25. _Modes of Transference._--There are three principal modes of
transference of heat, namely (1) convection, (2) conduction, and (3)
radiation.
(1) In convection, heat is carried or conveyed by the motion of heated
masses of matter. The most familiar illustrations of this method of
transference are the heating of buildings by the circulation of steam or
hot water, or the equalization of temperature of a mass of unequally
heated liquid or gas by convection currents, produced by natural changes
of density or by artificial stirring. (2) In conduction, heat is
transferred by contact between contiguous particles of matter and is
passed on from one particle to the next without visible relative motion
of the parts of the body. A familiar illustration of conduction is the
passage of heat through the metal plates of a boiler from the fire to
the water inside, or the transference of heat from a soldering bolt to
the solder and the metal with which it is placed in contact. (3) In
radiation, the heated body gives rise to a motion of vibration in the
aether, which is propagated equally in all directions, and is
reconverted into heat when it encounters any obstacle capable of
absorbing it. Thus radiation differs from conduction and convection in
taking place most perfectly in the absence of matter, whereas conduction
and convection require material communication between the bodies
concerned.
In the majority of cases of transference of heat all three modes of
transference are simultaneously operative in a greater or less degree,
and the combined effect is generally of great complexity. The different
modes of transference are subject to widely different laws, and the
difficulty of disentangling their effects and subjecting them to
calculation is often one of the most serious obstacles in the
experimental investigation of heat. In space void of matter, we should
have pure radiation, but it is difficult to obtain so perfect a vacuum
that the effects of the residual gas in transferring heat by conduction
or convection are inappreciable. In the interior of an opaque solid we
should have pure conduction, but if the solid is sensibly transparent in
thin layers there must also be an internal radiation, while in a liquid
or a gas it is very difficult to eliminate the effects of convection.
These difficulties are well illustrated in the historical development of
the subject by the experimental investigations which have been made to
determine the laws of heat-transference, such as the laws of cooling, of
radiation and of conduction.
26. _Newton's Law of Cooling._--There is one essential condition common
to all three modes of heat-transference, namely, that they depend on
difference of temperature, that the direction of the transfer of heat is
always from hot to cold, and that the rate of transference is, for small
differences, directly proportional to the difference of temperature.
Without difference of temperature there is no transfer of heat. When two
bodies have been brought to the same temperature by conduction, they are
also in equilibrium as regards radiation, and vice versa. If this were
not the case, there could be no equilibrium of heat defined by equality
of temperature. A hot body placed in an enclosure of lower temperature,
e.g. a calorimeter in its containing vessel, generally loses heat by all
three modes simultaneously in different degrees. The loss by each mode
will depend in different ways on the form, extent and nature of its
surface and on that of the enclosure, on the manner in which it is
supported, on its relative position and distance from the enclosure, and
on the nature of the intervening medium. But provided that the
difference of temperature is small, the rate of loss of heat by all
modes will be approximately proportional to the difference of
temperature, the other conditions remaining constant. The rate of
cooling or the rate of fall of temperature will also be nearly
proportional to the rate of loss of heat, if the specific heat of the
cooling body is constant, or the rate of cooling at any moment will be
proportional to the difference of temperature. This simple relation is
commonly known as Newton's law of cooling, but is limited in its
application to comparatively simple cases such as the foregoing. Newton
himself applied it to estimate the temperature of a red-hot iron ball,
by observing the time which it took to cool from a red heat to a known
temperature, and comparing this with the time taken to cool through a
known range at ordinary temperatures. According to this law if the
excess of temperature of the body above its surroundings is observed at
equal intervals of time, the observed values will form a geometrical
progression with a common ratio. Supposing, for instance, that the
surrounding temperature were 0 deg. C., that the red-hot ball took 25
minutes to cool from its original temperature to 20 deg. C., and 5
minutes to cool from 20 deg. C. to 10 deg. C., the original temperature
is easily calculated on the assumption that the excess of temperature
above 0 deg. C. falls to half its value in each interval of 5 minutes.
Doubling the value 20 deg. at 25 minutes five times, we arrive at 640
deg. C. as the original temperature. No other method of estimation of
such temperatures was available in the time of Newton, but, as we now
know, the simple law of proportionality to the temperature difference is
inapplicable over such large ranges of temperature. The rate of loss of
heat by radiation, and also by convection and conduction to the
surrounding air, increases much more rapidly than in simple proportion
to the temperature difference, and the rate of increase of each follows
a different law. At a later date Sir John Herschel measured the
intensity of the solar radiation at the surface of the earth, and
endeavoured to form an estimate of the temperature of the sun by
comparison with terrestrial sources on the assumption that the intensity
of radiation was simply proportional to the temperature difference. He
thus arrived at an estimate of several million degrees, which we now
know would be about a thousand times too great. The application of
Newton's law necessarily leads to absurd results when the difference of
temperature is very large, but the error will not in general exceed 2 to
3% if the temperature difference does not exceed 10 deg. C., and the
percentage error is proportionately much smaller for smaller
differences.
27. _Dulong and Petit's Empirical Laws of Cooling._--One of the most
elaborate experimental investigations of the law of cooling was that of
Dulong and Petit (_Ann. Chim. Phys._, 1817, 7, pp. 225 and 337), who
observed the rate of cooling of a mercury thermometer from 300 deg. C.
in a water-jacketed enclosure at various temperatures from 0 deg. C. to
80 deg. C. In order to obtain the rate of cooling by radiation alone,
they exhausted the enclosure as perfectly as possible after the
introduction of the thermometer, but with the imperfect appliances
available at that time they were not able to obtain a vacuum better than
about 3 or 4 mm. of mercury. They found that the velocity of cooling V
in a vacuum could be represented by a formula of the type