Appendix A The International Temperature Scale of 1990

Transcription

1 Appendix A The International Temperature Scale of 1990 Annotated text of the parts of the definition that concerns the temperature range below K. (BIPM 1989; Preston-Thomas 1990) The International Temperature Scale of 1990 was adopted by the International Committee of Weights and Measures at its meeting in 1989, in accordance with the request embodied in Resolution 7 of the 18th General Conference of Weights and Measures of This scale overcomes the International Practical Temperature Scale of 1968 (amended edition of 1975) and the 1976 Provisional K Temperature Scale. A.1 Units of Temperature The unit of the fundamental physical quantity known as thermodynamic temperature, symbol T, is the kelvin, symbol K, defined as the fraction 1/ of the thermodynamic temperature of the triple point of water. 1 Because of the way earlier temperature scales were defined, it remains common practice to express a temperature in terms of its difference from K, the ice point. A thermodynamic temperature, T, expressed in this way is known as a Celsius temperature, symbol t, defined by t/ C = T /K (A.1) The unit of Celsius temperature is the degree Celsius, symbol C, which is by definition equal in magnitude to the kelvin. A difference of temperature may be expressed in kelvins or degrees Celsius. 1 Comptes Rendus des Seances de la Treizième Conférence Générale des Poids et Mesures ( ), Resolutions 3 and 4, p F. Pavese, G. Molinar Min Beciet, Modern Gas-Based Temperature 495 and Pressure Measurements, International Cryogenics Monograph Series, DOI / , Springer Science+Business Media New York 2013

2 496 Appendix A The International Temperature Scale of 1990 The International Temperature Scale of 1990 (ITS-90) defines both International Kelvin Temperatures, symbol T 90, and International Celsius Temperatures, symbol t 90. The relation between T 90 and t 90 is the same as that between T and t, that is t 90 / C = T 90 /K (A.2) The unit of the physical quantity T 90 is the kelvin, symbol K, and the unit of the physical quantity t 90 is the degree Celsius, symbol C, as is the case for the thermodynamic temperature T and the Celsius temperature t. A.2 Principles of the International Temperature Scale of 1990 (ITS-90) The ITS-90 extends upwards from 0.65 K to the highest temperature practicably measurable in terms of the Planck radiation law using monochromatic radiation. The ITS-90 comprises a number of ranges and sub-ranges throughout each of which temperatures T 90 are defined. Several of these ranges or sub-ranges overlap, and where such overlapping occurs, differing definitions of T 90 exist: these differing definitions have equal status. For measurements of the very highest precision, there may be detectable numerical differences between measurements made at the same temperature but in accordance with differing definitions. Similarly, even using one definition, at a temperature between defining fixed points two acceptable interpolating instruments (e.g., resistance thermometers) may give detectably differing numerical values of T 90. In virtually all cases, these differences are of negligible practical importance and are at the minimum level consistent with a scale of no more than reasonable complexity: for further information on this point, see Supplementary Information for the ITS-90. This scale concept is new with respect to the former issues. In the ITS-90, generally near the end of a definition field, a multiple definition is available. All definitions are equivalent and their use is equally allowed. Small differences between the temperature scale i.e. in the numerical values of T 90 obtained using different definitions are known to exist, but they have been studied and checked to be within ITS-90 accuracy. The ITS-90 has been constructed in such a way that, throughout its range, for any given temperature, the numerical value of T 90 is a close approximation to the numerical value of T according to best estimates at the time the scale was adopted. By comparison with direct measurements of thermodynamic temperatures, measurements of T 90 are more easily made, are more precise, and are highly reproducible. There are significant numerical differences between the values of T 90 and the corresponding values of T 68 measured on the International Practical Temperature Scale of 1968 (IPTS-68), see Fig. A.1 and Table A.6.

3 A.3 Definition of the International Temperature Scale of Fig. A.1 Temperatures differences (t 90 t 68 ) It must be clearly noted that the accuracy which can be obtained from these differences in no way can be better than that allowed by the less accurate term of the difference, i.e., by the older scale, the IPTS-68. The number of digits of the differences reported in Table A.6 is generally larger than justified by the actual accuracy: it simply permits a smooth interpolation or to compute smooth functions for use in automatic computation. Some of these functions are reported in the Note to Table A.6. Similarly there were differences between the IPTS-68 and the International Practical Temperature Scale of 1948 (IPTS-48), and between the International Temperature Scale of 1948 (ITS-48) and the International Temperature Scale of 1927 (ITS-27). See the Appendix and, for more detailed information, Supplementary Information for the ITS A.3 Definition of the International Temperature Scale of 1990 Between 0.65 K and 5.0 K T 90 is defined in terms of the vapor-pressure temperature relations of 3 He and 4 He. The ITS-90 definition supercedes the old scales T 62 and T The text in italic is out of the scope of this book (most is omitted).

