## Entropy of radiation on Earth

and its applications

# Entropy budget of the Earth's atmosphere

(\Huge{In}) the following figure, the radiation emitted by the Earth is analysed. The entropy spectrum is represented by a red line and the energy one by a blue. It has been obtained by evaluating the spectral distribution of the energy of radiation, solving the radiative transfer equation under clear sky conditions for the US standard atmosphere, and determining the associated entropy afterwards. The black line represents a blackbody at temperature $T$ = 285 K. The simulation does not include scattering or splitting entropies, and the deviations from the blackbody behaviour are due only to emission/absorption processes.

As it can be seen, the ratio of entropy to energy $($green line$)$ at certain wavelengths contains more entropy than the expected for a blackbody $($black line$)$. This entropy is not a consequence of blackbody emission, and is generated by the irreversible processes that take place in the atmosphere. By making the difference at individual wavelengths between the magnitude of its ratio and the expected for a blackbody, the entropy production in the atmosphere by absorption/emission processes is characterized as the strength of each line.

Different chemical species in the atmosphere will produce more or less radiation entropy, and in this way we can actually measure their contribution. The next figure represents the same calculations for different atmospheric profiles.

The equivalent blackbody temperature is different for each atmospheric profile. In order to have a clearer picture, we can eliminate the trend of the spectra. After that, the deviation from the blackbody is characterized as the integral under the ratio:

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