Heat distribution amongst materials in thermal contact is controlled by respective thermal conductivities rather than any putative optical properties. The relationship between thermal gradient -the change in temperature per unit length- and heat flux -the rate of energy flow across a unit area- is key to understanding the relationship between thermal conductivity and heat distribution within a material or materials in thermal contact. This is limited by the overall power available via the heat flux, which may come from another body in thermal contact or as radiation from a body isolated by a vacuum. However, the amount of heat available to a system due to increased absorption, is lost to corresponding emission. Thus a change in materials without a change in incident radiation -the radiation that falls on a body- can, at most, alter the distribution of heat within those materials.
The Physics of Nitrogen, Oxygen, and Carbon Dioxide
The relationship between conductivity and net heat transfer explains why physicists, as Gerlich & Tscheuschner (2007 and 2009) point out, only consider the question of heat and temperature in terms of measurable physical properties such as thermal conductivity and heat capacity, unless that heat is being radiated across a vacuum. The latter case presents a question only answered by the Stefan-Boltzmann Equation, explained below. However, in terms of bodies in thermal contact, such as the atmosphere and the surface of the earth, the assertions of Arrhenius with respect to backradiation must necessarily be accompanied by a great variation in thermal conductivity in order to account for a comparably greater change in thermal gradient. This question is addressed in Gerlich & Tscheuschner (2007 and 2009, pp. 6-10), which shows an insufficient difference in the thermal conductivities of carbon dioxide, nitrogen, and oxygen to account for the claims of Arrhenius.
Carbon dioxide does, in fact, have a lower thermal conductivity than either nitrogen or oxygen (by roughly 36%, calculated from the figures of Gerlich & Tscheuschner, 2007 and 2009). So a large increase (i.e. by hundreds of thousands of parts per million) in atmospheric carbon dioxide concentration that would increase the thermal gradient accordingly, could produce a measurable surface warming. As this cannot change the amount of heat flowing through the system, the effect would be manifest by a decrease in atmospheric temperature offset by a corresponding increase in surface temperature. However, a meagre doubling of the presently insignificant levels of atmospheric carbon dioxide cannot have a measurable effect. In fact, geological history records that other factors have a much greater influence on global climate than carbon dioxide.
If carbon dioxide produced the backradiation claimed by Arrhenius, thermal conductivity measurements of carbon dioxide would be so suppressed by the backradiation of heat conducted into this material, that the correspondingly steep temperature gradient would yield a negative thermal conductivity of carbon dioxide. In reality, a 10,000ppm increase in carbon dioxide could, at most, reduce the conductivity of air by 1%. Given the actual difference between the thermal conductivities of carbon dioxide (0.0168) and zero grade air (0.0260), a 10,000ppm increase in carbon dioxide would lower the thermal conductivity of zero grade air by 0.36%. That would represent a 0.36% increase in thermal gradient, or a surface warming of 0.18% and a ceiling cooling of 0.18% of the total difference in temperature between the top and bottom of the affected air mass. In the case of a tropospheric carbon dioxide increase of 10,000ppm, that would correspond to a warming of 0.125ºC, or one eighth of a degree Celsius at the earth’s surface, offset by a cooling of 0.125ºC at the tropopause. On the scale of doubling the troposphere’s carbon dioxide, the surface warming predicted by this simple and materialistic thermodynamic approach is on the order of 0.004ºC.
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