4 498 Appendix A The International Temperature Scale of 1990 Between 3.0 K and the triple point of neon ( K) T 90 is defined by means of a helium gas thermometer calibrated at three experimentally realizable temperatures having assigned numerical values (defining fixed points) and using specified interpolation procedures. This is one of the major new features of the ITS-90. Between the triple point of equilibrium hydrogen ( K) and the freezing point of silver ( C), T 90 is defined by means of platinum resistance thermometers calibrated at specified sets of defining fixed points and using specified interpolation procedures. Above the freezing point of silver ( C) T 90 is defined in terms of a defining fixed point and the Planck radiation law. The defining fixed points of the ITS-90 are listed in Table A.1. The effects of pressure, arising from significant depths of immersion of the sensor or from other causes, on the temperature of most of these points are given in Table A.2. A.3.1 From 0.65 K to 5.0 K: Helium Vapor-Pressure Temperature Equations In this range, T 90 is defined in terms of the vapor pressure p of 3 He and 4 He using equations of the form T 90 /K = A A i[(ln (p/pa) B)/C] i (A1.3) i=1 The values of the constants A 0, A i, B, and C are given in Table A.3 for 3 He in the range K and for 4 He in the ranges K (the λ point) and K. No fixed points are used in the definition and, consequently, no calibration at fixed points is needed. A thermometer is designed according to the state-of-the-art, then the T 90 values are obtained from the measured values of p and from Eq. (A.3; see Chap. 4). A.3.2 From 3.0 K to the Triple Point of Neon ( K): Gas Thermometer In this range, T 90 is defined in terms of a 3 He or a 4 He gas thermometer of the constantvolume type that has been calibrated at three temperatures. These are the triple point of neon ( K), the triple point of equilibrium hydrogen ( K), and a temperature between 3.0 and 5.0 K. This last temperature is determined using a 3 He or a 4 He vapor pressure thermometer as specified in Sect. A.3.1.

5 A.3 Definition of the International Temperature Scale of Contrarily to the vapor-pressure thermometer, the gas thermometer is used as an interpolating instrument (ICVGT) between fixed points. Three of them are defined. There are two definitions for the ICVGT. In the first (Sect. A.3.2.1), only the use of 4 He is allowed in a range above 4.2 K and with a single Eq. (A.4). In the second (Sect. A.3.2.2), both helium isotopes can be used in the full range above 3 K and two equations are needed: one, Eq. (A.6), with defined coefficients, is specific for each isotope and takes into account the gas non-ideality, the other, Eq. (A.5), similarly to Eq. (A.4), has a quadratic form whose coefficients must be determined by measurements at the fixed points. A From 4.2 K to the Triple Point of Neon ( K) with 4 He as the Thermometric Gas In this range, T 90 is defined by the relation T 90 = a + bp + cp 2 (A.4) where p is the pressure in the gas thermometer and a, b, and c are coefficients the numerical values of which are obtained from measurements made at the three defining fixed points given in Sect. A.3.2, but with the further restriction that the lowest one of these points lies between 4.2 and 5.0 K. A From 3.0 K to the Triple Point of Neon ( K) with 3 He or 4 He as the Thermometric Gas For a 3 He gas thermometer, and for a 4 He gas thermometer used below 4.2 K, the non-ideality of the gas must be accounted for explicitly, using the appropriate second virial coefficient B 3 (T 90 )orb 4 (T 90 ). In this range, T 90 is defined by the relation T 90 = a + bp + cp2 1 + B x (T 90 )n/v (A.5) where p is the pressure in the gas thermometer, a, b, and c are coefficients the numerical values of which are obtained from measurements at three defining temperatures as given in Sect. A.3.2 n/v is the gas density with n being the amount of gas and V the volume of the bulb, x is 3 or 4 according to the isotope used, and the values of the second virial coefficients are given by the relations. For 3 He B 3 (T 90 )/m 3 mol 1 = { (T90 /K) (T 90 /K) (T 90 /K) 3} 10 6 (A.6a)

