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