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The determination of temperature has long been recognized as a problem of the
greatest importance in physical science. It has accordingly been made a
subject of most careful attention, and, especially in late years, of very
elaborate and refined experimental researches; and we are thus at present in
possession of as complete a practical solution of the problem as can be
desired, even for the most accurate investigations. The theory of thermometry
is however as yet far from being in so satisfactory a state. The principle to
be followed in constructing a thermometric scale might at first sight seem to
be obvious, as it might appear that a perfect thermometer would indicate equal
additions of heat, as corresponding to equal elevations of temperature,
estimated by the numbered divisions of its scale. It is however now recognized
(from the variations in the specific heats of bodies) as an experimentally
demonstrated fact that thermometry under this condition is impossible, and we
are left without any principle on which to found an absolute thermometric
scale.
Next in importance to the primary establishment of an absolute scale,
independently of the properties of any particular kind of matter, is the
fixing upon an arbitrary system of thermometry, according to which results of
observations made by different experimenters, in various positions and
circumstances, may be exactly compared. This object is very fully attained by
means of thermometers constructed and graduated according to the clearly
defined methods adopted by the best instrument-makers of the present day,
when the rigorous experimental processes which have been indicated,
especially by Regnault, for interpreting their indications in a comparable
way, are followed. The particular kind of thermometer which is least liable
to uncertain variations of any kind is that founded on the expansion of air,
and this is therefore generally adopted as the standard for the comparison of
thermometers of all constructions. Hence the scale which is at present
employed for estimating temperature is that of the air-thermometer; and in
accurate researches care is always taken to reduce to this scale the
indications of the instrument actually used, whatever may be its specific
construction and graduation.
The principle according to which the scale of the air-thermometer is
graduated, is simply that equal absolute expansions of the mass of air or gas
in the instrument, under a constant pressure, shall indicate equal
differences of the numbers on the scale; the length of a “degree” being
determined by allowing a given number for the interval between the freezing-
and the boiling-points. Now it is found by Regnault that various
thermometers, constructed with air under different pressures, or with
different gases, give indications which coincide so closely, that, unless
certain gases, such as sulphurous acid, which approach the physical condition
of vapours at saturation, are made use of, the variations are inappreciable
. This remarkable circumstance enhances very much the practical value of
the air thermometer; but still a rigorous standard can only be defined by
fixing upon a certain gas at a determinate pressure, as the thermometric
substance. Although we have thus a strict principle for constructing a
definite system for the estimation of temperature, yet as reference is
essentially made to a specific body as the standard thermometric substance,
we cannot consider that we have arrived at an absolute scale, and we can only
regard, in strictness, the scale actually adopted as an arbitrary series of
numbered points of reference sufficiently close for the requirements of
practical thermometry.
In the present state of physical science, therefore, a question of extreme
interest arises: Is there any principle on which an absolute thermometric
scale can be founded? It appears to me that Carnot’s theory of the motive
power of heat enables us to give an affirmative answer.
The relation between motive power and heat, as established by Carnot, is such
that quantities of heat, and intervals of temperature, are involved as the
sole elements in the expression for the amount of mechanical effect to be
obtained through the agency of heat; and since we have, independently, a
definite system for the measurement of quantities of heat, we are thus
furnished with a measure for intervals according to which absolute
differences of temperature may be estimated. To make this intelligible, a few
words in explanation of Carnot’s theory must be given; but for a full
account of this most valuable contribution to physical science, the reader is
referred to either of the works mentioned above (the original treatise by
Carnot, and Clapeyron’s paper on the same subject).
In the present state of science no operation is known by which heat can be
absorbed, without either elevating the temperature of matter, or becoming
latent and producing some alteration in the physical condition of the body
into which it is absorbed; and the conversion of heat (or caloric) into
mechanical effect is probably impossible , certainly undiscovered. In
actual engines for obtaining mechanical effect through the agency of heat, we
must consequently look for the source of power, not in any absorption and
conversion, but merely in a transmission of heat. Now Carnot, starting from
universally acknowledged physical principles, demonstrates that it is by the
letting down of heat from a hot body to a cold body, through the medium of an
engine (a steam-engine, or an air-engine for instance), that mechanical
effect is to be obtained; and conversely, he proves that the same amount of
heat may, by the expenditure of an equal amount of labouring force, be raised
from the cold to the hot body (the engine being in this case worked
backwards); just as mechanical effect may be obtained by the descent of water
let down by a water-wheel, and by spending labouring force in turning the
wheel backwards, or in working a pump, water may be elevated to a higher
level. The amount of mechanical effect to be obtained by the transmission of
a given quantity of heat, through the medium of any kind of engine in which
the economy is perfect, will depend, as Carnot demonstrates, not on the
specific nature of the substance employed as the medium of transmission of
heat in the engine, but solely on the interval between the temperature of the
two bodies between which the heat is transferred.