6 500 Appendix A The International Temperature Scale of 1990 For 4 He B 4 (T 90 )/m 3 mol 1 ={ (T 90 /K) (T 90 /K) (T 90 /K) (T 90 /K) (T 90 /K) 5 } 10 6 (A.6b) Gas molar density (n/v) is obtained with sufficient accuracy from the pressure value measured at the upper fixed point, assuming an ideal gas (n/v )/mol m 3 = p( )/pa R The accuracy with which T 90 can be realized using Eqs. (A.4) and (A.5) depends on the design of the gas thermometer and the gas density used. Design criteria and current good practice required to achieve a selected accuracy are given in Supplementary Information for the ITS-90. A.3.3 The Triple Point of Equilibrium Hydrogen ( K) to the Freezing Point of Silver ( C): Platinum Resistance Thermometer In this range, T 90 is defined by means of a platinum resistance thermometer calibrated at specified sets of defining fixed points, and using specified reference and deviation functions for interpolation at intervening temperatures. Below 0 C, there are several differences with respect to the IPTS-68 definition that will be noted in the following. No single platinum resistance thermometer can provide high accuracy, or is even likely to be usable, over the entire range K C. The choice of temperature range, or ranges, from among those listed below for which a particular thermometer can be used is normally limited by its construction. For practical details and current good practice, in particular concerning types of thermometer available, their acceptable operating ranges, probable accuracies, permissible leakage resistance, resistance values, and thermal treatment, see Supplementary Information for the ITS-90. It is particularly important to take account of the appropriate heat treatments that should be followed each time a platinum resistance thermometer is subjected to a temperature above about 420 C. Temperatures are determined in terms of the ratio of the resistance R(T 90 )ata temperature T 90 and the resistance R( K) at the triple point of water. This ratio, W(T 90 ), is 3 3 Note that this definition of W(T90) differs from the corresponding definition used in the ITS-27, ITS-48, IPTS-48, and IPTS-68: for all of these earlier scales W(T) was defined in terms of a reference temperature of 0 C, which since 1954 has itself been defined as K.

7 A.3 Definition of the International Temperature Scale of W (T 90 ) = R(T 90 )/R( K) (A.7) Warning: This definition is different from that of the IPTS-68, where R( K) was used. A mistake produces a sizeable error! An acceptable platinum resistance thermometer must be made from pure, strain-free platinum, and it must satisfy at least one of the following two relations W ( C) W ( C) (A.8a) (A.8b) These criteria are different from that used in the IPTS-68, where R(100 C)/R(0 C) was used. This is due to the fact that the boiling point of water is no more a definition point of the scale (its numerical value is also different: T 90 (H 2 O) = C). An acceptable platinum resistance thermometer that is to be used up to the freezing point of silver must also satisfy the relation W ( C) (A.8c) In each of the resistance thermometer ranges, T 90 is obtained from W r (T 90 )asgiven by the appropriate reference function (Eq. (A.9b) or Eq. (A.10b)), and the deviation W (T 90 ) W r (T 90 ). At the defining fixed points, this deviation is obtained directly from the calibration of the thermometer: at intermediate temperatures it is obtained by means of the appropriate deviation function (Eqs. (A.12), (A.13), and (A.14)). The structure of the ITS-90 definition in this range is the same of that of the IPTS-68: a reference function W r (with respect to K in the ITS-90!) and deviation functions. However, both functions are different, and deviation functions are differently used, as shown in the following. In addition, both T 90 (W r ) and W r (T 90 ) are defined. i. For the range K, the following reference function is defined ln[w r (T 90 )] = A i=1 [ ] ln(t90 / K) i A i (A.9a) 1.5 An inverse function, equivalent to Eq. (A.9a) within ±0.1 mk, is 15 [ Wr (T 90 ) 1/6 ] i 0.65 T 90 / K = B 0 + B i (A.9b) 0.35 i=1 The values of the constants A 0, B 0, A i and B i are given in Table A.4.

8 502 Appendix A The International Temperature Scale of 1990 A thermometer may be calibrated for use throughout this range or, using progressively fewer calibration points, for ranges with low temperature limits of , , and K, all having an upper limit of K. ii. For the range 0 C to C, the following reference function is defined: [...text omitted] iii. A thermometer may be calibrated for use in the range K ( C) to C, the calibration being made at these temperatures and at the triple point of water. Both reference functions (Eqs. (A.9a, b) and Eqs. (A.10a, b) omitted) are required to cover this range. The defining fixed points and deviation functions for the various ranges are given below, and in summary form in Table A.5. The ITS-90, as the IPTS-68, defines subranges, however differently. In fact in the ITS-90 they always extend from the same upper limit ( K) down to a decreasing limit (i.e., the subranges are set in parallel, not in series as in the IPTS-68). In addition there is a narrow subrange crossing 0 C. A The Triple Point of Equilibrium Hydrogen ( K) to the Triple Point of Water ( K) The thermometer is calibrated at the triple points of equilibrium hydrogen ( K), neon ( K), oxygen ( K), argon ( K), mercury ( K), and water ( K), and at two additional temperatures close to 17.0 K and 20.3 K. These last two may be determined either: by using a gas thermometer as described in Sect. A.3.2, in which case the two temperatures must lie within the ranges 16.9 K 17.1 K and K respectively; or by using the vapor pressure-temperature relation of equilibrium hydrogen, in which case the two temperatures must lie within the ranges K and K respectively, with the precise values being determined from Eqs. (A.11a) and (A.11b) respectively T 90 /K = (p/kpa )/13.32 (A.11a) T 90 /K = (p/kpa )/30 (A.11b) The deviation function is 4 W(T 90 ) W r (T 90 ) = a[w (T 90 ) 1] + b[w(t 90 ) 1] c i [lnw (T 90 )] i+n i=1 (A.12) 4 This deviation function [and also those of Eqs. (A.13) and (A.14)] may be expressed in terms of W r, rather than W; for this procedure see Supplementary Information for ITS-90 (BIPM 1990).

