J7 Heat

The Gay-Lussac gas law p_TV_T = p₀V₀·aT together with the constant a = 1/273.2 is the foundation of the temperature scale. All thermometry is based on the gas thermometer. Its action rests on the fact that a gas presses on the wall of its container with a constant volume in accordance with this law. You set the increase in temperature proportional to the increase of the pressure of the gas; you allot to the pressure at the temperature of melting ice the degree 0 and to the pressure at the temperature of (at normal pressure) boiling water the degree 100. Fig. 385 shows a gas thermometer for exact measurements. The formulae for the measurement of temperature of the gas thermometer defined in this manner only apply, if all parts of the gas have the temperature to be measured and the volume of the gas really remains constant. In practice, neither of these conditions can be met fully. The largest part of the capillary K and the gas space over the tip at the mark A are always at the room temperature. This detrimental space of the gas thermometer demands a correction of the simple formulae. The condition of constant volume cannot therefore be met strictly, because the volume of the vessel G changes with the temperature. For measurements of the lowest temperatures up to 450º, at a rule, glass vessels are used (Jena glass 59 III), at higher temperatures up to about 1700º platinum iridium, and beyond tungsten, which melts only at 3 300º. The limit for fireproofness and impermeability is also the upper limit for gas thermometry.

Absolute zero of the temperature

If the gas has at the temperature of melting ice the pressure 1 000 mm mercury, it has - apart from corrections for the detrimental space and expansion of the vessel - at 100º the pressure 1 366 mm. If you compute form this the temperature to be allotted to the pressure 0, you find, maintaining the value of a degree (3.66 mm Hg per degree) -1000/3.66 = - 273.2. This temperature, the absolute zero, cannot be measured with a gas thermometer, since every gas approaches with a falling temperature the point, when it becomes fluid and has a smaller pressure than an ideal gas would have at the same temperature. Hence the gas thermometer indicates the pressure zero above the absolute zero.

Different gas thermometers (air, hydrogen) only agree, when the gases are very diluted. However, it is difficult to measure with very diluted gases, because the gas pressures to be measured are then inconveniently small. Yet, the temperature readings of less diluted gases differ from each other by several tenths of degrees, depending on the nature of the gas and its dilution. For everyday measurements, this is of little consequence, but not for precision measurements. Hence it was agreed internationally in 1886 to use as a normal thermometer a hydrogen thermometer of constant volume which has at the ice melting point a pressure of 1000 mm mercury ; at the International Bureau at Paris, four mercury thermometers were compared between 0º and 100º and corrected, in order to achieve complete agreement with the hydrogen thermometer. These four mercury thermometers represent the actual international hydrogen scale. It cannot be applied for very low and very high temperatures, because hydrogen attacks and penetrates at high temperatures every material and becomes a fluid at very low temperatures. Helium would only reduce slightly.the range of these difficulties. In the end, the question of the temperature scale and its realisation can only be solved in the wake of the second main theorem and by reduction of the readings from useable thermometers to the thermodynamic scale.

Realization of the thermodynamic scale

The Joule-Thomson effect is much more suitable for a realization of the thermodynamic scale than the Carnot-process. Instead of measuring quantities of heat, which a substance takes in from outside during isothermal expansion, it is more convenient to measure the change of temperature of a gas, escaping slowly through a throttling section. The application of the second main theorem to the Joule-Thomson effect yields a relationship between the gas-thermometric and thermodynamic temperatures. You can employ it to find out how to correct the readings of a gas thermometer (constant pressure), in order to convert them to the thermodynamic scale. The degrees of the thermodynamic scale are denoted by ºK (say: Degrees Kelvin).

It can be shown that the scale of the gas thermometer of constant volume as well as of constant pressure agrees completely with the thermodynamic scale, if the filling gas is ideal. An ideal gas is molecular theoretically a gas, the particles of which have neither extension nor attract each other. This ideal fulfils almost a very diluted real gas. The larger the volume of a mass of gas, the more vanishes the volume of its particles compared with it and as the distance between the particles increases (as a result of dilution) the mutual forces of attraction weaken. An infinitely diluted real gas agrees as a thermometric substance completely with an ideal gas.

In general, gas thermometers deviate between 0º and 100ºC by a small fraction of a degree from the thermodynamic scale, the helium thermometer least of all. A helium thermometer of constant volume with an ice point pressure of p <= 1000 mm realizes best to the upper limit of its usefulness (in a platinum iridium vessel to 1 600º) the thermodynamic scale. For the purposes of the temperature scale, you must measure gas thermometrically up to about 1100ºC. Beyond this temperature, in the range of glowing temperatures, optical radiation instruments are used.

Mercury thermometers for different purposes

The familiar mercury thermometer is used daily. Its application depends on the fact that mercury expands on being heated and contracts on being cooled and eventually stands higher or lower in a capillary. During their production, air must be removed completely from the mercury and the internal wall of the glass capillary, in order that in the end the capillary contains only mercury and a trace of mercury vapour (Torricelli vacuum). For a new thermometer, you find first the point, to which the mercury column extends when the mercury container is completely covered by melting ice, and then the point it reaches (as in Fig. 401) when it is completely surrounded by steam (not water!); this point, the boiling point, must be found taking into consideration the present reading of the barometer, as the boiling point depends on it; it changes by about 0.03º per mm Hg.