Carnot examines in detail the ideal construction of an air-engine and of a
steam-engine, in which, besides the condition of perfect economy being
satisfied, the machine is so arranged, that at the close of a complete
operation the substance (air in one case and water in the other) employed is
restored to precisely the same physical condition as at the commencement. He
thus shews on what elements, capable of experimental determination, either
with reference to air, or with reference to a liquid and its vapour, the
absolute amount of mechanical effect due to the transmission of a unit of
heat from a hot body to a cold body, through any given interval of the
thermometric scale, may be ascertained. In M. Clapeyron’s paper various
experimental data, confessedly very imperfect, are brought forward, and the
amounts of mechanical effect due to a unit of heat descending a degree of the
air-thermometer, in various parts of the scale, are calculated from them,
according to Carnot’s expressions. The results so obtained indicate very
decidedly, that what we may with much propriety call the value of a degree
(estimated by the mechanical effect to be obtained from the descent of a unit
of heat through it) of the air-thermometer depends on the part of the scale
in which it is taken, being less for high than for low temperatures.
The characteristic property of the scale which I now propose is, that all
degrees have the same value; that is, that a unit of heat descending from a
body A at the temperature T° of this scale, to a body B at the temperature
(T-1)°, would give out the same mechanical effect, whatever be the number T.
This may justly be termed an absolute scale, since its characteristic is
quite independent of the physical properties of any specific substance.
To compare this scale with that of the air-thermometer, the values (according
to the principle of estimation stated above) of degrees of the
air-thermometer must be known. Now an expression, obtained by Carnot from the
consideration of his ideal steam-engine, enables us to calculate these
values, when the latent heat of a given volume and the pressure of saturated
vapour at any temperature are experimentally determined. The determination of
these elements is the principal object of Regnault’s great work, already
referred to, but at present his researches are not complete. In the first
part, which alone has been as yet published, the latent heats of a given
weight, and the pressures of saturated vapour at all temperatures between 0°
and 230° (Cent. of the air-thermometer), have been ascertained; but it
would be necessary in addition to know the densities of saturated vapour at
different temperatures, to enable us to determine the latent heat of a given
volume at any temperature. M. Regnault announces his intention of instituting
researches for this object; but till the results are made known, we have no
way of completing the data necessary for the present problem, except by
estimating the density of saturated vapour at any temperature (the
corresponding pressure being known by Regnault’s researches already
published) according to the approximate laws of compressibility and expansion
(the laws of Mariotte and Gay-Lussac, or Boyle and Dalton). Within the limits
of natural temperature in ordinary climates, the density of saturated vapour
is actually found by Regnault (Études Hydrométriques in the Annales de
Chimie) to verify very closely these laws; and we have reasons to believe
from experiments which have been made by Gay-Lussac and others, that as high
as the temperature 100° there can be no considerable deviation; but our
estimate of the density of saturated vapour, founded on these laws, may be
very erroneous at such high temperatures at 230°. Hence a completely
satisfactory calculation of the proposed scale cannot be made till after the
additional experimental data shall have been obtained; but with the data
which we actually possess, we may make an approximate comparison of the new
scale with that of the air-thermometer, which at least between 0° and 100°
will be tolerably satisfactory.
The labour of performing the necessary calculations for effecting a
comparison of the proposed scale with that of the air-thermometer, between
the limits of 0° and 230° of the latter, has been kindly undertaken by Mr.
William Steele, lately of Glasgow College, now of St. Peter’s College,
Cambridge. His results in tabulated forms were laid before the Society, with
a diagram, in which the comparison between the two scales is represented
graphically. In the first table, the amounts of mechanical effect due to the
descent of a unit of heat through the successive degrees of the
air-thermometer are exhibited. The unit of heat adopted is the quantity
necessary to elevate the temperature of a kilogramme of water from 0° to 1°
of the air-thermometer; and the unit of mechanical effect is a
metre-kilogramme; that is, a kilogramme raised a metre high.
In the second table, the temperatures according to the proposed scale, which
correspond to the different degrees of the air-thermometer from 0° to 230°,
are exhibited. [The arbitrary points which coincide on the two scales are 0°
and 100°.]
Note.—If we add together the first hundred numbers given in the first table,
we find 135.7 for the amount of work due to a unit of heat descending from a
body A at 100° to B at 0°. Now 79 such units of heat would, according to
Dr. Black (his result being very slightly corrected by Regnault), melt a
kilogramme of ice. Hence if the heat necessary to melt a pound of ice be now
taken as unity, and if a metre-pound be taken as the unit of mechanical
effect, the amount of work to be obtained by the descent of a unit of heat
from 100° to 0° is 79x135.7, or 10,700 nearly. This is the same as 35,100
foot pounds, which is a little more than the work of a one-horse-power engine
(33,000 foot pounds) in a minute; and consequently, if we had a steam-engine
working with perfect economy at one-horse-power, the boiler being at the
temperature 100°, and the condenser kept at 0° by a constant supply of ice,
rather less than a pound of ice would be melted in a minute.
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