Thermometric property

Since most of the properties of materials depend on temperature, there are a lot of possible choices for a thermometer. Some thermometric properties tike Mossbauer effect or osmotic pressure, of historical interest, but no longer in use, are reported in ref. [[1], pp. 200-206], Hereafter, some thermometric properties useful at low temperature are described (see Table 9.1). Due to the enormous amount of papers on the subject, the bibliography cannot be complete. References before 1980 are reported in ref. [2],... 

The three modern types of gas thermometry - constant volume gas thermometry (CVGT), acoustic gas thermometry (AGT) and dielectric constant gas thermometry (DCGT) - are presently considered primary . They are based on simple relations between the properties of an ideal gas and temperature T. However, the departure from the ideal behaviour must be carefully considered in view of the desired level of accuracy. This is done by measuring the thermometric property as a function of density. Then the ideal... 

Even if nowadays, the MCT may be considered a primary thermometer only on a narrow temperature range, it is considered the best dissemination standard in the millikelvin range [56-59], In fact, the 3He melting pressure is a good thermometric property because of its sensitivity over three decades of temperature with a resolution A T/T up to 10 5 [56], The good repeatability, the insensitivity to magnetic fields up to 0.5 T [60] and the presence of temperature-fixed points allow for the control of possible shifts in the calibration curve of the pressure transducer. The usefulness of these fixed points is evident, considering that the ITS-90 is based just on the definition of fixed points. 

There is, however, a temperature range in which the y emission is a function of temperature. In this range, the anisotropy of y emission can be used as thermometric property. The advantage of using y emitters is that the detection can be done from outside the cryostat (no wiring necessary inside the cryostat). 

As the magnirnde of the heat exchanged in an isothermal step of a Carnot cycle is proportional to a function of an empirical temperature scale, the magnitude of the heat exchanged can be used as a thermometric property. An important advantage of this approach is that the measurement is independent of the properties of any particular material, because the efficiency of a Carnot cycle is independent of the working substance in the engine. Thus we define a thermodynamic temperature scale (symbol T) such that... 

T he thermometric property is the product pV extrapolated to zero pressure, i.e. ... 

If the temperature is considered to be a linear function of the thermometric property, then ... 

If linear interpolation is applied in this way then two thermometers using different thermometric properties brought into contact with the same heat reservoir will give identical readings only at the fixed points. 

Lavoisier followed the outline of Rouelle s lectures in juxtaposing Stahl s principles with Boerhaave s elements. He would consider the four elements only as instruments chemistry utilized to arrive at its goal, rather than as integrant parts of bodies. His extensive treatment of fire resembled Boerhaave s rather than Rouelle s. He did not endorse phlogiston, but tried to characterize fire in terms of the thermometric properties of heat. He had been unhappy with the way La Blanche handled the issue ... 

Since the property X of different thermometric substances, or the different thermometric properties of a given substance, do not vary in an identical manner with temperature, various thermometers, all of which have been standardized at 0 and 100° C, may indicate different temperatures when in thermal equilibrium with the same body at an intermediate point. A mercury thermometer and a toluene thermometer, for example, which agree at 0 and 100° C, would differ by several degrees in the vicinity of 60° C. Even mercury thermometers in tubes made of various types of glass indicate slightly different temperatures. ... 

It follows, therefore, that when gases approximate to ideal behavior, i.e., at very low pressures, the differences in their thermometric properties disappear. This fact presents the possibility of devising a temperature scale which shall be independent of the thermometric substance, the latter being a hypothetical ideal gas. Such a scale is the so-called absolute ideal gas scale, in which the (absolute) temperature is taken as direcUy proportional to the volume of a definite mass of an ideal gas at constant pressure or to the pressure at constant volume. For convenience, the magnitude of the degree on the absolute scale is usually taken to be the same as on the centigrade scale ( 2b), so that the absolute temperature T on the ideal gas scale is given by... 

An excellent feature of the NQR thermometer is that the thermometric property involved is a fundamental property of a substance, a unique frequency-temperature relationship that must be established only once and is always thereafter applicable for that substance. Thus, once the frequency-temperature relationship has been determined for a suitable sensor material, such as KClOg, that calibration will apply to all other samples of that material provided that the material has been prepared with consistent purity. This, then, eliminates the need to calibrate each thermometer individually as is required for most practical thermometers. Another advantage is that frequency can be easily and accurately measured and the thermometer can be easily made a part of an automated system for temperature monitoring and control. Through the use of standard frequency broadcasts by NBS, the accuracy of the frequency counter used in making measurements can be easily checked. 

The product of PV for a low-density gas is said to be a thermometric property in that to each value of FV there corresponds only a single value of temperature. The ideal gas thermometer is not convenient to use. however, because of both its mechanical construction (see Fig. 1.4-3) and the manipulation required to make a measurement. Therefore, common thermometers make use of thermometric properties of other materials—for example, the single-valued relation between temperature and the specific volume of liquid mercury (Problem 1.2) or the electrical resistance of platinum wire. There are two steps in the construction of thermometers based on these other thermometric propenies first, fabrication of the device, such as sealing liquid mercury in an otherwise evacuated tube and second, the calibration of the thermometric indi-... 

The procedure is easily reduced to a formula by which the temperature can be calculated from the measured value of the thermometric property y. Let y be the value at the ice point and y be the value at the steam point. These points are separated by 100 degrees. Then... 

More generally, suppose we choose any two fixed temperatures to which we assign the arbitrary values and t2 If yi and 2 are the values of the thermometric property at these temperatures, the thermometric equation, Eq. (6.2), becomes... 

What is the thermometric property employed in ordinary mercury thermometers ... 

The quantitative definition of temperature is completed by establishing a partially arbitrary functional relationship between the temperature t and a suitably selected property P of the thermometer. The thermometric property P and those other properties of the thermometer which are held constant in the operation of measurement must determine the thermodynamic state of the thermometer. The care necessary in choosing the variables to be held constant is illustrated by the fact that p and v are not always sufficient to determine the thermodynamic states of a pure system. Thus, for example, in water at temperatures between 0°C and 8°C, the dielectric constant may have two different values at the same values of p and v. The relationship between t and P, t = t P), though partially arbitrary, must be such that t P) is a continuous, monotonic, and single-valued function of P. Single-valuedness is required so that a set of systems with the same value of P remain in equilibrium on contact with each other, i.e., there is only one value of t for each P monotonicity... 

One of the possible choices of a thermometer is a pure gas or liquid at constant pressure. In this case, the volume V of the fluid is the thermometric property, and Eqs. (1-1) and (1-2) become... 

Equation (1-4) is used for the mercury or alcohol thermometer, as well as for gas thermometers containing or He. It is found experimentally that the niimerical value of the temperature, except the values at the ice and steam points which are fixed, depends upon the particular system and thermometric property employed. Because there is less variation among gas thermometers, a gas is usually chosen as the standard thermometric substance. 

Ideal Gas Scale. It is found experimentally that the temperature measured in the constant-pressure gas thermometer, with V as the thermometric property, has a limiting value as the pressure tends to zero ... 

This means that these three systems have a common property called empirical temperature. Choosing, say, the first system as thermometer, we can take, in thermal equilibrium, as the numerical value of empirical temperature the thermometric property V of this first system because it is the same in all systems in our experiments it has the value Vi. 

Or the pressure P—thermometric property at a fixed volume V of thermometer. 

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