Thermometric points

The values of the constants in the Uiermometric function are determined with reference to fixed thermometnc points whose temperatures are arbitrarily assumed. The fixed thermometric points most frequently employed are the ice point, steam point and triple point of water. 

The end point is indicated by the intersection of the titration branch and the excess titrant branch. In the idealized thermometric titration curve (see Figure 9.14a) the end point is easily located. When the intersection between the two branches is curved, the end point can be found by extrapolation (Figure 9.14b). 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

The idea that certain physical states could reproduce always the same temperature rises in the second half of seventeenth century (Hooke, 1664 Renaldini, 1694, see e.g. ref. [8]). Intuitions of this idea can be also found in Aristotele and Galeno. Nowadays, the importance of the control of the thermometric calibration is underestimated and the use of reference fixed points is usually limited to metrological laboratories. 

The definition of reference thermometric fixed point is an equilibrium state of a definite substance the realization of a fixed point must depend only on the composition and on the substance . Hence boiling points, for example, cannot be considered fixed points, since they depend on pressure. Only triple points fulfil this definition as can be deduced from the Gibbs rule for pure substances ... 

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. 

The CPA [188], marketed by ThermoMetric AB (Sweden), is frequently used in Europe. It operates on the principle of power compensation, which is based on the supply or withdrawal of heat to and from the reactor, respectively, in order to keep the temperature at the set-point and, thus, to compensate for energy differences (either shortage or surplus). The heat is supplied or withdrawn by means of special (Peltier) elements, which produce a cold or a hot surface area if subjected to an electrical current. An accurate measurement of the heat supply/withdrawal is possible as the heat flow is directly proportional to the current supplied to the Peltier elements. 

The thermometric titrations (TT) make use of heats of reaction to obtain titration curves. In usual practice, the temperature of solution is plotted against the volume of titrant. TT is performed by allowing the titrant to flow from a thermostated-burette directly into a solution contained in a thermally-insulated vessel, and subsequently the observed change in temperature of the solution is recorded precisely either during continuous addition of titrant or after every successive incremental addition. The end-point is aptly indicated by a sharp break in the curve. 

Thermometric titration curves usually represent both the entropy and the free energy involved. The titrant is added to the solution at a constant rate in order that the voltage output of the thermister-temperature-transducer changes linearly with time upto the equivalence point. 

Amplification of the sensitivity of substrate or co-en me recycling is especially efficient in thermometric analysis since all the reactions involved frequently contribute to increasing the overall temperature change. One case in point is the determination of lactate or pyruvate by substrate recycling using co-immobilized lactate oxidase and lactate dehydrogenase [160]. 

However, it is clear that slight variations in vessel shape, etched markings, or external pressure can lead to disagreements as to which thermometer gives the true temperature. Moreover, the reference points chosen to standardize the readings between different thermometers could be subject to disagreements (see Sidebar 2.4), as could the choice of thermometric fluid (e.g., Hg vs. water, each of which has different values of aP in different temperature ranges). Under these circumstances, the choice of the true temperature scale may become subject to non-scientific influences. We therefore seek a universal standard that avoids such arbitrary choices. 

ACIDIMETRY. An analytical method for determining the quantity of arid in a given sample by titration against a standard solution of a base, or, more broadly, a method of analysis by titration where the end point is recognized by a change in pH (hydrogen ion concentration). See also Analysis (Chemical) pH (Hydrogen Ion Concentration) Titration (Potentiometric) and Titration (Thermometric). 

TITRATION (Thermometric). This technique consists of the detection and measurement of the change in temperature of a solution as the titrant is added to it, under as near adiabatic conditions as possible. Experimentally, the titrant is added from a constant-delivery burette into die titrate (solution to be titrated) which is contained in an insulated container such as a Dewar flask. The resultant temperature-volume (or time) curve thus obtained is similar to odier titration curves, e.g., acid-base, in that the end point of the reaction can be readily ascertained. Since all reactions involve a detectable... 

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. 

Fig. 9.11. The vapor-pressure thermometer. The manometer is filled as described in the caption to Fig. 7.1. The manometer is then evacuated and outgassed through a joint attached at point A. A pure compound is condensed into the probe, and the apparatus is sealed off under vacuum at point A. For thermometric compounds which boil below room temperature, care must be taken not to overfill the apparatus.

FIGURE 11.2 Rough and precise end points of the thermometric titration of HN03 with NaOH. 

Each thermometer reads the true Celsius temperature at 0 and 100 because each was calibrated at these points. At other points, however, the readings may differ from the true values of the temperature. Water is seen to be a singularly poor thermometric fluid. Mercury, on the other hand, is good, which accounts for its widespread use in thermometers. Hydrogen at l(atm) makes a very good thermometric fluid, but is not practical for general use. Hydrogen at 100 atm) is no more practical and is less satisfactory. 

All thermometers, regardless of fluid, read the same at zero and 100 if they are calibrated by the method described, but at other points the readings do not usually correspond, because fluids vary in their expansion characteristics. An arbitrary choice could be made, and for many purposes this would be entirely satisfactory. However, as will be shown, the temperature scale of the SI system, with its kelvin unit, symbol K, is based on the ideal gas as thermometric fluid. Since the definition of this scale depends on the properties of gases, detailed discussion of it is delayed until Chap. 3. We note, however, that this is an absolute scale, and depends on the concept of a lower limit of temperature. 

When the temperature of pure ice is gradually raised under the ordinary atmospheric pressure, melting always commences sharply at a certain invariable temperature, which remains constant until fusion is complete. On account of the ease with which this constant temperature can be attained it has been chosen as the standard zero for the Celsius (Centigrade) and Reaumur thermometric scales. The melting-point is slightly affected by pressure, eaeh increase of one atmosphere lowering the transition temperature of ice to water by approximately 0-0075. 

If it were desired to have ice, water, and steam coexist, then there is no degree of freedom left The system must be maintained at the point T - 273.16 K and P - 4.58 torr. For this reason, the triple point of water serves as a convenient thermometric reference standard (see Section 1.2). 

Practical difficulties arise in making very precise determinations of temperature on the thermodynamic scale the precision of the more refined thermometric techniques considerably exceeds the accuracy with which the experimental thermometer scale may be related to the thermodynamic scale. For this reason, a scale known as the International Temperature Scale has been devised, with several fixed points and with interpolation formulas based on practical thermometers (e.g., the platinum resistance thermometer between 13.803 K and 1234.93 K). This scale is intended to correspond as closely as possible to the thermodynamic scale but to permit more precision in the measurement of temperatures. Further details about this scale are given in Chapter XVII. 

The establishment of the International Temperature Scale has required that the thermodynamic temperatures of the fixed points be determined with as much accuracy as possible. For this purpose a device was needed that measures essentially the thermodynamic temperature and does not depend on any particular thermometric substance. On the other... 

Boiling-point apparatus. The mercury thermometer can be replaced by a resistance thermometer or other direct-reading thermometric device. 

---