The Locomotive - Lighthouse Survival Blog

1901.] THE LOCOMOTIVE. 59
gas would behave; but so do numerous other gases. The question arises, therefore, why
we should prefer air to hydrogen, or nitrogen, or any other gas which shows a similarly
close approach to the state of a perfect gas. Let us see how much difference would be
introduced if we should apply Tyndall's argument to some of them.
Beginning with air itself, let us note that the recent accurate measurements of
Chappuis show that the fraction for air, which we have taken above as 1/460, ought
really to be 1/458; so that if we accept his measurements, we should conclude, from air,
that the absolute zero is 458° below the ordinary Fahrenheit zero. Chappuis found
1/450 as the corresponding fraction for hydrogen, and 1/453 for carbonic acid gas; so
that from these two gases, respectively, we should conclude that the absolute zero is
459° and 453° below the Fahrenheit zero. These differences cannot be attributed to
errors in the experimental data, for Chappuis worked with the greatest care; and moreover
it has been known, for a long time, that small differences of this order of magni-
tude do really exist among the various " permanent " gases. The differences referred
to, therefore, prove one of two things. Either there is no such thing as a real, absolute
zero, or else the method that we have been using in this paper to determine it is not
strictly correct. Some will doubtless take the former position; but this would be an
error. The trouble is, that we have sacrificed accuracy to simplicity of treatment, just
as all other writers of popular articles and books on this subject do.
We can reconcile the data given by different nearly-perfect gasses, in the way
pointed out by Rankine. (See his paper, entitled On the Al>soht.fe Zero of the Perfect Gas
Thermometer, in his ''Miscellaneous Scientific Papers," page 307.) Rankine takes the
position that the actual gases of nature differ from the ideal perfect gas, for the sole
reason that their molecules are near enough together to exert a sensible amount of
attraction upon one another ; and he points out that we can approach as nearly as we
please to the ideal condition of a perfect gas by working with gases at small densities.
In a rarefied gas the molecules are (on the whole) so much further apart that their attrac-
tive action on one another may be quite negligible, so that the gas, in its rarefied state,
would be indistinguishable from a perfect gas. The behavior of a perfect gas may
therefore be taken to be the same as the behavior of any of the so-called permanent
gases, when the said permanent gas is taken in a sufficiently rarefied state. Practically,
it is difficult to experiment with a highly rarefied gas, and so we have to carry out the
idea that Rankine suggests in something like the following manner: We first experiment
witli the gas in its ordinary state, and we then calculate, just as Tyndall does, the posi-
tion of the absolute zero. Next, we experiment with the same gas after reducing its
density to (say) one-half what it was at first, and again calculate the position of the
absolute zero. This process is repeated as many times as we find it convenient to do so,
and then we compare the various estimates that have been so obtained of the position of
the absolute zero. As the gas grows rarer and rarer, the estimated position of the absolute
zero may be expected to approximate nearer and nearer to the true position, as it would be
found if we could work with an ideally perfect gas. We regret that we have no data
at hand more recent than those of Regnault for carrying out the calculation thus described.
Using his data, however, the results are interesting and instructive, even if they are not
as accurate as might be wished. He found that carbonic acid gas, of such a density
that it has a pressure of 0.9980 of an atmosphere at 32° Fahr., gives — 450.4° as the posi-
tion of the absolute zero; and that the same gas, when of such a density that it
has a pressure of 4.7225 atmospheres at 32° Fahr., gives — 434.4° as the position
of the absolute zero. Two other experiments were also made with carbonic acid
gas at the initial pressures 1.1857 and 2.2931 atmospheres, respectively, the resulting