9 A.3 Definition of the International Temperature Scale of with values for the coefficients a, b, and c i being obtained from measurements at the defining fixed points and with n = 2. For this range and for the subranges The Triple Point of Neon ( K) to the Triple Point of Water ( K), The Triple Point of Oxygen ( K) to the Triple Point of Water ( K), The Triple Point of Argon ( K) to the Triple Point of Water ( K), the required values of W r (T 90 ) are obtained from Eq. (A.9a) or from Table A.1. There are changes with respect to the fixed points used in the IPTS-68 definition. The triple points of neon and argon are substituted for the normal boiling points of neon and oxygen. The triple point of mercury is substituted for the normal boiling point of water, thus eliminating the need to heat the thermometers above room temperature during calibration. Only in the full range, which extends below the triple point of neon (and overlaps the range of gas thermometry), there is a need for pressure measurements. These points can be realized by means of two e-h 2 vapor-pressure points: for both of them, selection of any accurate temperature value in a small interval is allowed, instead of the fixed value required by the IPTS-68. Alternatively, these points can be obtained from the ICVGT used for the realization of the 3 25 K range. All other subranges require the use of triple points only. The same deviation function is defined for the range and most of the subranges, simply omitting some terms according to the number of the fixed points required. A The Triple Point of Neon ( K) to the Triple Point of Water ( K) The thermometer is calibrated at the triple points of equilibrium hydrogen ( K), neon ( K), oxygen ( K), argon ( K), mercury ( K), and water ( K). The deviation function is given by Eq. (A.12) with values for the coefficients a, b, c 1, c 2, and c 3 being obtained from measurements at the defining fixed points and with c 4 = c 5 = n = 0. A The Triple Point of Oxygen ( K) to the Triple Point of Water ( K) The thermometer is calibrated at the triple points of oxygen ( K), argon ( K), mercury ( K), and water ( K). The deviation function is given by Eq. (A.12) with values for the coefficients a, b, and c 1 being obtained from measurements at the defining fixed points, with c 2 = c 3 = c 4 = c 5 = 0 and with n = 1. A The Triple Point of Argon ( K) to the Triple Point of Water ( K) The thermometer is calibrated at the triple points of argon ( K), mercury ( K), and water ( K).

10 504 Appendix A The International Temperature Scale of 1990 Table A.1 Defining fixed points of the ITS-90 Number Temperature Substance a State b W r (T 90 ) T 90 /K t 90 / C to He V e-h 2 T e-h 2 (or He) V (or G) e-h 2 (or He) V (or G) Ne T O 2 T Ar T Hg T H 2 O T Ga M In F Sn F Zn F Al F Ag F Au Cu a All substances except 3 He are of natural isotopic composition. e-h 2 is hydrogen at the equilibrium concentration of the ortho and para molecular forms b For complete definitions and advice on the realization of these various states, see Supplementary Information for the ITS-90. The symbols have the following meanings: V vapor pressure point, T triple point (temperature at which the solid, liquid, and vapor phases are in equilibrium), G gas thermometer point, M, F melting point, freezing point (temperature, at a pressure of Pa, at which the solid and liquid phases are in equilibrium) Note: Entries in italics are beyond the scope of this book The deviation function is W (T 90 ) W r (T 90 ) = a[w (T 90 ) 1] + b[w (T 90 ) 1] ln W (T 90 ) (A1.13) with the numerical values of a and b being obtained from measurements at the defining fixed points. In this subrange, the deviation function is defined in a different way, being only three of the fixed points involved. A From 0 C to the Freezing Point of Silver ( C) (... text omitted)

11 A.3 Definition of the International Temperature Scale of Table A.2 Effect of pressure on the temperature of some defining fixed points dt /dh / Substance T tp (K) dt tp /dp/10 8 KPa 1a tp L mk m 1b Hydrogen c Deuterium c Neon Oxygen Nitrogen Argon Methane Krypton Xenon Carbon dioxide Mercury Water Italic denotes the defining ITS-90 value a Equivalent to mk bar 1 b h L = depth of condensed phases c In spin equilibrium Table A.3 Values of the constants for the helium vapor pressure Eqs. (A.3a, b), and the temperature range for which each equation, identified by its set of constants, is valid 3 He 4 He 4 He K K K A A A A A A A A A A B C Table A.4 The constants A 0, A i ; B 0, B i in the reference functions of Eqs. (A.9a) and (A.9b), respectively A B B A B B A B B A B A B A B A B A B A B A B A B A B A B

