Jennifer Coopersmith ©2023
Two famous laws of physics are relevant to our understanding of the climate. The First Law concerns the conservation of energy, the Second Law concerns the distribution of that energy. Energy comes in different forms and can be inter-converted between these forms. Overall, it’s conserved (First Law) but the conversions prefer to go in one direction rather than another direction. Specifically, the preferred direction is towards more heat (Second Law).
What is heat ? It is a statistical form of energy, that is to say, it is made up from gazillions of microscopic ever-jiggling parts (e.g. molecules in a gas, atoms in a solid, photons in a cavity). Add together the energy of each microscopic part, and the sum total is the heat. The Second Law mandates that when heat is added to a system, the (average) rate of jiggling goes up. This implies that the system is warmed – but the true import of the Law is that (as the molecules jiggle around more) the system becomes ‘messier’, and so the energy gets to be distributed in a more ‘disorganized’ fashion.
Lets switch the discussion to planets. Ideally, when sunlight falls on a rocky planet then that planet acts as a gigantic mirror and reflects all the radiation it receives. In actual practice, no planet is a perfect reflector and so ‘the mirror’ (the planet) warms up slightly. This is what happens to bodies like the Moon. Bodies that in addition have an atmosphere (e.g. Earth, Venus, and Titan) are more than just reflectors and so they warm up even more. But here’s the thing : the more and more complex and different from a perfect reflector the planet is, the more and more planet-warming there is. For example, going from a hypothetical planet that is a perfect reflector to one whose surface is un-shiny and rough, or from a planet that is an imperfect reflector and then also has an atmosphere, or from one with an atmosphere of monoatomic molecules to one of diatomic molecules, or from diatomic to triatomic molecules, or one type of molecule to mixtures of types – all this leads to greater and greater warming. Why ? Because as there are more and more (microscopic) ways that the system can become energized, so the energy will get to be distributed in a more and more ‘disorderly’ fashion.
From now on, we consider specifically planet Earth. The sun’s rays warm the Earth’s surface, and then the surface heats up a thin layer of air adjacent to it, and then this first layer of air heats up a second thin layer of air on top of it, and then this second layer of air heats up a third layer of air on top of it … and so on and so on. But how does this heating happen ?
Heat can be transmitted in two main ways – by conduction and by radiation (we ignore convection). It is seldom emphasized how very different these processes are : conduction requires the presence of molecules whereas radiation can cross a vacuum. Also conduction is slow whereas radiation is fast – the speed of light ! Finally, it’s not either/or ; whether there’s conduction or not, there’s always radiation.
Let’s explain conduction through the atmosphere – the first 10 km or so. Atoms of rock and molecules of air are forever jiggling (ultimately, the reason is quantum mechanical). Also, as the temperature increases the jiggling gets to be more and more energetic (again, the reason is quantum mechanical). When air molecules bounce off the warmed rocky surface then – more often than not – they will jiggle more energetically whereas the rock atoms will jiggle less energetically. In short, some heat has been conducted away from the rock and into the air.
The air molecules are not locked into a lattice but they nevertheless maintain roughly constant positions, jiggling all the while, and having collisions with other nearby jiggling air molecules. After a collision, molecules that are jiggling quickly tend to get slowed-down, molecules that are jiggling slowly tend to get speeded-up. In this way the energy is shared around ; it therefore spreads, and it is thereby conducted through the atmosphere. The scale of this process is mind-boggling : under everyday conditions (in the kitchen, in the street), there are around a billion molecule-to-molecule collisions per second in every cubic centimetre of air! (An air molecule moves at around one thousand miles per hour! but it doesn’t get very far because after only six to seven millionths of a centimetre it has another collision!) It’s impossible to visualize this but we’re going to try anyway : think of a blur of a near-infinite number of tiny bumper-cars having non-stop bumper-car collisions. What this leads to is the ‘jiggle-energy’ per bumper-car – whoops, molecule – getting redistributed more and more evenly through time. What about the radiation (“it’s always there”) ?
