2 8 8 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
290. “On the Theory of Radiometer Forces”[1]
[Einstein 1924k]
Received 21 July 1924
Published August–September 1924
In: Zeitschrift für Physik 27 (1924): 1–6.
The forces acting on bodies that are small compared to the free path length λ, as well as those act-
ing on large bodies compared to λ in the edge zone of heat flow, are here calculated approximately,
based on schematic assumptions about the mechanism of molecular motion in gases.
The theory of the dynamic effects of temperature differences and pressure dif-
ferences in gases has been satisfactorily cleared up by Knudsen for the case that the
free path length is large compared to the relevant dimensions of the
vessel.[2]
How-
ever, some lack of clarity still predominates about the causes of the thermal forces
in cases where the free path length is of the same order of magnitude or smaller
than the relevant vessel dimensions. In the following I would like to offer a more
qualitative consideration of the conditions prevailing here; quantitative ones are
taken into account only by order of magnitude. Although the observations offered
here are of a quite elementary nature, they have nevertheless helped me to over-
come some ambiguities; and I may surely hope that readers may be well served by
this brief exposition.
§1. Bodies in a Heat Flow That Are Small Compared to the Path Length. We ini-
tially imagine a gas of infinite extension in which a stationary, homogeneous flow
of heat exists along the positive x-axis. We conceive the molecular motion largely
schematically in that we assign the same velocity u to all the molecules, apart from
small differences, which we need to schematically account for the heat flow. Fur-
thermore, we calculate as if the molecules were only flying along the coordinate
axes. We treat the free path length λ as a constant length. All these simplifications
can produce for us merely inessential falsifications of the numerical coefficients in
the formulas, without affecting the conception of the essential relations.
We first observe the molecular motion through a surface element σ perpendicu-
lar to the x-axis and small compared to λ. Material flow should not be present.
Therefore, exactly as many molecules run through σ in both directions per second,
that is,
[p. 1]
[p. 2]