12 506 Appendix A The International Temperature Scale of 1990 Table A.5 Deviation functions and calibration points for platinum resistance thermometers in the various ranges in which they define T 90 Section Lower Deviation Calibration temperature function points (see limit T/K Table A.1) (a) Ranges with an upper limit of K A a[w (T 90 ) 1] + b[w(t 9 0) 1] c i [W (T 90 )] i+n, n = 2 A As for A with c 4 = c 5 = n = 0 A As for A with c 2 = c 3 = c 4 = c 5 = 0, n = 1 A a [W(T 90 ) 1] + b[w(t 90 ) 1] lnw(t 90 ) i=1 2, 5 9 Section Upper Deviation Calibration temperature function points (see limit t/ C Table A.1) (b) Ranges with a lower limit of 0 C A a a[w (T 90 ) 1] + b[w(t 90 ) 1] 2 + 9, c[w (T 90 ) 1] 3 + d[w(t 90 ) W ( C)] 2 A As for A with d = 0 9, A As for A with c = d = 0 9, 12, 13 A As for A with c = d = 0 9, 11, 12 A As for A with b = c = d = 0 9,11 A As for A with b = c = d = 0 9,10 (c) Range from K ( C) to C A As for A with c = d = a Calibration points 9, are used with d = 0 for t 90 < C; the values of a, b, and c thus obtained are retained for t 90 > C with d being determined from calibration point

13 A.3 Definition of the International Temperature Scale of Table A.6 Differences between ITS-90 and EPT-76, and between ITS-90 and IPTS-68 for specified values of T 90 below K (and derivatives of these differences) dt = (T 90 T 76 )mk dδt/dt 10 3 T 90 /K dt = (T 90 T 68 )/K dδt/dt 10 3 T 90 /K T 90 /K Notes to Table A.6 1. Equations giving the differences T 90 T 68 shown in Table A.6. The polynomial representations of the differences between 13.8 K and C are due to R. L. Rusby (1990). 5 From 13.8 and 83.8 K (accuracy ±1 mk) (T 90 T 68 )/K = a i=1 a i ((T K)/40 K) i 5 The two functions show a discontinuity of the value of 0.6 mk and of the first derivative at their joining point K. This discontinuity, inconvenient when calculating scale conversion of thermophysical or thermodynamic data, is better removed if the joining point is moved to 63 K (Pavese 1993).

14 508 Appendix A The International Temperature Scale of 1990 From 83.8 K to C (accuracy approximately ±1.5 mk below 0 C and ±1 mk above 0 C) (t 90 t 68 )/ C = 8 b i ((t 90 /630 C) i ) i=1 The coefficients a i and b i of the equations are (after BIPM 1990) i a i b i Conversion of thermodynamic quantities (Douglas 1969): Enthalpy: dh = (T 90 T 68 )c p Specific heat capacity: dc p = (T 90 T 68 )dc p /dt c p d(t 90 T 68 )/dt Entropy: T ds = 0 ((T 90 T 68 )dc p /dt 2 )dt (T 90 T 68 )c p /T (after Goldberg and Weir (1991)) 3. Conversion of T 90 to thermodynamic temperature T: see discussion and equations for T T 90 in Sect (Pavese et al. 2011) 4. Conversion between older temperature scales and ITS-90. In general, for a quantity X(T) the conversion from a scale T X T 90 is X(T 90 ) = X(T 9X )dx/dt (T 90 T X ) a. Scale different from the ITS-90 in the value of the reference temperature T 0 T 90 = T (273.16/T 0 )

15 A.3 Definition of the International Temperature Scale of b. Scale with the value of a fixed point T1 different from T 90,1 with p 90,1 = p1 or p 90,1 = p1, with T 90,1 = T1. In a vapor pressure equation in the range (T1, T max,) or(t max, T1 )is p A90 + f (T90) where the coefficient A 90 = A 1 + δa with δa such as p(t 90,1) = p 90,1 c. Scale different from the ITS-90 in the value of the reference temperature T0 and of a second fixed point T1. Assuming a linear correction between the two points is d. Scale IPTS-48 T 90 = (T T 1 )( T 90,1)/(T 0 T 1 ) + T 90,1 T 90 (K) t 90 ( C) δt = T 90 T 48 (mk) dδt (dt) e. Scale EPT-76 (after BIPM 1990b). T 90 T 76 = (T 76 ) 2

