4. There are [at present known] two, and only two, distinct ways in
which mechanical effect can be obtained from heat. One of these is by
means of the alterations of volume, which bodies may experience through
the action of heat; the other is through the medium of electric agency.
Seebeck’s discovery of thermo-electric currents enables us at present to
conceive of an electro-magnetic engine supplied from a thermal origin,
being used as a motive power; but this discovery was not made until
1821, and the subject of thermo-electricity can only have been generally
known in a few isolated facts, with reference to the electrical effects
of heat upon certain crystals, at the time when Carnot wrote. He makes
no allusion to it, but confines himself to the method for rendering
thermal agency available as a source of mechanical effect, by means of
the expansions and contractions of bodies.
5. A body expanding or contracting under the action of force may, in
general, either produce mechanical effect by overcoming resistance, or
receive mechanical effect by yielding to the action of force. The amount
of mechanical effect thus developed will depend not only on the
calorific agency concerned, but also on the alteration in the physical
condition of the body. Hence, after allowing the volume and temperature
of the body to change, we must restore it to its original temperature
and volume; and then we may estimate the aggregate amount of mechanical
effect developed as due solely to the thermal origin.
6. Now the ordinarily-received, and almost universally-acknowledged,
principles with reference to “quantities of caloric” and “latent heat”
lead us to conceive that, at the end of a cycle of operations, when a
body is left in precisely its primitive physical condition, if it has
absorbed any heat during one part of the operations, it must have given
out again exactly the same amount during the remainder of the cycle. The
truth of this principle is considered as axiomatic by Carnot, who admits
it as the foundation of his theory; and expresses himself in the
following terms regarding it, in a note on one of the passages of his
treatise:[37]
“In our demonstrations we tacitly assume that after a body has
experienced a certain number of transformations, if it be brought
identically to its primitive physical state as to density, temperature,
and molecular constitution, it must contain the same quantity of heat as
that which it initially possessed; or, in other words, we suppose that
the quantities of heat lost by the body under one set of operations are
precisely compensated by those which are absorbed in the others. This
fact has never been doubted; it has at first been admitted without
reflection, and afterwards verified, in many cases, by calorimetrical
experiments. To deny it would be to overturn the whole theory of heat,
in which it is the fundamental principle. It must be admitted, however,
that the chief foundations on which the theory of heat rests, would
require a most attentive examination. Several experimental facts appear
nearly inexplicable in the actual state of this theory.”
7. Since the time when Carnot thus expressed himself, the necessity of a
most careful examination of the entire experimental basis of the theory
of heat has become more and more urgent. Especially all those
assumptions depending on the idea that heat is a _substance_, invariable
in quantity; not convertible into any other element, and incapable of
being _generated_ by any physical agency; in fact the acknowledged
principles of latent heat,—would require to be tested by a most
searching investigation before they ought to be admitted, as they
usually have been, by almost every one who has been engaged on the
subject, whether in combining the results of experimental research, or
in general theoretical investigations.
8. The extremely important discoveries recently made by Mr. Joule of
Manchester, that heat is evolved in every part of a closed electric
conductor, moving in the neighborhood of a magnet,[38] and that heat is
_generated_ by the friction of fluids in motion, seem to overturn the
opinion commonly held that heat cannot be _generated_, but only produced
from a source, where it has previously existed either in a sensible or
in a latent condition.
In the present state of science, however, no operation is known by which
heat can be absorbed into a body without either elevating its
temperature or becoming latent, and producing some alteration in its
physical condition; and the fundamental axiom adopted by Carnot may be
considered as still the most probable basis for an investigation of the
motive power of heat; although this, and with it every other branch of
the theory of heat, may ultimately require to be reconstructed upon
another foundation, when our experimental data are more complete. On
this understanding, and to avoid a repetition of doubts, I shall refer
to Carnot’s fundamental principle, in all that follows, as if its truth
were thoroughly established.
9. We are now led to the conclusion that the origin of motive power,
developed by the alternate expansions and contractions of a body, must
be found in the agency of heat entering the body and leaving it; since
there cannot, at the end of a complete cycle, when the body is restored
to its primitive physical condition, have been any absolute absorption
of heat, and consequently no conversion of heat, or caloric, into
mechanical effect; and it remains for us to trace the precise nature of
the circumstances under which heat must enter the body, and afterwards
leave it, so that mechanical effect may be produced. As an example, we
may consider that machine for obtaining motive power from heat with
which we are most familiar—the steam-engine.
