36 
THERMODYNAMICS OF RADIATION 
decrease or increase until the loss by absorption just balances the steady 
emission from the walls. In practice the time required to reach this equi 
librium condition is extremely short*. 
The equilibrium distribution of radiation, both as regards density and 
quality ( wave-length ), is fixed entirely by the temperature T of the walls. 
For suppose that by constructing the walls of different materials we 
could have two enclosures A and B with walls at the same temperature 
T but with the equilibrium density of radiation within a certain range of 
wave-length SA greater in A than in B. Let us open momentarily a passage 
between A and B crossed by a screen transparent only to radiation in the 
range 8A. More radiation of this quality will fall on the A side of the screen 
than on the B side and more will pass through from A to B than from 
B to A. Close the channel after a small but finite transfer has occurred. 
The enclosure B now contains more radiation than initially and therefore 
more than can be in equilibrium with its walls at temperature T\ the 
surplus will pass into the walls which must accordingly rise in temperature. 
Similarly the walls of A will fall in temperature. We next bring the walls 
of B and A to the same temperature by allowing the necessary quantity 
of heat to flow from B to A. This flow of heat from a higher temperature 
T r to a lower temperature T 2 is irreversible and creates a quantity of 
entropy dQ ( ^ — Jp'). But the whole system has returned exactly to 
V-i 2 d\J 
its original condition so that it is impossible that entropy should have 
been created. 
The contradiction can perhaps be realised more vividly if we suppose 
the passage to be opened and closed periodically. Then the temperature 
difference between A and B is continually renewed, and we can use B as 
the source and A as the sink of a heat-engine which develops mechanical 
work. This continuous conversion of heat originally at a uniform tempera 
ture T into mechanical work is obviously contrary to the principles of 
thermodynamics. 
Since the energy-density of radiation in the enclosure depends only 
on the temperature it follows that the pressure of the radiation depends 
only on the temperature. 
A word of explanation may be desirable as to the employment in 
thermodynamical arguments of ideal contrivances such as the screen 
transparent to an arbitrary range of wave-length. It is not at all essential 
to the argument that the processes referred to should be practicable; but 
it is essential that the ideal processes should not destroy entropy, if as 
usual the argument assumes that entropy is indestructible. The ideal 
* In theoretical arguments we sometimes introduce walls which are perfect 
reflectors (for some or all frequencies). The approach to equilibrium then becomes 
infinitely slow.