CHAPTER II 
THERMODYNAMICS OF RADIATION 
Radiation Pressure. 
21 . Radiant energy or radiation consists of electromagnetic waves in 
the aether. Maxwell’s electromagnetic theory showed that these waves 
possess momentum. If E is the energy of the waves, c the velocity of light, 
the momentum is E\c in the direction in which the waves are travelling. 
According to the modern view energy and mass are inseparable, 
c 2 ergs corresponding to 1 gm. This leads immediately to the same result. 
For the energy E ergs indicates a mass E/c 2 gm., and since the velocity 
is c the momentum is ( E/c 2 ) x c = E/c. 
A material screen which absorbs the waves absorbs also their momen 
tum. Thus the momentum of the screen changes, which is another way of 
saying that it is acted on by a force. Suppose that waves containing 
E ergs per cu. cm. impinge normally on a perfectly absorbing surface. 
A column of radiation of height c passes into and is absorbed by each 
sq. cm. of the surface per sec.; this column contains Ec ergs and the 
momentum is thus Ec/c or E units. The force on the screen is thus E dynes 
per sq. cm. 
For imperfect absorbers we must deduct the proportion of the momentum 
which is not passed on to the material screen, viz. that of the transmitted, 
scattered or reflected waves. For example, a perfect reflector would 
experience a pressure 2 E ; half of this is due to its stoppage of the incident 
waves and half is the recoil due to the projection of the train of reflected 
waves. Again, if the screen is semi-transparent and transmits waves of 
reduced energy-density E' the force per sq. cm. is E — E '. This may be 
analysed into a pressure E of the incident waves and a recoil pressure — E' 
of the transmitted waves, as though the screen had wholly absorbed the 
incident beam and had itself originated the transmitted beam on the other 
side. 
If we regard the incident, reflected, scattered, transmitted or emitted 
beams as each exerting its own pressure on the side of the screen at which 
it arrives or originates, we need not trouble to discriminate the different 
cases of absorption, reflection, etc. The pressure on either side of the 
screen is equal to the energy-density of the radiation on that side, and the 
force on the screen corresponds to the difference of the pressures on its 
two sides. For example, in the case of the perfect reflector the pressure 
is equal to the total energy-density 2 E on one side of the screen, viz. the 
energy-density E of the incident waves + the energy-density E of the