J13 Heat

Heat spreads in a space from one location to another by conduction, convection and radiation. It comes by conduction to us, when our hand in touching one end of an iron bar lying in a fire senses it, by convection during a heat wave - transport of heated air -, by radiation of Sun's heat which we even sense as heat at temperatures below 0ºC.

The effects of heat input tell us that heat spreads in bodies, that is, it does not accumulate at the point of entry. A thermometer would not indicate a change of the temperature of its environment, if the heat were to bring the surface of the mercury container to the temperature of the environment, but would not enter through the glass wall into the mercury and spread there. (If you pour hot water on a thermometer with a very large mercury container, the mercury drops before it rises, the heat first affects the container and expands it prior to reaching the mercury and expanding it.)

Heat flows while expanding from points of higher temperatures to lower ones. If you dip a cold metal spoon into a hot fluid, at first the submerged part accepts the temperature of the fluid; only then rises the temperature of its part extending from the fluid; the heat flows first into the parts of the spoon, closest to the fluid, and raises there the temperature until it proceeds along it and reaches the handle. The temperature of the handle of the spoon will never be equal to that of the fluid, because it is surrounded by air to which it passes on some of its heat. - Time passes until the heat from the fluid reaches the furthest part of the spoon. The heat arrives at the handle earliest, if the spoon is made out of silver, and progressively later, if it is made out of copper, gold, brass, tin, iron, palladium, steel, lead, bismuth. If it is made out of wood, horn or ivory, you do not immediately sense a change in temperature. This difference in the heat conductivity distinguishes substances as good or bad heat conductors. Ahead of all of them are the metals, then come the minerals. Organic substances like wool, feathers, straw, moreover, fluids and gases do not conduct heat well.

The heat conductivity of a substance is measured by the quantity of heat, which in a given substance under given conditions flows from points of higher temperature to those of lower temperature. Image a flat plate of thickness 1 cm. Measure the amount of heat (cal) which in 1 sec passes through 1 cm² of the plate while its flat faces are kept at a temperature difference of 1ºC. The temperature of each face must be assumed everywhere to be equally high, whence the flow of heat is perpendicular to the plate; in practice, these conditions are not readily realized. The heat conductivity in cal·cm^-1·sec^-1·degree^-1 - the thermal conductivities - are :

silver	1.01	platinum	0.17
copper	0.90	nickel silver	0.07-0.09
gold	0.70	bismuth	0.019
brass	0.15-0.30	brick	0.001
zinc	0.27	silk	0.00012
tin	0.15	water	0.0016
iron	0.14-0.17	ait	0.000067
lead	0.08	hydrogen	0.00040

The thermal conductivity referred to here is inside a body. The external conducting capacity, according to the older terminology - heat-transfer coefficient of industry - during heat transfer from one body to another is measured in terms of the calories, which one body in the case of an excess temperature of 1ºC above its environment passes on through 1 cm² of its surface per second to the outside. Fig. 417 shows the temperature distribution in a metal bar, one end of which remains at a high constant temperature and which is otherwise surrounded by air, that is, it is cooled. Fig. 418 displays the temperature drops in

bars of silver, brass, iron, bismuth and glass under the conditions in Fig. 417 (Gustav Heinrich Wiedemann 1826-1899, Franz). The rate at which the heat propagates in a substance depends essentially also on its specific heat. This is shown clearly by an experiment

of Tyndall: Two equally sized bars of bismuth and iron, each covered at one end by wax, are placed side by side simultaneouly, on a hot base, the wax at the top. Then the wax on the bismuth bar melts first, although bismuth is a worse conductor than iron. In fact, before the ends of the bars reach the melting temperature of the wax, the layers between the heat source and the ends covered by wax must be correspondingly warm, but iron demands more heat than bismuth, because its specific heat is four times as large. Hence the mass of iron between the wax and the heat source demands at equal heat input more time for its heating up than the corresponding mass of bismuth. In the bismuth bar, the adjustment occurs faster, whence at continuing heat input the heat flow inside it becomes stationary sooner than in the iron bar.

