air at ordinary temperatures at about 20,000 times less than that
of copper. This has been verified experimentally by Kundt and
Warburg, Stefan and Winkelmann, by taking special precautions
to eliminate the effects of convection currents and radiation.
It was for some time doubted whether a gas possessed any true
conductivity for heat. The experiment of T. Andrews, repeated
by Grove, and Magnus, showing that a wire heated by an electric
current was raised to a higher temperature in air than in
hydrogen, was explained by Tyndall as being due to the greater
mobility of hydrogen which gave rise to stronger convection
currents. In reality the effect is due chiefly to the greater
velocity of motion of the ultimate molecules of hydrogen, and is
most marked if molar (as opposed to molecular) convection is
eliminated. Molecular convection or diffusion, which cannot be
distinguished experimentally from conduction, as it follows the
same law, is also the main cause of conduction of heat in liquids.
Both in liquids and gases the effects of convection currents are
so much greater than those of diffusion or conduction that the
latter are very difficult to measure, and, except in special cases,
comparatively unimportant as affecting the transference of heat.
Owing to the difficulty of eliminating the effects of radiation
and convection, the results obtained for the conductivities of
liquids are somewhat discordant, and there is in most cases great
uncertainty whether the conductivity increases or diminishes
with rise of temperature. It would appear, however, that liquids,
such as water and glycerin, differ remarkably little in conductivity
in spite of enormous differences of viscosity. The viscosity
of a liquid diminishes very rapidly with rise of temperature,
without any marked change in the conductivity, whereas the
viscosity of a gas increases with rise of temperature, and is
always nearly proportional to the conductivity.
33. Difficulty of Quantitative Estimation of Heat Transmitted.—The conducting powers of different metals were compared by C. M. Despretz, and later by G. H. Wiedemann and R. Franz, employing an extension of the method of Jan Ingenhousz, in which the temperatures at different points along a bar heated at one end were measured by thermometers or thermocouples let into small holes in the bars, instead of being measured at one point only by means of melting wax. These experiments undoubtedly gave fairly accurate relative values, but did not permit the calculation of the absolute amounts of heat transmitted. This was first obtained by J. D. Forbes (Brit. Assoc. Rep., 1852; Trans. Roy. Soc. Ed., 1862, 23, p. 133) by deducing the amount of heat lost to the surrounding air from a separate experiment in which the rate of cooling of the bar was observed (see Conduction of Heat). Clément (Ann. chim. phys., 1841) had previously attempted to determine the conductivities of metals by observing the amount of heat transmitted by a plate with one side exposed to steam at 100° C., and the other side cooled by water at 28° C. Employing a copper plate 3 mm. thick, and assuming that the two surfaces of the plate were at the same temperatures as the water and the steam to which they were exposed, or that the temperature-gradient in the metal was 72° in 3 mm., he had thus obtained a value which we now know to be nearly 200 times too small. The actual temperature difference in the metal itself was really about 0.36° C. The remainder of the 72° drop was in the badly conducting films of water and steam close to the metal surface. Similarly in a boiler plate in contact with flame at 1500° C. on one side and water at, say, 150° C. on the other, the actual difference of temperature in the metal, even if it is an inch thick, is only a few degrees. The metal, unless badly furred with incrustation, is but little hotter than the water. It is immaterial so far as the transmission of heat is concerned, whether the plates are iron or copper. The greater part of the resistance to the passage of heat resides in a comparatively quiescent film of gas close to the surface, through which film the heat has to pass mainly by conduction. If a Bunsen flame, preferably coloured with sodium, is observed impinging on a cold metal plate, it will be seen to be separated from the plate by a dark space of a millimetre or less, throughout which the temperature of the gas is lowered by its own conductivity below the temperature of incandescence. There is no abrupt change of temperature in passing from the gas to the metal, but a continuous temperature-gradient from the temperature of the metal to that of the flame. It is true that this gradient may be upwards of 1000° C. per mm., but there is no discontinuity.
34. Resistance of a Gas Film to the Passage of Heat.—It is possible to make a rough estimate of the resistance of such a film to the passage of heat through it. Taking the average conductivity of the gas in the film as 10,000 times less than that of copper (about double the conductivity of air at ordinary temperatures) a millimetre film would be equivalent to a thickness of 10 metres of copper, or about 1.2 metres of iron. Taking the temperature-gradient as 1000° C. per mm. such a film would transmit 1 gramme-calorie per sq. cm. per sec., or 36,000 kilo-calories per sq. metre per hour. With an area of 100 sq. cms. the heat transmitted at this rate would raise a litre of water from 20° C. to 100° C. in 800 secs. By experiment with a strong Bunsen flame it takes from 8 to 10 minutes to do this, which would indicate that on the above assumptions the equivalent thickness of quiescent film should be rather less than 1 mm. in this case. The thickness of the film diminishes with the velocity of the burning gases impinging on the surface. This accounts for the rapidity of heating by a blowpipe flame, which is not due to any great increase in temperature of the flame as compared with a Bunsen. Similarly the efficiency of a boiler is but slightly reduced if half the tubes are stopped up, because the increase of draught through the remainder compensates partly for the diminished heating surface. Some resistance to the passage of heat into a boiler is also due to the water film on the inside. But this is of less account, because the conductivity of water is much greater than that of air, and because the film is continually broken up by the formation of steam, which abstracts heat very rapidly.
35. Heating by Condensation of Steam.—It is often stated that the rate at which steam will condense on a metal surface at a temperature below that corresponding to the saturation pressure of the steam is practically infinite (e.g. Osborne Reynolds, Proc. Roy. Soc. Ed., 1873, p. 275), and conversely that the rate at which water will abstract heat from a metal surface by the formation of steam (if the metal is above the temperature of saturation of the steam) is limited only by the rate at which the metal can supply heat by conduction to its surface layer. The rate at which heat can be supplied by condensation of steam appears to be much greater than that at which heat can be supplied by a flame under ordinary conditions, but there is no reason to suppose that it is infinite, or that any discontinuity exists. Experiments by H. L. Callendar and J. T. Nicolson by three independent methods (Proc. Inst. Civ. Eng., 1898, 131, p. 147; Brit. Assoc. Rep. p. 418) appear to show that the rate of abstraction of heat by evaporation, or that of communication of heat by condensation, depends chiefly on the difference of temperature between the metal surface and the saturated steam, and is nearly proportional to the temperature difference (not to the pressure difference, as suggested by Reynolds) for such ranges of pressure as are common in practice. The rate of heat transmission they observed was equivalent to about 8 calories per sq. cm. per sec., for a difference of 20° C. between the temperature of the metal surface and the saturation temperature of the steam. This would correspond to a condensation of 530 kilogrammes of steam at 100° C. per sq. metre per hour, or 109 ℔ per sq. ft. per hour for the same difference of temperature, values which are many times greater than those actually obtained in ordinary surface condensers. The reason for this is that there is generally some air mixed with the steam in a surface condenser, which greatly retards the condensation. It is also difficult to keep the temperature of the metal as much as 20° C. below the temperature of the steam unless a very free and copious circulation of cold water is available. For the same difference of temperature, steam can supply heat by condensation about a thousand times faster than hot air. This rate is not often approached in practice, but the facility of generation and transmission of steam, combined with its high latent heat
