We shall now remove a restricting assumption made in order to enable us to apply the value of Maxwell's radiation pressure, calculated in the preceding chapter. Up to now we have assumed the cylinder to be fixed and only the piston to be free to move. We shall now think of the whole of the vessel, consisting of the cylinder, the black bottom, and the piston, the latter attached to the walls in a definite height above the bottom, as being free to move in space. Then, according to the principle of action and reaction, the vessel as a whole must remain constantly at rest, since no external force acts on it. This is the conclusion to which we must necessarily come, even without, in this case, admitting a priori the validity of the principle of action and reaction. For if the vessel should begin to move, the kinetic energy of this motion could originate only at the expense of the heat of the body forming the bottom or the energy of radiation, as there exists in the system enclosed in a rigid cover no other available energy; and together with the decrease of energy the entropy of the body or the radiation would also decrease, an event which would contradict the second principle, since no other changes of entropy occur in nature. Hence the vessel as a whole is in a state of mechanical equilibrium. An immediate consequence of this is that the pressure of the radiation on the black bottom is just as large as the oppositely directed pressure of the radiation on the reflecting piston. Hence the pressure of black radiation is the same on a black as on a reflecting body of the same temperature and the same may be readily proven
for any completely reflecting surface whatsoever, which we may assume to be at the bottom of the cylinder without in the least disturbing the stationary state of radiation. Hence we may also in all the foregoing considerations replace the reflecting metal by any completely reflecting or black body whatsoever, at the same temperature as the body forming the bottom, and it may be stated as a quite general law that the radiation pressure depends only on the properties of the radiation passing to and fro, not on the properties of the enclosing substance.