The quotient of the thermal conductivity and the product of the density with the specific heat of a substance is called its heat transfer coefficient. It is always of concern when you are not dealing with stationary, but varying heat flow, especially with storage of heat, for example, when answering the question: How deep penetrates the annual temperature oscillation into Earth.

In isotropic substances, the thermal conductivity at a given point is equally large in all directions, not so in anisotropic materials. Henri Hureau de Senarmont 1808-1862 has provided the following proof: A thin plate of the substance to be examined is covered with wax and perforated perpendicularly to its faces. A wire is passed through the hole and touches the plate; the wire is heated (the plate being protected against a direct effect of the heat source. If the plate is made out of an isotropic material, the wax melts in a circle around the wire, if it is made out of an anisotropic material, for example, a crystal, it melts in an ellipse. In the latter case, the ellipse depends on the direction of the axes of the crystal, forming the plate. Fig. 419a shows the result for a quartz plate, cut vertically to the main axis, Fig. 419 b for a plate, cut parallel to that axis.

Pure metals, ordered according to their thermal conductivities, form the same sequence as when ordered according to their electrical conductivity. The ratio of the two conductivities is almost the same for many metals. It depends on the temperature and, in general, increases proportional to the absolute temperature (Lorenz 1881). But this rule is not strict, especially not for very low temperatures. - For many metals, the electrical conductivity is according to its magnitude inversely proportional to the absolute temperature, whence Lorenz's law says: The thermal conductivity changes much less with the temperature than the electrical conductivity.

This parallelism between the capabilities of metals to conduct heat and

electricity suggests that these properties have a similar character. Attempts have been undertaken to explain both of them by the motion of electrons, which are to obey in a metal similar laws to those governing the motion of molecules in a gas. The theory of Sommerfeld 1927 leads especially during the derivation of the law of Wiedemann-Franz to very satisfying agreement with observations (in the case of many metals). However, also electrical isolators conduct heat and their mechanism of heat conduction seems to differ from that of metals.

For every day needs, the thermal conductivity of substances is more important than their heat transfer coefficient. For example, heat transfer is the transport of heat through our clothes* between our bodies and the outside air or that through the walls of a house from outside or that through the heat insulation of a steam pipe between the steam and the atmosphere, etc. - The heat transfer coefficient is important wherever one surrounds objects by good or bad heat conductors depending on whether they are to lose heat or retain it. We cover our bodies with badly conducting materials such as wool, furs, feather beds, in order to protect them against cooling; in order to protect plants from getting frozen, you cover them with straw, that is, with porous shrouds, inside which badly

conducting air is at rest. The badly conducting air layer between double windows protects rooms against the cold; the double walls of fire safe safes are separated from each other by ash as a

protection against heat; metal containers for hot fluids have handles, made out of wood, horn, glass or badly conducting materials. The small capability of snow and ice to conduct heat explains the protection which snow cover gives to plants.

*The reciprocal value of the thermal transfer coefficient is called heat resistance. According to a list of measurements, communicated by John Tyndal and obtained by Rumford, the thermal conductivity of clothes, ordered according to their heat resistance, are: Hare's hairs, eiderdown, beaver skin, raw silk, taffeta, sheep's wool, cotton, fine flax, spun silk.

On the large rate, at which metals take away heat, depends the miner's safety lamp of Sir Humphry Davy 1815; the protection arises from fine wire netting facing the

flame (Fig. 420). If you press such a net on a flame (Fig. 421), it limits the flame, although the inflammable gases pass through (Fig. 422). In fact, the gases must have a certain inflammation temperature in order to burn. The wire netting takes away so much heat that they are no longer hot enough beyond the netting and do not ignite. - Employment of the lamp: While gases (fire damp) which reach the flame of the lamp through the netting, ignite, their flame only extends to the netting and not to the gas in the mine shaft.

