Electromagnetic radiation thermodynamic properties

To prepare for the thermodynamic properties of radiation effects, we consider the pressure exerted by electromagnetic radiation based on Maxwell s equations for electromagnetic fields. The analysis is not as difficult as may appear at first glance. But if you do not wish to wade through the rather lengthy derivation, please note the final result (Eq. (5.5.11)) which is needed for the next section. 

In the late nineteenth century, a whole set of experiments progressively lead to the conclusion that classical physics, namely, Newtonian mechanics, thermodynamics, and nascent electromagnetism, were unable to explain empirical evidence gathered by experimentalists. Scientists of that time were unable to conciliate two apparent contradictory aspects exhibited by radiation and matter. Some experiments demonstrated that light behaved like a wave, while others showed a rather corpuscular nature. On the other hand, electrons, protons, and the other massive particles would manifest wave-like properties in certain experimental conditions. 

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