16 Appendix B List of Temperature and Pressure Fixed Points (Table B.1, B.2, and B.3) Table B.1 Best-quality temperature and pressure fixed points (ITS-90 fixed points in italics) Equilibrium state a T 90 /K Uncertainty Purity of References g (p/pa) b δt (mk) material (δp/pa) c (%) d Triple point of equilibrium hydrogen Triple point of equilibrium deuterium Triple point of normal deuterium (0.5) f Ancsin 1977; Pavese and Ferri 1982; Kemp and Kemp 1979b; Hoge and Arnold Pavese and McConville 1987; McConville and Pavese 1988; Ancsin 1988; Kemp 1982; Pavese and Barbero 1979; Schwalbe and Grilly 1984; Khnykov et al Pavese and McConville 1987; McConville and Pavese 1988; Ancsin 1988; Kemp 1982; Pavese and Barbero 1979; Schwalbe and Grilly 1984; Khnykov et al Pavese et al. 2011b Triple point of neon isotope 20 Ne Triple point of natural (0.2) f Pavese et al. 2010b neon e (0.5) f Triple point of neon Pavese et al. 2011b isotope 22 Ne Triple point of oxygen (1) f h Kemp et al. 1976; Pavese 1978b; Ancsin 1974b; Compton and Ward 1976 (146.25) (0.1) Pavese 1981 Triple point of nitrogen (0.1) f Pavese 1981; Pavese and Ferri 1982; Ancsin 1974a Boiling point of nitrogen Ancsin 1974a Triple point of argon (0.15) f Kemp and Kemp 1978; Seifert 1983; Ancsin 1974a; Tiggelman and Durieux 1972; Ancsin 1973b; Furukawa et al. 1972; Furukawa 1982; Kemp et al. 1976; Khnykov et al. 1978; Blanke and Thomas 1981; Pavese 1978b (68 890) (1.5) f (1) Pavese 1981; Bonhoure and Pello 1983 Boiling point of argon Pavese 1981; Ancsin 1973b; Kemp et al Triple point of methane f (0.3) Khnykov et al. 1978; Pavese et al. 1975b; Pavese 1979; Bonhoure and Pello 1978, 1980 (11 696) (0.7) Pavese 1981 Triple point of xenon k Inaba and Mitsui 1978; Kemp et al. 1982; Ancsin 1988b; Khnykov 1989b; Head et al. 1989; Hill and Steele 2004, 2005 Triple point of carbon dioxide ( ) 1 (50) Pavese and Ferri 1982; Ambrose 1957; Bonnier et al. 1984; Head et al F. Pavese, G. Molinar Min Beciet, Modern Gas-Based Temperature 511 and Pressure Measurements, International Cryogenics Monograph Series, DOI / , Springer Science+Business Media New York 2013

17 512 Appendix B List of Temperature and Pressure Fixed Points Table B.1 (continued) Equilibrium state a T 90 /K Uncertainty Purity of References g (p/(pa)) b δt (mk) material (δp(pa)) c (%) d Triple point of mercury (1.5) f Furukawa and Bigge 1976 (Furukawa et al. 1982) Freezing point of water Boiling point of carbon dioxide at t.p. H 2 O ( (170) Bignell and Bean 1988 MPa) Useful low-melting metals Triple point of gallium i (1) f (See Bedford et al. 1996; Ambrose and Crovini 1987) Triple point of gallium i,j Triple point of indium j Freezing point of indium j (3) f Freezing point of tin j (5) f Freezing point of bismuth j Freezing point of cadmium j Freezing point of lead j a The equilibrium states in this table are for a pressure p ref = Pa (one standard atmosphere), except for the triple points. The defining points of the ITS-90 are shown in italics. For these points, the references are simply a representative subset of the available literature see Sect. 2 are related references for more recent information b All temperature values are given in ITS-90, and are mostly taken from Bedford et al. (1996), directly from the scale definition for the defining fixed points, and by applying the differences in Table A.6 to the IPTS-68 values for the others, whose accuracy becomes, consequently, limited in general to three decimal figures c The indicated uncertainty is, where possible, the standard deviation of the consensus values see Bedford et al. (1984, 1996) for details in the uncertainty evaluation. Otherwise, uncertainties are best estimates based upon the information available in the references and upon the agreement between results of comparable experiments. For the points that are not defining points of the ITS-90 below 273 K and are relatively distant from a defining fixed point, the largest contributor to the uncertainty is non-uniqueness of the IPTS-68 (note, not of the ITS-90), which has not been suppressed by the temperature recalculation used here (see above, note b). Only direct re-determinations in ITS-90 will allow reducing this uncertainty d The minimum purity of the material to which the listed values of temperature and uncertainty apply is given in percent by volume when the material is liquid or gaseous at 0 C and Pa, and in percent by weight when the material is solid at 0 C and Pa (except for mercury) e These values are for neon with an isotopic composition close to that specified in BIPM (1990) f The inherent accuracy of several triple points is better than indicated. One of the chief contributors to the tabular uncertainties is the nonuniqueness of the IPTS-68 (see above, note c). In the inter-comparison of cryogenic triple-point cells (Pavese et al. 1984), where it was possible to exclude the non-uniqueness component, nor the effect of isotopic composition variability in H 2 and Ne was taken into account. It was found that a group of each of hydrogen, neon, nitrogen, argon and methane triple-point realizations of various manufactures agreed to within ±0.3 mk, ±0.20 mk, ± 0.15 mk, ± 015 mk and ± 0.3 mk, respectively. This reproducibility value, when better, is reported in round brackets. Insquare brackets is the estimated thermodynamic standard uncertainty (BIPM 1990) of the ITS-90 defining points. For methane, the T 90 value was obtained from T 68,Ar the IPTS-68 definition using argon triple point, since it was found that [T 68,Ar (CH 4 ) T 68,O2 (CH 4 )] = 0.7 ± 0.7 mk (Pavese et al. 1984) Parenthetic reference provides more information but appears to relate to the same experiment as described in the non-parenthetic reference h For possible problems with oxygen purity, see Appendix C i Measured temperatures were based upon samples ranging from to % in purity and were adjusted to the equivalent of purity % j The effect of pressure on these freezing points is the following (see Table 2.7 for the same effect on substances below K): Substance a dt/dp (10 8 KPa 1 ) b dt/dh L (10 8 mk m 1 ) Gallium Indium Tin Bismuth Cadmium Lead Italics denotes defining ITS-90 fixed points a Equivalent to (mk bar 1 ) b h L depth of condensed phases k Its reproducibility is limited by isotope composition and distillation effects