Two problems of Geophysics concern heat conduction: To what extent affects the heat of Earth's interior by conduction the temperature at the

surface ? How far inward and in what manner propagate daily and seasonal temperature variations at Earth's surface? These questions can only be answered under simplifying assumptions. The answer of the theory of Kelvin to the first question is: A stationary thermal state near Earth's surface, which maintains the heat of its interior, demands a uniform temperature gradient per metre inwards from the surface to the centre, provided all the different layers have the same thermal conductivity. Depending on their locations, temperature measurements in bore holes have yielded different results, on the average about 1ºC per 33m (medium geothermal depth gradient)

An answer to the second question is best based on the observations of the Edinburgh Observatory (since 1837). Four thermometers were placed inside a rock of porphyry at depths of 0.97, 1.94, 3.88 and 7.76 m. An average over many years has established that the first of these shows a maximum temperature on 19th August, the second on 8th September, the third on 19th October and the fourth on 6th January. These results yielded that the seasonal oscillations propagate at 17.81 m/year. - At the depths of these thermometers are not only differently high mean temperatures, but also differently sized oscillations. The thermometer, which is closest to Earth's surface, has oscillation of 8.2ºC, that furthest away only of 0.7C, the two in the middle of 5.6ºC and 2.7ºC. These differences give the explanation: The deeper the layer to which the heat has to penetrate, the more heat is held back by the layers above for their own rise in temperature, that is, the less heat reaches the layers below.

The thermal conductivity of water is 700 times that of air and about 1/20 000 that of copper; that of

hydrogen - the best heat conductor among the gases - is only about 7 times that of air. (An attempt to employ hydrogen for cooling dynamos). Rumford has proposed that fluids and gases do not at all conduct heat; however, this idea is not compatible with the mechanical theory of heat; during lasting motion, the molecules must impact and transfer energy. Thermal conduction of heat of fluids and gases was first based on theory and later confirmed experimentally.

Johann Gottlieb Leidenfrost 1715-1794 1756 has observed the phenomenon, named after him: A water drop does not boil away immediately on hot, smooth metal face (flatiron), but becomes a flatted sphere and evaporates slowly without boiling. It explains the smallness of the thermal conduction capacity of vapours. It is characteristic that the drop does not touch the plate, as long as it is sufficiently hot (Fig. 423) and its temperature lies throughout below the boiling point. Between the drop and the plate forms a layer of steam, which carries the drop like a cushion, protects it from touching the plate and due to its small thermal conductivity brings the drop little heat. However, if the plate gets cool enough while the drop is still there, the drop touches it and evaporates suddenly with splashes. (This event reminds of boiler explosions, which occur when due to lack of water a boiler's wall has become too hot and water enters it; the intruding water does not touch the wall immediately, only its temperature has dropped sufficiently, but is still high enough to cause excessive development of steam.) The temperature, which a plate must have, depends on the nature of the fluid and is the higher, the higher is its boiling point; the temperature of the fluid in this state - spheroidal state (Boutigny 1798-1894) - remains always below the boiling point and is for water about 97ºC. Faraday has placed in a glowing platinum pot a mixture of solid carbonic acid and ether in the spheroidal state, then placed it into a second pot and caused the mercury in it to freeze.

Although fluids and gases conduct heat very badly, they can nevertheless spread it well in another manner. If you heat water from underneath as you do while boiling it, the lower layers become hot first. As their thickness decreases (during their expansion due to heat input), they rise and make room for other layers. In this way there arises an energetic motion, which spreads the heat quickly throughout the water. {Like in the Hope experiment, the layers which were in the middle of the vessel sink due to the increase in their density (during their contraction following loss of heat) to the bottom and those cooled below 4ºC rise.] The same happens in gases during heat input. In brief: The heated masses move towards other masses, with which they mix and to which they transfer their heat. This process is called: Propagation of heat by convection. In fluids, it is avoided by heating them from above so that heat can only be transferred from above to below. Heat supply by convection is employed technically in central water heating. The circulation of air, the draft which arises when heated air rises, serves in chimneys to bring air to the fuel from below. The higher the chimney, the better is the draft. (Application in ventilation.)

