The Law of Radiation for a Perfect Black Body

Consider a Prevost chamber of volume V (whose walls are impermeable to heat). Let its temperature be T and the energy density of the radiation in its interior be u. Let the chapiber be furnished with a movable and frictionless piston (also impermeable to heat) which separates the interior of the chamber from the external (empty) space. 

Let us now push forward the piston so as to diminish the volume of the chamber from 7 to V. If it were possible to perform this operation without doing work, the total energy of the chamber would be the same as before, but the energy density of the radiation would have increased, since 

We have therefore u u, and hence T T. Thus we should have raised the temperature of the chamber without doing work and without altering its internal energy. This is incompatible with the second law of thermodynamics, and we conclude therefore that our original assumption must be false, i.e. that it is impossible to displace the piston without doing work. The radiant energy in the Prevost chamber must therefore exert a Digitized by Microsoft  

The magnitude of this pressure cannot be calculated by thermodynamical methods. From Maxwell s electromagnetic theory of radiation, however, it follows that the pressure exerted by radiation (force per unit area) is given by 

This is in accord with the experimental determinations of Lebedew and of Nichols and Hull. 

---