18 Appendix B List of Temperature and Pressure Fixed Points 513 Table B.2 Second-quality temperature fixed points Equilibrium state a T 90 /K b Uncertainty Purity of References i (mk) c material (%) d Triple point of normal hydrogen Ancsin 1977 Boiling point of normal hydrogen Ancsin 1977 α β transition point of solid oxygen Pavese and Ferri 1982; Ancsin 1975; Kemp and Pickup 1972; Orlova 1962; Muijlwijk et al Boiling point of natural neon e Ancsin 1978 α β transition point of solid nitrogen Kemp and Kemp 1979a β γ transition point of solid oxygen Pavese and Ferri 1982; Ancsin 1975; Kemp and Pickup 1972; Orlova 1962; Muijlwijk et al. 1969; Cowan et al Boiling point of oxygen Ancsin 1974b; Compton and Ward 1976 Triple point of krypton Seifert 1983; Inaba and Mitsui 1978 Sublimation point of carbon dioxide Barber 1966 Low-melting non-gaseous substances Triple point of bromobenzene f (see Bedford et al. 1984; Ambrose and Crovini 1987) Triple point of phenoxybenzene g (diphenyl ether) Triple point of succinonitrile Freezing point of sodium Triple point of benzoic acid Triple point of benzoic acid h a The equilibrium states in this table are for a pressure p ref = Pa (one standard atmosphere), except for the triple points. The defining points of the ITS-90 are shown in italics. For these points, the references are simply a representative subset of the available literature see Sect. 2 and related references for more recent information b All temperature values are given in ITS-90, and are mostly taken from Bedford et al. (1996), directly from the scale definition for the defining fixed points, and by applying the differences in Table A.6 to the IPTS-68 values for the others, whose accuracy becomes, consequently, limited in general to three decimal figures c The indicated uncertainty is, where possible, the standard deviation of the consensus values see Bedford et al. (1984, 1996) for details in the uncertainty evaluation. Otherwise, uncertainties are best estimates based upon the information available in the references and upon the agreement between results of comparable experiments. For the points that are not defining points of the ITS-90 below 273 K and are relatively distant from a defining fixed point, the largest contributor to the uncertainty is non-uniqueness of the IPTS-68 (note, not of the ITS-90), which has not been suppressed by the temperature recalculation used here (see note b ). Only direct re-determinations in ITS-90 will allow reducing this uncertainty d The minimum purity of the material to which the listed values of temperature and uncertainty apply is given in percent by volume when the material is liquid or gaseous at 0 C and Pa, and in percent by weight when the material is solid at 0 C and Pa (except for mercury) e These values are for neon with an isotopic composition close to that specified in BIPM (1990b) f The published value has been lowered 2 mk to obtain the temperature corresponding to the liquidus point (1/F = 1) g The listed temperature is estimated to be the triple-point temperature of the ideally pure substance. In practice it is difficult to achieve a purity higher than %, for which the triple-point temperature is ( ± 0.002) K h Freezing point given is the value under one atmosphere of dry air. Different values are obtained under an atmosphere of nitrogen or oxygen i Parenthetic reference provides more information but appears to relate to the same experiment as described in the non-parenthetic reference

