204
IX
VAPOUR-PRESSURE OF MERCURY
out any external work. The vapour, again without external
work, is brought back to the temperature T and reduced to
liquid. During these processes the fluid can neither have
absorbed nor given out heat. Now according to the laws of
the mechanical theory of heat p₁ = Au(Tdp/dT —p), where p
denotes the pressure of the saturated vapour and u its specific
volume. Hence we can put u RT/p. If we eliminate pr
and u from the above three equations, we obtain for the curve
of the vapour pressure a differential equation which gives the
following integral
=
p = k₂ T¹-Re-?
For mercury s is known. From his own experiments, and
from a result given by Regnault, Winkelmann¹ finds that this
quantity decreases slightly as the temperature increases; the
mean value of s between 0 and 100° is 0.0330. Experiments
made by Dr. Ronkar of Liège in the Berlin Physical Institute
have shown that the change between -20° and +200° is
exceedingly small. These experiments give 0.0332 as the
mean value of s, and I shall use this value in the calculation.
Kundt and Warburg have shown that the ratio of the specific
heats for mercury is : hence it follows that the quantity c
is equal to 0.0149. From this it follows that the exponent of
T is equal to 0.847. The two remaining constants are to be
determined from the observations. Two of them are sufficient
for this: if we choose from the first series the observation at
206°, and from the second series the observation at 154°,
we obtain a formula which represents all the observations
satisfactorily. The constants thus determined can be im-
proved by applying the method of least squares.
In doing
this we naturally assume the pressures to be correct, and
therefore make the sum of the squares of the temperature-
errors a minimum. In this way I find that
-
log k₁ 10.59271,
=
log ka 3.88623.
=
Introducing these constants into the formula, and throwing
it into a form more convenient for calculation, we get
log p = 10.59271 – 0·847 log T-3342/T.
¹ See Poggendorff's Ann. 159, p. 152, 1876.