posters who clearly knew one another, and were generally in agreement. I read that the "science was settled", and that phrase alone alerted me that there was a little too much certainty in these discussions.

One item on one website was the clincher - an article on "acid rain". This had been a great scare many years ago, but the subject had disappeared from news reports once it became clear that many of the scientific studies were badly flawed. Trees were not dying at an unprecedented rate worldwide, much of the observed "damage" had been occurring for decades if not centuries, and the acid that was detected in the soil around the trees was mostly created naturally. The article was unquestioning; acid rain was a serious problem, it was entirely due to the burning of coal in power stations and from some industrial processes, and the forests were doomed to all but disappear within decades. The fact that decades had already elapsed since the "problem" was identified, and no arboreal disaster had occurred was clearly being ignored.

The author had penned several other articles, which now received my critical attention. One of these claimed that carbon dioxide (CO2) had increased since the start of the industrial revolution, and now stood at over 3% of the atmosphere, due to the burning of coal and other fossil fuels. I knew that CO2 was considered to be a "trace gas" and so couldn't possibly occupy 3% of the atmosphere, so dug around a little to discover that the correct figure was just over 0.03%, which is 100 times lower. En route I also found that water vapour was the main "greenhouse gas" and was in fact more powerful, molecule-for-molecule, than CO2. I commented on the article, pointing out the error, and was rebuffed - "How could a gas at only 0.03% of the atmosphere have much effect? The correct figure is the quoted 3%". However, I had by then discovered an authoritative report, which had been published by a body called the IPCC, which confirmed my figure, so I returned to the article to find that I'd been labelled as a "skeptic". Undaunted, I provided details of my source, with several other references and posted another comment, which I later found had been deleted. Seemingly, facts were inconvenient for the author and his supporters. I had learned a valuable lesson. I had also noted his response - how could a gas at only 0.03% of the atmosphere have much effect?