198
VIII
EVAPORATION OF LIQUIDS
These values, reckoned in mm./min., are given in the second
row of the above table; they are about ten times greater than
the highest values observed at the corresponding temperatures.
The latter are given in the sixth row as lower limits. They
are not lower limits for evaporation in general, for this can
fall to zero; but they are lower limits for the greatest possible
rate of evaporation. The other limits given in the table hold
good also for the case in which the evaporation has reached
its greatest value. Those given in the third, fourth, and fifth
rows also hold good in general; for we may assume that the
maximum of u and the minimum of P and d occur simultane-
ously with the maximum of m. In deducing these limits we
have first u = (P− p)/mg = m/d; and since m>mmin.,
P-p<P1,
andɗ<d, it follows that p/mmin.>u>mmin./d₁. Again P=p+m²/d,
and since m>mmin, and ded,, it follows that P>p+ m² min./dp.
But the expression on the right hand has a minimum, since it
becomes infinite when p = 0, and when p∞; this minimum
value is given in the table. Finally d = m²/(P− p) and P-p
m²/d. Hence d/d>m² min./d1P1, and (P-p)/p>m² min./d₁₂pı-
=
=
The meaning of the table may be illustrated by an example
of what it asserts, such as the following. From a mercury
surface at 100° C. we cannot cause a layer of more than 0.7
mm. to evaporate per minute; its vapour will not issue from
the surface with a greater velocity than 2110 m./sec.; the
pressure upon the surface will not be less than 4 to 5
hundredths of a millimetre, nor will the density of the vapour
which issues from it be less than 3 of the density of the
saturated vapour. On the other hand, we can in any case
cause the evaporation to exceed 0.08 mm. per minute; the
velocity of the vapour to exceed 7.3 m./sec.; and the pressure
of the issuing vapour to differ from the saturation-pressure by
more than of the latter.
In conclusion, I would further point out that the existence
of a limited rate of evaporation, peculiar to each fluid, is also
in accordance with the kinetic theory of gases; and that with
the aid of this conception a fairly reliable upper limit for this
rate can be deduced. Let T, p, and d denote the temperature,
pressure, and density of the saturated vapour. Then the
weight which impinges in unit time upon unit area of a
solid surface bounding the vapour is m=pdg/2π. And in