The earth is an open system. It obsorbs energy from sun and release energy from some events in the earth, such as earthquake and volcano etc. Can these energies balance in a long time scale? How to estimate the internal energy of the earth from thermodynamics?
That you don't mention the energy loss through thermal radiation (most ovious over night where there is no much thermal radiation coming in) shows that you are just at the beginning of your thinking about the problem.
The idea that thermodynamics could allow to estimate the internal energy of the earth looks a bit strange. Of course thermodynamics (and mechanics) sets the framework but without specific data on e.g. material composition you can gain nothing. An example: a significant part of the internal thermal energy of the earth is known to come from radioactiv decay of nuclei in earth's own matter. So, if during earth formation much less unstable nuclei would have been involved, the earth would have significantly less thermal energy now.
Thank you for your answer and comments. It is difficult to set up a scheme to measure the internal or thermal eergy of the earch. Anyway I think that thermodynamics should provide a way to understand the long-term behavior and evolution of the earch if one can find an efficienct method to measure the thermodynamical variables.
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