ical element characteristic of the body
considered, and is called its entropy. Entropy, thus defined, is a
variable which, like pressure or volume, might serve concurrently with
another variable, such as pressure or volume, to define the state of a
body.

It must be perfectly understood that this variable can change in an
independent manner, and that it is, for instance, distinct from the
change of temperature. It is also distinct from the change which
consists in losses or gains of heat. In chemical reactions, for
example, the entropy increases without the substances borrowing any
heat. When a perfect gas dilates in a vacuum its entropy increases,
and yet the temperature does not change, and the gas has neither been
able to give nor receive heat. We thus come to conceive that a
physical phenomenon cannot be considered known to us if the variation
of entropy is not given, as are the variations of temperature and of
pressure or the exchanges of heat. The change of entropy is, properly
speaking, the most characteristic fact of a thermal change.

It is important, however, to remark that if we can thus easily define
and measure the difference of entropy between two states of the same
body, the value found depends on the state arbitrarily chosen as the
zero point of entropy; but this is not a very serious difficulty, and
is analogous to that which occurs in the evaluation of other physical
magnitudes--temperature, potential, etc.

A graver difficulty proceeds from its not being possible to define a
difference, or an equality, of entropy between two bodies chemically
different. We are unable, in fact, to pass by any means, reversible or
not, from one to the other, so long as the transmutation of matter is
regarded as impossible; but it is well understood that it is
nevertheless possible to compare the variations of entropy to which
these two bodies are both of them individually subject.

Neither must we conceal from ourselves that the definition supposes,
for a given body, the possibility of passing from one state to another
by a reversible transformation. Reversibility is an ideal and extreme
case which cannot be realized, but which can be approximately attained
in many circumstances. So with gases and with perfectly elastic
bodies, we effect sensibly reversible transformations, and changes
of physical state are practically reversible. The discoveries of
Sainte-Claire Deville have brought many chemical phenomena into a