Part I. Temperature Measurements in the Range from 0.1 K to 300 K

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1 Part I Temperature Measurements in the Range from 0.1 K to 300 K

2 Introduction Part I describes modem methods for measuring temperatures lower than O C based on the use of substances that are gaseous at room temperature. The lower limit of the temperature range where these substances can be used is arbitrarily set at ~0.1 K, but 3He melting-curve thermometry, described in Chapter 5, extends down to ~O.OOl K. Figure I. shows the typical range for each of these gas-based types of thermometry. The present state of the art allows a top measurement accuracy of ± mk for all of them. Each of the fixed points described in Chapter 2 realizes a single temperature value. Gas thermometry, described in its various forms below O C in Chapter 3, can be used as well above room temperature. Vapor-pressure thermometry too, described in Chapter 4, can be used above room temperature: each substance spans only a narrow interval of the whole temperature range, and in some intervals no substance is available. Finally, Chapter 6 describes thermostats that are used for performing all these thermometric measurements, and temperature controls and devices that are based on the use of gases.,! FIXED POINTS! (phase transitions) L' ---,3""'H.----, I ", -.. ",,; K MELTING CURVE VAPOR ~ PRESSURE T (K) Fig Typical range of gas-based thermometry types. 3

3 List of Symbols Symbols in order of appearance. Some symbols differ from chapter to chapter. Chapter 1 Q T t P V v W S '1 J.l J.l J Amount of heat (J, joule) Heat rate (or "heating"), such as bq=c bt, (W, watt) Specific heats Heat flow direction, defined as q = -k grad () Thermal conductivity (W mol- 1 K -1 ) Boltzmann constant = (12) x (J K -1) [1986] Empirical temperature First Kelvin temperature definition Thermodynamic temperature, second Kelvin temperature definition Empirical kelvin temperature: International Scale temperature (K, kelvin) Kinetic temperature Norm of a (statistical) distribution: definition of temperature Celsius temperature (OC, degree Celsius) Celsiuslike temperature Time (s, second) (Static) pressure (Pa, pascal) Volume (m 3, cubic meter) Velocity (m S-1) (External) mechanical work (J) Entropy (J K -1) Efficiency of a cycle Carnot function (K -1 ) Integrating factor of the Pfaffian Mechanical equivalent of heat Mass of substance B (kg, kilogram) Relative molecular mass s

4 6 List of symbols Part I J Phase of a substance U Internal energy of a system (J) E (Kinetic) energy (J) N Number of molecules ex Cubic (thermal) expansion coefficient (K - 1 ) P Physical quantity nb Amount of substance B, defined as nbil (mol, mole) L Avogadro constant = (36) x mol - I [1986] R Gasconstant= (70)JK- l mol - 1 [1986] X Magnetic susceptibility, defined as X = /11/10-1, where /10 = 4n x 10-7 H m -I exactly (henry per meter) Chapter 2 p T;';, A rus Hm x F A Arus T tp /1 X T). AvapHm Chapter 3 B(T) qt) Tb, Pb' nb nd' Vd K d h H P* Room temperature, room pressure Triple point temperature, triple point pressure (of an impure substance) Critical temperature, critical pressure Density (kg m 3 ) Triple point temperature of the pure substance Molar enthalpy of fusion (J mol-i) Amount fraction Melted fraction (%) First cryoscopic constant, defined as A = II KT~p (K - I), where K = RIArusHm (K -1) Melting range (K) Chemical potential (J mol-i) "Driving capability" of sealed-cell (kg K mol-i) 4He lambda point temperature Molar enthalpy of vaporization Second virial coefficient (m 3 mol-i) Third virial coefficient (m 6 mol- 2 ) Values of T, p, or n for the gas thermometer bulb Amount of substance and volume for the dead volume, including n" Vr in the room temperature dead volume, and nco Vc for the capillary tube. Adsorption coefficient or factor Adsorbed film thickness (measured in number of layers) Capillary diameter Capillary axial coordinate (m, meter) (Portion of the) capillary length Pressure value measured at the manometer (or diaphragm) level.

5 List of symbols Part I 7 IXI IX A VIVo ()p C A. b,c C y n Eg E g Aerostatic pressure head Thermomolecular pressure difference Compression modulus (Pa) Linear (thermal) expansion coefficient (K -1 ) Atomic polarizability, where 1X0 = in vacuum Volume relative contraction Pressure error due to manometer uncertainty Velocity of sound (m S-I, meter per second), where in vacuo Co = m s -1 exactly [1986] Relative permittivity (dielectric constant), where in vacuo ~o = 1/1l0c~ Molar polarizability Dielectric virial coefficients Electrical capacitance (F, farad) Relative capacitance change Refractive index, defined as n = colc Adiabatic bulk modulus of the gas (Pa) Young's modulus of elasticity (Pa) Acceleration due to gravity (m s -2) Chapter 4 Pi p~ KH n L, m L, V L n V, m V, VV n b, m b, Vb n" m" V, nco me' Vc Vr Pf H SL Ii h f ATK Partial pressure Pressure of the pure solvent Henry's law constant Quantity of substance, mass and volume of the liquid phase Same of the vapor phase Same in the bulb Same in the room temperature volume Same in the connecting tube Volume of the room-temperature filling reservoir Condensation pressure at thermometer filling temperature T f Magnetic field strength (A m - 1, ampere per meter) Surface area of the liquid phase Molar flow rate of refluxing film (mol s -1) Elevation of the superfluid film above the liquid surface Temperature difference caused by the Kapitza effect Chapter 5 T min' Pmin T A Temperature and pressure at the point of minimum of the melting curve Temperature of the second-order transition from normal liquid to superfluid A phase

6 8 List of symbols Part I T B Temperature of the first-order transition from superfluid A and B phases T s Temperature of the first-order transition in solid 3He to the ferromagnetically ordered phase Pm Melting pressure " Dynamic viscosity (Pa s, pascal second) Chapter 6 x A Kn C Gap in a gas-filled heat switch Mean free path of gas molecules (A, angstrom), where Ao is at high temperature Knudsen number Conductance in the molecular regimen (1 s -1, liter per second) Appendix A T90, t90 T68, 168 T76 W(T90} W r (T 90 } Kelvin and Celsius temperature for ITS-90 scale Kelvin and Celsius temperature for IPTS-68 scale Kelvin temperature for EPT-76 scale Ratio of R(T 90}/R( K} ITS-90 reference function

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