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Aerosols, Climate Change and The Dramatic Failure of Planck's Law

Physicists show how Planck’s law of black body radiation breaks down for nanoparticles, a discovery that could have huge implications for climate science

  • September 6, 2012

In 1991, the eruption of Mount Pinatubo in the Philippines released some 20 million tonnes of sulphur dioxide into the upper atmosphere. Sulphur dioxide reacts with other substances to produce airborne nanoparticles called sulphate aerosols, which tend to reflect sunlight.

Consequently, in the two years after the eruption, the global temperature dropped by about half a degree. 

The effect of aerosols on the Earth’s climate is hugely important but mind-bogglingly complex. In addition to cooling the Earth, some aerosols, such as soot, tend to absorb sunlight and so heat up the atmosphere. 

A huge outstanding question in climate science is how these processes of heat absorption and reflection balance out.  

Part of the problem is that nobody understands how nanoparticles absorb and emit heat. In theory, this process is governed by Planck’s law, which describes the amount of electromagnetic radiation emitted by a perfect black body at a given temperature.  

But in practice, real objects don’t emit heat perfectly so physicists have to apply a correction factor called the spectral emissivity. This depends on the properties of the object’s surface–it’s material and roughness, for example. 

In recent years, however, tantalising evidence has emerged indicating that an object’s shape and volume may also play a role in this process.

Today, Christian Wuttke and Arno Rauschenbeutel at The Vienna University of Technology in Austria show for the first time how and why this true. 

They point out that when an object is large compared to the wavelength of the radiation it is emitting, then surface effects dominate. But when an object is small compared to the wavelength, then radiation can be emitted from any point within its volume. In that case the geometry of the particle must play a role.

To prove the point, they measured the heat radiated by a silicon nanofibre with a diameter of 500nm, which is much smaller than the wavelength of thermal radiation.   

They show that this heat emission cannot be described by Planck’s law, even when a correction factor is applied. 

Instead, Wuttke and Rauschenbeutel accurately model the output using another theory called fluctuational electrodynamics, which takes into account the geometry of the experiment. 

In effect, they show that fluctuational electrodynamics can accurately model the heat absorption and emission characteristics of nano-objects, the first time this has been possible.

That will have important implications for the manufacture of heat-emitting devices such as incandescent lamps, which could be made much more energy efficient if their heat emission were more carefully controlled.

But the biggest impact is likely to be in climate science. “These results might also lead to a better understanding of the impact of particulate matter, such as mineral dust aerosols from soil erosion and soot from combustion sources, on the climate system via absorption and emission of solar and thermal radiation,” say Wuttke and Rauschenbeutel.

This new approach means that it ought to be possible to work out the thermal properties of individual nanoparticles from first principles. 

It’ll be a long and complex process but that should be a crucial building block in future models of the way aerosols influence the climate.  

Ref: arxiv.org/abs/1209.0536: Probing Planck’s Law for an Object Thinner than the Thermal Wavelength

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