At this stage of the explanation there is another input from quantum mechanics ; it’s called ‘wave-particle duality’. The duality asserts that the radiation exists both as particles (known as photons) and as waves (btw, we sometimes say rays for waves). The blur of bumper-car collisions continues as before but photons are now included in the mix. Let’s imagine that the photons are like bowling balls (at screaming speeds, and of a ‘weight’ proportionate to their energy), and the bumper-cars each have a little ramp (like a mini snow plough). A bowling ball can slide up the ramp and come to rest on a little shelf (the shelf has little hollows in it). The bumper car is then said to be in an ‘excited state’ (yet more quantum mechanics). After a short while the bowling ball rolls off the shelf, down the ramp, and whizzes up the ramp of another bumper car.
It’s like a bubbling brew of bumper-car and bowling-ball collisions. But that’s not all. Because of ‘wave-particle duality’, we also have radiation-as-waves added to the brew : these waves ‘bathe’ the ingredients of this soup and in so doing they ‘keep the soup warm’. (By yet more quantum mechanics, the little shelves are at just the right height, the bowling balls are exactly the right ‘size’, and the waves are of just the right length! And so the soup approaches a certain temperature, T.)
The Greenhouse Effect
The greenhouse effect (GHE) is a very successful analogy for how planets with atmospheres stay warm. Recently, there is evidence that ‘greenhouse gases’ have led to Earth’s stratosphere becoming cooler rather than warmer. It is understandable that some people are perplexed by this result : how can cooling be consistent with the Second Law which requires heating ? and whoever heard of a greenhouse warming up and then you put your hand on the glass on the sunny-side and its gotten cooler ?
Don’t worry, all can be explained. First, cooling does not automatically contradict the Second Law because we must always look at the overall picture (e.g. a fridge gets to be cold inside but the fridge surroundings have got hotter). Second, no wonder the GHE is counter to everyday intuitions because whoever heard of a greenhouse that was thirty miles high and where one needed breathing apparatus? However when we explain the GHE with a planetary-sized greenhouse, the analogy works rather well. Here goes.
Near Earth’s surface, the air is a flurry of activity between molecules, excited molecules, and radiation (the ‘soup’ mentioned before). However, not all air molecules are the same. The nitrogen and oxygen molecules have no low-lying ‘shelves’ whereas the carbon dioxide molecule (CO2) has three ‘shelves’, each of which can act as a parking place for a ‘bowling ball’ : but it’s a parking place reserved for bowling balls of a specific ‘size’ (photons of a specific energy, equivalent to radiation of a specific wavelength). In detail, the wavelength is ‘long’ (between 2 and 15 microns) and corresponds to infrared radiation (IR). Now air molecules of whatever type whizz about more as the temperature rises but carbon dioxide molecules, because they can get ‘excited’ as well as whizzing about, they act as an extra storehouse of energy, and so the atmosphere is warmed (this is the famous ‘greenhouse warming’). But again that’s not all…
We explained earlier that the atmosphere’s particles are forever ‘bathed’ in radiation. This radiation has a smooth ‘spectrum’ (range of wavelengths) shaped like a hill. However the CO2 molecules are storehouses of energy – a specific amount of Joules for each excited molecule. They have extracted this energy from the smooth background spectrum leaving a tooth-shaped chunk missing in the IR region. At greater and greater heights above the Earth’s surface the atmosphere gets thinner and thinner and so conduction stops working (it needs crowds of molecules) and radiation takes on the burden of responsibility for heat-transfer. Radiation is happy to oblige – it vaults across the voids – but its spectrum has a ‘tooth’ missing. So the net energy that gets transferred is reduced – it is not the full set of dentures ! – and this leads to cooling at high altitudes (the beginning of the stratosphere). This effect was predicted in the 1960s and has been observed since the 2010s – the stratosphere between 15 to 20 km altitude is cooling by about 0.5 degrees C per decade.
In summary, there is greenhouse warming in the lower atmosphere (due to CO2 trapping of heat) and there is cooling of the stratosphere (due to CO2 trapping of heat). Apart from the fact that these effects were predicted, and then experimentally confirmed, I hope you’re impressed – as I am – that scientists have arrived at a beautifully consistent explanation. (Of course the detailed explanation is much more complicated incorporating other ‘greenhouse gases’, aerosol particles, the ozone layer, and so on.) By the way, the lower stratosphere was already a very cold place (around −50 degrees C) so to simply say ‘stratospheric cooling’ is rather misleading.
Jennifer Coopersmith 