In order to determine temperatures between the freezing and boiling points, you subdivide their distance into equal parts and number them; this subdivision is continued beyond and below these points. The readings from mercury thermometers then agree very closely with those from a gas thermometer. (For great accuracy, corrections are needed.!) The measuring range of ordinary mercury thermometers is limited by the freezing point of mercury at -38.87ºC and its normal boiling point at + 356ºC. For temperatures from -35ºC to -100ºC, alcohol replaces mercury, because it only freezes at -130ºC. Thermometers for temperatures above 350ºC, you place nitrogen (or carbonic acid) over the mercury . The rising mercury then condenses the gas, experiences thereby a high counterpressure and is stopped from boiling. The range of such a mercury thermometer (made out of sufficiently resistant glass) can be up to 500ºC; if it is made out of quartz glass, up to 750ºC. Yet higher temperatures are measured with electrical (platinum) thermometers or with a radiation pyrometer.

Maximum- and minimum-thermometers mark the highest and lowest temperature during a certain duration of measurement by markers. For example (Fig, 387), you employ mercury, which during expansion pushes ahead of it an iron plug to the maximum reading and leaves it behind as it contracts; in a minimum thermometer, alcohol, which carries by means of its surface skin during contraction a glass plug to the minimum and leaves it behind on expansion. - These thermometers mark only the limits of temperature; thermographs record the course of the temperature by drawing curves. -

The fever thermometer(Fig. 386) is designed for the measurement of humans' body temperature. It is a mercury thermometer, the column of which is torn at a (by a protruding glass pin) narrowed section of the capillary, as soon as it tends to contract. The torn column stays behind during cooling. Since the body temperature lies normally around 37ºC and measurements range only over a few degrees, the scale is only marked in tenths of degrees between 35ºC and 42ºC.

The deep sea thermometer (Richter) also marks by means of such a torn mercury column the water temperature, to be read later on board the ship. When the thermometer reaches the bottom, the thermometer is turned upside down, the mercury column tears as its narrowed section and drops into the empty space below the inverted capillary. The length of the mercury thread tells the temperature down below, whence the capillary is calibrated for the inverted position. These thermometers require special protection against the enormous pressure at the bottom of the sea (about 1 atm for every 10 m).

In order to measure the lowering or rising of the boiling point - that is, not absolute, but relative temperatures -, that is, changes in temperature of a few degrees very exactly, you use Beckmann's thermometer. Its quantity of mercury, employed for measurement of the temperature, can be increased out of a container, into which the mercury column leads at the top, or reduced by pouring it out (Fig. 388). For example, you can shift the deepest degree of temperature, from which the increase of the boiling temperature is to be measured, to the zero point and then measure from there every higher temperature within the instrument's range. The scale embraces only a very few degrees, subdivided into 0.01 º; you can estimate 0.001 º.

Also the temperature dependence of the lengths of solids is at times employed in thermometry (Bréguet 1747-1823) in the metal strip thermometer (Fig. 389). Like in the chronometer balance wheel, you have two or, in order to increase the sensitivity, three bands of silver, gold and platinum, the gold one in the centre, because its coefficient of expansionlies between the two other metals; the coiled spring, made out of these materials, deforms due to a change in temperature and turns a pointer in from of a scale, calibrated thermometrically.

Platinum thermometer (electrical measurement of temperature)

While the handling of a mercury thermometer is most convenient, the platinum wire resistance thermometer is more reliable: Between -200ºC and +650ºC, it is the most important temperature measuring device for scientific purposes, for example, during experiments with explosions or measurements of adiabatic volume changes of gases and of the saturation pressure of steam; it is also used as telethermometer. A resistance thermometer depends on the fact that the electrical resistance of a wire rises and drops with its temperature. Once you know the formula for the relationship between these two quantities and you measure the resistance of the thermometer wire at a given temperature, you can compute the temperature from it. Platinum is most suitable (basic idea: Werner von Siemens 1870, formula: Hugh L. Callendar 1863-1930 1886): It does not change in air, has a very high melting point, its resistance formulae above -40ºC are strictly quadratic (R_t = R₀(1 + at + bt²), whence you need only measure the resistances at three fixed points (you use the melting point of ice and the boiling points of water and sulphur for the determination of the constants R₀, a and b). Fig. 390 shows a suitable form of the thermometer containers in the Pt-thermometer for scientific purposes: A Pt-wire with a diameter of 0.1mm and about 10 Ohm resistance is wound around a hard burned porcelain, isolating rod with a cross section shape of a plus sign (+) so that it only touches it in a few points. You handle it (inside a protective cover) like an Hg-thermometer. Wires lead to a resistance measuring device. - At extremely deep temperatures, the lead wire thermometer of Nernst is better then the Pt-thermometer: Near the temperature of liquid hydrogen, the temperature coefficient of many metals becomes very small, whence their thermometric sensitivity is too small and lead supercedes platinum by far.

A resistance thermometer of a special kind is the bolometer of Samuel Pierpont Langley 1834-1906 1881. It consists in essence of one or several (linear- or area-bolometer) platinum strips, less than 1 m thick (blackened with platinum-black). It measures the energy of the radiation it has absorbed by changes of its electrical resistance, which is proportional to the change of its temperature. In order to measure this, it is included in one branch of a Wheatstone bridge (Wheatstone). The galvanometer's deflections - set to zero before radiation is applied to the bolometer - are proportional to the absorbed energy. For a long time, the bolometer was widely used as the most sensitive instrument for radiation measurements (most sensitive in a vacuum container), however, it places too large demands on the user (sources of errors!), whence other, meanwhile greatly improved radiation sensors are being used (in 1935).

For measurements of temperatures in blast furnaces, glass ovens, etc., an optical pyrometer with thermo-elements is preferred to thermometers.

continue step back