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28 THERMODYNAMICS OF RADIATION
reflected waves. It makes no difference whether the waves are travelling involv<
towards or away from the screen, because on reversing the direction of pressu:
conveyance of momentum we also reverse the sign of the momentum that Th<
is being conveyed; so that a wave-train conveying positive momentum withor
away from the screen gives the same pressure as a wave-train conveying screen,
negative momentum into the screen. A pressure system cannot be repre- in the
sented by a vector; it may be associated with an axis but not with a positfv
direction. from t
The rule that of negi
pressure = energy-density defines
applies only to radiation travelling normal to the surface; oblique incidence accour
must be considered separately. region
23
22 . Consider as in the last section a column of radiation travelling in ‘
a fixed direction, and place in its track a screen of area S inclined so that ^ .
the angle of incidence is 9. The cross-section of the column obstructed by
the screen is S cos 6, and accordingly the force, which would be ES for ^
normal incidence, is ES cos 9 for oblique incidence. This force is in the
direction of the momentum of the beam; resolving it into components
normal and tangential to the screen the force is for ms
ES cos 2 9 normal, ES cos 9 sin 9 tangential. kinetic
a • . , pressu
An important case is when the radiation is isotropic, i.e. consists of .^ g ^
waves of equal intensity in all directions. Since the average value of cos 2 9
over a sphere is ^ and of cos 9 sin 9 is zero the force becomes in this case render
ES normal to the surface. Thus we have the important law— moleci
The pressure of isotropic radiation is | of its energy-density . elemer
This pressure is exerted normally on any surface exposed to the radia sharin;
tion and is entirely analogous to the hydrostatic pressure of a fluid. In degree
a gas the momentum is conveyed by the molecules; and a gas at rest, in a § as 1
which the velocities of the molecules are symmetrical as regards direction ratio c
so that the momentum is being conveyed at the same rate in all directions,
is analogous to isotropic radiation. In non-isotropic radiation or in a later,
disturbed gas with unsymmetrical distribution of molecular velocities pressic
there is no longer a simple hydrostatic pressure; a stress-system with six calculi
different components is involved. P ass ^
When the radiation is not isotropic the normal pressure on a surface su ^
is given by using the weighted mean of cos 2 9 instead of the factor |. mater.
It is to be noted that an increase of flow in a particular direction 9 at the throu^
expense of flow in the opposite direction does not alter the pressure. In approi
the interior of a star we have often to consider radiation which is nearly mstea
isotropic but with a slight preponderant outward flow; this kind of
asymmetry does not in itself affect the pressure, though it is likely to