Convection of gases and fluids is fundamental for Meteorology. In fact, the basic circulation of the atmosphere is generated by heated air rising in the tropics and hence colder air flowing from the higher latitudes along Earth's surface to the tropics. The winds directed towards the equator are influenced by Earth's rotation and become the North-East trade wind on the northern, the South-East trade wind on the southern hemisphere (the average width of each trade wind belt over the oceans is about 23º). The ascended stream of hot air changes above its direction towards the poles (counter trade wind). The directions of the trade winds persist. However, there also exist convective currents, the directions of which change daily and those the directions of which change seasonally. With daily periods, this is done by the sea and land breezes. During the day, while the air over the land gets heated and rises, the wind comes from the sea: Sea breeze; in the evening, it comes from the opposite direction: Land breeze. The monsoons (from Arabic: Mausim = spring) change seasonally between the sea and the continents. They arise in a similar manner to the land and sea breezes, but cover much larger sections of Earth's surface.

Ocean currents are of great importance for Earth's heat budget, because they bring huge masses of warm water from the lower latitudes to the higher latitudes, and cold water and drift ice into lower latitudes. Their primary cause are winds (Zöppritz 1838-1885) - not the individual ones which occur locally and change much in time, but the large systems of the atmospheric circulation. Of greatest importance for the northern parts of Western Europe is the Gulf Stream (called after the Gulf of Mexico, from where it partly originates) or the Atlantic Current (the larger part of which comes from the open ocean). The further north and east the current moves, the clearer becomes its climatic impact. G. Schott ("Physical Oceanography") writes:

"Along the Norwegian coast, the Atlantic current keeps also in winter ice away from all fjords, and even in the waters of Spitsberg, at least on its West side, as far north as 80º the sea is navigable in Summer. This warm water heating of the most northern parts of Europe is the most dynamic climatic favouritism anywhere on Earth; at the same latitude, at which in Norway barley is still being harvested, in America the expedition of Sir John Franklin 1786-1847 perished among eternal snow and ice.

It seems to be obvious that a warm or cold current must have a decisive influence on the climate of nearby regions, especially along their coasts; nevertheless, you hear rarely the correct explanation regarding the processes involved. Currents are only then of climatic importance for land, if the warm or cold air lies over them and afterwards really flows inland. The so highly praised and indeed for Europe inestimable value of the Gulf Stream would be of no value if not simultaneously the prevailing SW- and W-winds carried its warm air into Western Europe. The best proof for this is the East coast of the USA during winter: Th Gulf Stream flows along it, but cannot alleviate severe winters in the Southern States, because the direction of the prevailing winds during that season blow outwards (NW). Norway's west coast would, if East winds prevailed instead of Westerlies, partake in Sweden's and Russia's severe winters; at the same time, the Gulf Stream would be distanced from the coast by such winds, just as what happens along the East American coast. Norway's city Christiania, which lies deeper inland, has a mostly severe winter with ice and snow; in contrast, Bergen, in spite of its more northern location, has in winter weather with rain, winds and cloud cover, because the west winds bring the warm air of the Gulf Stream."

We sense the heat of a heat source (oven, lamp) without touching it, so that the heat does not reach us by conduction, and also, while we are above them, so that it does not come to us by convection. If you hold a hot tea can above your hand without touching it, you sense the heat immediately on the side of your hand, turned towards the can. If the heat were transmitted by conduction, it would not be sensed immediately, because air conducts too slowly and convection would not be the cause, because hot air only rises. Heat transfer, which is neither by conduction nor convection, is called heat radiation, because essentially it has the same mechanism as light transmission; you speak of heat rays just as you speak of light rays. Heat transmission by conduction and convection differ fundamentally from that by radiation: Heat conduction and convection transmit heat by heating of intermediate layers, radiation does not. It is true that matter lies between the heat radiator and a radiated body. However, this is of no consequence for the mechanism of heat transfer by radiation. Intermediate layers only do not let all of the radiation pass, but absorb a part of it, that is, they also heat up.

