2 9 0 D O C . 2 9 0 T H E O R Y O F R A D I O M E T E R F O R C E S
in that the body imparts, on average, the momentum mv to each impacting mole-
cule. By executing the corresponding elementary calculation, one obtains
(4)
Equating K and yields
. (5)[3]
These velocities, which—as long as the particles are small compared to the free
path length—are independent of the size of the particle, can become quite consid-
erable. Given λ = 0.1 cm and , T = 300, and as a gas, one obtains about
1 m per second, and at normal pressure and otherwise the same conditions, over
0.1 mm per second.
These forces play a decisive role, e.g., in hoarfrost precipitation and the electri-
cal heaters for purifying the air of smoke particles.
§2. Small Hole in a Thin Wall Standing against the Heat Flow. We now come to
a phenomenon that forms the counterpart to the one just considered. The consider-
ation in §1 was mainly based on the assumption that, in the interior of a flux-free
gas, the number of molecules hitting two sides of a surface element is equal on both
sides. We express this thus: The condition of flow equality is satisfied in the interior
of the gas undergoing thermal flux. The calculated force exerted on a particle re-
sulted because equally as many molecules bring along momentum of differing
quantities on the front and rear of the particle.
This “flow equality” in the interior of the gas is set against a “pressure equality”
with reference to the walls of the gas space. For, it is well known and easy to show
that even with an uneven temperature distribution in the gas, pressure forces of the
same magnitude must act per unit area everywhere on the surface wall of the gas
cavity, provided only that the observed parts of the wall are large enough compared
to the free path length, that they themselves are of sufficiently even temperature,
and that they are separated from one another by gas cross sections that in all their
dimensions are large compared to the free path length. Then the concepts and laws
of the continuum hydrostatics are, of course, applicable.
Let there be a flat vane in the previously considered gas, which is perpendicular
to the heat flow, hence oriented parallel to the yz-plane. Let it be large compared to
the free path length and let its edges be at distances large compared to λ away from
the rest of the gas cavity’s wall. Then, pressure equality prevails despite the pres-
ence of the heat flow.
K′
4
3
--nσu - mv ⋅ –=
–K′
v
1
4RTη
------------ -
f
-
1
8
-
λ∂T
T∂x
- –--u--
1
4p
---- -
f
- = = =
∂x
∂T
30 = H2
[p. 4]