Franco Pavese

Modern gas-based temperature and pressure measurements

The concept of temperature.- Gas-based fixed points for thermometry.- Gas thermometry between 0.5 K and 273.16 K.- Vapor-pressure thermometry.- Thermometry based on the melting line of 3He.- Cryostats for thermometry and gas-based temperature control.- Primary standards for pressure measurements.- Pressure transducers for gaseous media.- Gas based pressure fixed points.- The thermomolecular pressure difference effect.- The Mutual Recognition Arrangement and its implementation in Temperature and Pressure.- Appendix A - The international Temperature Scale of 1990.- Appendix B - List of temperature and pressure fixed points - Appendix C - Reference data on gases.- Appendix D - Vapor pressure equations.- Appendix E - Reference data for liquid-column manometers.- Appendix F - Reference data for pressure balances.- Appendix G - The text of the Mutual Recognition Arrangement.- Appendix H - General terminology in measurements.- INDEX.

Vapor-Pressure Thermometry

Vapor pressures have been used for a long time for temperature measurements or for calibrating thermometers against a physical property, since the saturated vapor pressure of a pure substance above its liquid phase depends only on temperature. The physical basis of vapor-pressure thermometry has already been discussed in Sect. 2.1 (see Fig. 2.1). Vapor pressures are very commonly used as well for the realization of the fixed points called “boiling points”. These fixed points are simply specific points on the vapor pressure line, generally those at 101 325 Pa (normal boiling point). They do not deserve special attention, as they differ in no way from any other point of the vapor pressure line, and are often simply the highest point attained by the experimenter.

The Concept of Temperature

This monograph is intended for the use of low-temperature experimentalists, as well as those individuals interested in one or more aspects of thermometry. The concept of temperature, therefore, will only be given a brief introduction and review in this section. For a more complete treatment, the reader is directed to the textbooks listed in the section “Further Readings Part I” after the References.

Cryostats for Thermometry and Gas-Based Temperature Control

The “universal” cryostat and the “best” cryostat are ideal terms. The literature contains a very large number of papers describing cryostats. No attempt will be made to review all the papers, or to describe the extremely numerous and varied cryostats. Besides, many of them are specifically designed for types of applications other than thermometry and temperature control; indeed most are too specialized, since their function as thermostats has been unnecessarily confused with the requirements of a specific experiment mounted in them.

The Thermomolecular Pressure Difference Effect

The thermomolecular pressure difference is one of the several phenomena which are significant when pressure measurements are made under purely gaseous conditions, particularly when large differences in temperature exist between the place in which pressure measurements have to be carried out and a reference place, where temperature is generally room temperature and where precise pressure measurements can be made by primary or transfer standards. Such phenomena need careful consideration and corrections have to be applied.

Primary Standards for Pressure Measurements

The primary standards used for pressure measurements are measuring systems that can be metrologically characterized in a complete and independent way with reference only to the basic units of the S.I. system. When pressure is defined as force per unit area or as the height of a liquid column, pressure is, dimensionally, p = [M L − 1 T − 2 a primary pressure standard will thus involve the measurement of mass, length, and time.

Pressure Transducers for Gaseous Media

In this chapter an analysis will be made of the different pressure transducers for static gas pressure measurements in the pressure ranges from 100 Pa to about 100 MPa approximating those considered for absolute, gauge, and differential pressure measurements in Chapter 7. Many of these transducers can work as well in liquid media, but some, particularly those for absolute pressures typically between 100 Pa and some megapascals, are designed for operation only in gas media.

Gas-Based Pressure Fixed Points

In Chapters 7 and 8 we discussed the pressure measurements in gaseous media from 100 Pa to 100 MPa, as well as the appropriate primary and secondary pressure standards and the problems connected with their use at the lowest uncertainty level. The basic definition of the pressure is given, for the pressure range considered in this book, in terms of a force exerted on a known area or of the height of a liquid column. The relationship between well-defined states and pressure values has proved very useful from the metrological standpoint, particularly in view of the possible use of such states as transfer standards, for the verification of pressure values obtained from the measurement of force per unit area. The discussion in the present book being limited to gaseous substances, the establishment of a pressure fixed point involves the definition of a pressure-to-temperature relation generally occurring during a phase transition (triple point, melting or freezing curve, vapor-pressure equilibrium, critical point,...;), which is intrinsically based on some invariant properties of the substance (see Chapter 2).

Gas-Based Reference Points for Thermometry

For more than half a century after the fabrication of the first real thermometers, the only way to compare the values obtained from measurements made with two different thermometers was to place both instruments in the same “thermal bath”, e.g., air or water (chilled with ice or heated), and compare their readings. The idea that a certain physical state reproduces a unique temperature value, and consequently can be used to calibrate subsequently (or in different locations) different thermometers, was in fact not clearly understood until the second half of the seventeenth century, when experimental evidence arose from the readings of the thermometers, and freezing ice was first used for this purposes (Hooke 1664; Renaldini 1694). A kind of ice point is reported to be in use for a similar application in ancient China, about 2000 years ago (Chen Xi-guong 1986). The concept of fixed temperature can also be found in the work of Aristotle (circa A.D. 380), and, following his writings, Galen, the famous Greek physician (A.D. 130–200), introduced a “neutral degree of heat” obtained by mixing equal quantities of ice (his maximum degree of cold) and boiling water (his maximum degree of heat). However, the “neutral” degree so obtained was said to be halfway between these extremes, since at that time heat and cold both were considered substances. We know today that such a mixture has actually a temperature of only about 10 °C, because of ice enthalpy of fusion and of the variable specific heat of water in that range. These concepts only became clear in the nineteenth century.

Thermometry Based on the Melting Line of 3He

Few types of thermometry are available below 1 K, and none is sufficiently well established, readily available, or widely used in laboratories around the world. As discussed in the preceding chapters, even the ITS-90 below 1 K is affected by the degradation of the experimental data forming its basis. As far as the use of gases is concerned, the choice is restricted to 3He. In both vapor-pressure thermometry and gas thermometry, increasing experimental difficulties are encountered below 1,000 mK. In no way, can these techniques be applied much below 500 mK.