Depending on the degree of their permeability for heat rays, substances are said to be diathermal or athermal - diathermal if they let radiation pass more or less unhindered, athermal, if they partly absorb it and heat up themselves. For example, air and rock salt are diathermal; glass for long waves (>4m), metals and lampblack are athermal. We sense the action of the Sun's rays as heat, because our skin absorbs the radiation, while the air remains cold, because is lets the rays pass. The same explanation applies to the difference between the temperatures of thermometers and air.

Heat radiation and the diathermal property of air impose precautions, if you wish to measure the true air temperature. Joule placed a thermometer in a long copper tube, in order to remove it from the influence of radiation and only let heat arrive at it by convection (as a result of the air circulation which develops inside the tube). You can avoid these errors completely (Richard Asmann 1887), if you suck the air to be measured through a protective tube and lead it past the thermometer bulb at 2 - 3 m/sec.

In essence, heat and light radiation agree with each other: Also heat radiates along straight lines, follows the same laws of reflection and refraction, etc. This is the reason why one sees in the carrier of light radiation also that of heat radiation. We will discuss heat radiation when we deal with Optics.

The spreading of heat by radiation is decisive for Earth's heat budget. Thermo-chemical processes with heat output like oxidation during combustion of our fuels represent a powerful source of heat. They are employed almost exclusively for technical generation of heat. Our fuels come from plants and have developed in solar light and heat into the forms, in which they serve for heat generation, that is, the heat of our technical heat sources originates from the sun. The mechanical energy, employed in work, is partly of organic origin like that of men and animals, partly of inorganic origin like that of falling water and winds. The energy of Man and animals, their capacity to perform work, is solely maintained by input of food, which solely comes from plants. Helmholtz wrote: " For only plants or the meat from plant eating animals serve as food. Plant eating animals are only an intermediate stage, at which food is produced out of plant substances for the meat eaters including Man, unable to consume such food directly."

Development and ripening of vegetable substances demand the light and the heat of the Sun, which therefore must be viewed as the source of energy as far as its nature is organic. However, also the energy of winds and water originate from the heat of the Sun. In order to fall, water must first be raised - by evaporation, which due to the heat of the Sun persists at the surface of the seas and Earth; and the winds arise from air currents due to the heating of the air by the Sun on Earth's surface. Hence the heat of the Sun maintains all meteorological, climatic, geological and organic processes of Earth. Where does it come from? It is obvious to suspect that it arises out of chemical processes between the elements, contained in the Sun (spectral analysis). However, even if the Sun consisted totally out of hydrogen and oxygen, the substances the chemical combination of which generates the largest quantities of heat, it could have radiated heat and light at the prevailing rates only for 3000 years (Helmholtz). The radio-active decay of uranium and thorium, which exist in uranium and thorium minerals, suggests that Earth is at least 15x10⁸ years old. Today's view (1935) is that the main part of the energy of the sun originates in sub-atomic processes (radio-activity, conversion of matter into radiation).

The amount of heat, which Earth receives from the Sun, is determined with a special kind of water calorimeter (phyrheliometer). Taking into consideration the loss of energy, suffered by radiation in Earth's atmosphere, you find the value 1.93 cal (solar constant) at the mean Earth-Sun distance at the outer border of the atmosphere for the radiation energy, which 1 cm² of a black surface receives per minute perpendicular to it. The amount of heat which is transmitted to earth during one year, distributed uniformly all over it, would melt a 31 m thick layer of ice (if there were no atmosphere, which almost absorbs half of the incoming heat). But that is only the amount of heat, which is radiated towards Earth, that is, only a small part of the Sun's total radiation. It was assumed in 1935 that the temperature of the surface of the sun is about 6000ºC.