Tuesday, 28 June 2011

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.

Most of these arguments involve the Stefan-Boltzmann equation, which relates the radiation from a body to its temperature. The hotter a body, the greater the radiation. The physical system being discussed is the surface of the Earth (heated by the sun) and the atmosphere above. In a stable or "equilibrium" situation, incoming solar radiation impinges on the surface, which radiates infrared (invisible) energy to the atmosphere. The atmosphere absorbs much of this radiation, and in turn radiates both to the surface and to space. The outgoing radiation to space is equivalent in energy content to the incoming solar to the surface, maintaining the equilibrium.

On average, the surface is hotter than the atmosphere; it has to be, as it is the source of heat in the system (I'm ignoring atmospheric absorption of solar radiation for the moment) and radiates upwards only, while the atmosphere radiates both up (to space) and down. Most of the surface radiation is absorbed by the atmosphere, the rest escapes directly to space. Radiation from the surface has been measured, as has radiation from the atmosphere. The strength of the radiation, in both cases, agrees with the result calculated from temperature using the Stefan-Boltzmann equation correctly. The rate of heat loss from the surface can be calculated by simply subtracting downward radiation from surface radiation. It is this rate of heat loss which defines the surface temperature. If there is increased radiation from the atmosphere, the net rate of loss is less; the input from the sun to the surface is unchanged, so to re-attain equilibrium, the surface warms up until its increased upward radiation balances that from the sun once more. There is no "heating" of the surface by the atmosphere, and no violation of the Second Law.

To those familiar with the subject, this is a gross simplification; the surface also loses heat through evaporation of water to the atmosphere, especially from the ocean, and by direct heating of surface air - convection. The atmosphere absorbs some incoming solar radiation; ultraviolet light by ozone, infrared by the so-called "greenhouse gases" and some visible light. In fact all atmospheric gases are "greenhouse gases" to a greater or lesser degree, and I plan to explore this topic in a future post.

Let's look in detail at the (mis)use (more generously, misunderstanding) of the Stefan-Boltzmann law and equation in these arguments. The law states:

The total energy radiated per unit surface area of a black body per unit time (known variously as the black-body irradiance, energy flux density, radiant flux, or the emissive power), is directly proportional to the fourth power of the black body's thermodynamic temperature and is given by 
p = sT4
Where p is the radiated power in W/m² (watts/square metre), s is Stefan's constant and T is the temperature in °K (0°C = 273°K). That's it - no reference to surroundings or anything else. The radiation is electromagnetic radiation, and for the range of temperatures under considered is longwave infrared. The radiation is termed a flux and is a vector, that is it has direction. Where the blackbody has surroundings, the net radiation (or flux) is the difference between the two fluxes:

p(net) = sTb4 - sTs4

Where Tb and Ts  are the temperatures of blackbody and surroundings respectively. Perfect blackbody radiation is assumed; in reality emissivity factors should be included, for both blackbody and surroundings, but this doesn't affect the argument here. Both terms signify a radiation flux. The flux from the blackbody reaches the surroundings and vice-versa. If the result is positive, the net flux is from blackbody to surroundings; if negative from surroundings to blackbody.

The idea that the blackbody somehow suppresses radiation from its cooler surroundings so that the flux from the blackbody is equal to the calculated net flux violates the Stefan-Boltzmann law. The second term above becomes zero which implies its temperature has dropped to absolute zero. The blackbody is also not now emitting according to Stefan's Law. Energy has been destroyed or neutralised in some way, which of course violates the First Law of Thermodynamics. In order to have a net flux there must be two fluxes. Applying the law with the two terms for the fluxes, then claiming that neither of the two fluxes exists between the blackbody and surroundings is clearly a nonsense.

UPDATE - After re-reading the above, I have several observations to make:

1. The Second  Law says nothing about radiation, only heat.

2. It's known that  the Earth's surface radiates according to Stefan's Law and is not "inhibited" by radiation from the atmosphere. A good chunk of the surface radiation goes through the "atmospheric window" - that portion of the infrared spectrum to which the atmosphere is transparent. This radiation is "seen" by satellites, and correlates well with what Stefan's Law predicts.

3. Infrared radiation is in the form of photons emitted from matter. A photon emitted from the surface might be absorbed, reflected or transmitted to space. A photon doesn't "know" its destiny. How can a molecule of water vapour or CO2 high in the atmosphere in any way influence the emission (or not) of a photon at the surface?

4. Even if the "no back-radiation" hypothesis were true, it would make no difference to the outcome. The "net flux" result is the same. Increasing the temperature of the surroundings (atmosphere) reduces the net flux, so reducing the cooling rate at the surface, leading to a higher temperature of the surface at a new equilibrium

So why the title "Zen and the Second Law of Thermodynamics"? Zen "emphasizes experiential Wisdom in the attainment of enlightenment. As such, it de-emphasizes theoretical knowledge in favor of direct self-realization through meditation and dharma practice." Need I say more?

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