10. Here, we observe, that heat enters the machine from the furnace,
through the sides of the boiler, and that heat is continually abstracted
by the water employed for keeping the condenser cool. According to
Carnot’s fundamental principle, the quantity of heat thus discharged,
during a complete revolution (or double stroke) of the engine, must be
precisely equal to that which enters the water of the boiler;[39]
provided the total mass of water and steam be invariable, and be
restored to its primitive physical condition (which will be the case
rigorously, if the condenser be kept cool by the external application of
cold water instead of by injection, as is more usual in practice), and
if the condensed water be restored to the boiler at the end of each
complete revolution. Thus we perceive that a certain quantity of heat is
_let down_ from a hot body, the metal of the boiler, to another body at
a lower temperature, the metal of the condenser; and that there results
from this transference of heat a certain development of mechanical
effect.
11. If we examine any other case in which mechanical effect is obtained
from a thermal origin, by means of the alternate expansions and
contractions of any substance whatever, instead of the water of a
steam-engine, we find that a similar transference of heat is effected,
and we may therefore answer the first question proposed, in the
following manner:
_The thermal agency by which mechanical effect may be obtained is the
transference of heat from one body to another at a lower temperature._
11. On the measurement of Thermal Agency, considered with reference to
its equivalent of mechanical effect.
12. A _perfect_ thermodynamic engine of any kind is a machine by means
of which the greatest possible amount of mechanical effect can be
obtained from a given thermal agency; and, therefore, if in any manner
we can construct or imagine a perfect engine which may be applied for
the transference of a given quantity of heat from a body at any given
temperature to another body at a lower given temperature, and if we can
evaluate the mechanical effect thus obtained, we shall be able to answer
the question at present under consideration, and so to complete the
theory of the motive power of heat. But whatever kind of engine we may
consider with this view, it will be necessary for us to prove that it is
a perfect engine; since the transference of the heat from one body to
the other may be wholly, or partially, effected by conduction through a
solid,[40] without the development of mechanical effect; and,
consequently, engines may be constructed in which the whole or any
portion of the thermal agency is wasted. Hence it is of primary
importance to discover the criterion of a perfect engine. This has been
done by Carnot, who proves the following proposition:
13. _A perfect thermodynamic engine is such that, whatever amount of
mechanical effect it can derive from a certain thermal agency, if an
equal amount be spent in working it backwards, an equal reverse thermal
effect will be produced._[41]
14. This proposition will be made clearer by the applications of it
which are given later (§ 29), in the cases of the air-engine and the
steam-engine, than it could be by any general explanation; and it will
also appear, from the nature of the operations described in those cases,
and the principles of Carnot’s reasoning, that a perfect engine may be
constructed with any substance of an indestructible texture as the
alternately expanding and contracting medium. Thus we might conceive
thermodynamic engines founded upon the expansions and contractions of a
perfectly elastic solid, or of a liquid; or upon the alterations of
volume experienced by substances in passing from the liquid to the solid
state,[42] each of which being perfect, would produce the same amount of
mechanical effect from a given thermal agency; but there are two cases
which Carnot has selected as most worthy of minute attention, because of
their peculiar appropriateness for illustrating the general principles
of his theory, no less than on account of their very great practical
importance: the steam-engine, in which the substance employed as the
transferring medium is water, alternately in the liquid state and in the
state of vapor; and the air-engine, in which the transference is
effected by means of the alternate expansions and contractions of a
medium always in the gaseous state. The details of an actually
practicable engine of either kind are not contemplated by Carnot in his
general theoretical reasonings, but he confines himself to the ideal
construction, in the simplest possible way in each case, of an engine in
which the economy is perfect. He thus determines the degree of
perfectibility which cannot be surpassed; and by describing a
conceivable method of attaining to this perfection by an air-engine or a
steam-engine, he points out the proper objects to be kept in view in the
practical construction and working of such machines. I now proceed to
give an outline of these investigations.