19 514 Appendix B List of Temperature and Pressure Fixed Points Table B.3 Possible useful points deserving further studies a Equilibrium state T 90 /K Aimed References (p/kpa) uncertainty δt (mk) (δp/pa) α β transition point of solid methane Pavese and Ferri 1982 Triple point of propane Pavese and Besley 1981b; Goodwin 1977 Triple point of ethane Pavese 1978a; Straty and Tsumura 1976; Ziegler et al. 1964b Boiling point of methane Pavese et al. 1975b; Pavese and Ferri 1982 Boiling point of krypton Ziegler et al. 1964a; Lovejoy 1963 Boiling point of xenon Ancsin 1988b Triple point of sulfur exafluoride Schumb 1947 (225.05) ( b ) a For a far more complete list of secondary fixed points useful in chemistry (with values in IPTS-68) see (Staveley et al. 1981) b Unknown

20 Appendix C Reference Data on Gases In the first part of Appendix C, the sensitivity coefficient of the triple point temperature to chemical impurities are reported, together with the results of examples of correction of this effect using different methods illustrated in Sect. 2.2 and of the resulting increase of uncertainty. In the second part, the data sheets of a number of gases are collected. Temperatures are given in ITS-90, except when differently noted in the vapor-pressure tables (for the reason, see Note b in Appendix D, Table D.2). When T 68 or T 48 have been used, the linear term of the original vapor-pressure equation (given in Appendix D) has been adjusted so as the equation matches the numerical value of T 90 at the joining temperature (generally the t.p. or the n.b.p. temperature). The conversion of T 68 or T 48 to T 90 can be found in Appendix A, and Note 3 to Table A.6. Vapor pressure equations in T 90 can be found in Appendix D (Tables C.1.1, C.1.2). F. Pavese, G. Molinar Min Beciet, Modern Gas-Based Temperature 515 and Pressure Measurements, International Cryogenics Monograph Series, DOI / , Springer Science+Business Media New York 2013

21 516 Appendix C Reference Data on Gases Part C.1 Effect and Correction of Chemical Impurities Table C.1.1 Effect on Ttp per amount of substance fraction of various gaseous chemical impurities on the indicated pure substances (in italics are the principal impurities) see Sect. 2.2: initial liquidus-line slopes sl = dtliq/dci (in parentheses the initial solidus line slopes ss) and uncertainties u(dtliq/dci)inμk ppm 1 ; distribution coefficients k0 and their estimated uncertainties Chemical impurity e-hydrogen Neon Oxygen Argon sl (ss) k0 sl (ss) k0 sl (ss) k0 sl (ss) k0 He 11(2) (ss n.a.) 0.21(14) None +1.5(0.5) a (ss n.a.) 1.03(1) n.a. H2 7 ± n.a. None 3 c (ss n.a.) 0.53(20) Ne 2(0.5) 1(0.5) a None (ss n.a.) 0.86(4) (ss n.a.) 0.98(1) O2 None b n.a. 22(3) a ( 35) (5) N2 None b 6.6(0.5) a,c ( 21) d 0.47(13) 22(3) a ( 35) d 0.60(4) 22(3) a ( 50) d 0.52(4) Ar n.a. None +12(3) a (sl = ss) 1.23(5) CO None n.a. 24(4) a ( 50) 0.50(5) F2 n.a. 10(2) ( much larger ) 0.80(4) CH4 < 30 (ss n.a.) 0.45(18) 25(5) a ( 80) 0.42(5) Kr 5(1) a ( 9) d 0.92(2) +5(3) a (sl = ss) 1.11(5) Xe 8(2) ( 30) d 0.85(4) 6(2) (ss n.a.) 0.88(4) Notes: The entries in italics indicate the main chemical impurities All sl (ss) are from Pavese (2009), except for N2 in Ne that is from Pavese et al. (2012b). All k0 are from White et al. (2009): for F2 in Ar and Xe in O2, the reported liquidus slopes and solidus slopes are not consistent with each other; for Ar in O2 the value of k0 is not consistent with experimental data n.a. no data available a Estimated only from thermal metrology studies b Estimated from solubility data c Both H 2 and N2 impurities can easily removed today to much less than 10 6 amount of substance fraction with the use of a zirconium-getter based commercial filters d s S provided with no uncertainty estimate, to qualitatively evaluate from (sl ss) the value of k0

22 Part C.1 Effect and Correction of Chemical Impurities 517 Table C.1.2 Simulations of the effect of correcting or not correcting for chemical-impurity bias b in overall triple-point temperature determinations. (Δ, Uimp, Utot, Uobs in μk). (From Pavese et al. 2011a) (a) Using methods determining a correction Δ with uncertainty U Δ (expanded uncertainty, k 2).

23 518 Appendix C Reference Data on Gases Table C.1.2 (continued) (b) Using methods not performing a correction Δ with uncertainty U Δ (expanded uncertainty, k 2).

24 Part C.1 Effect and Correction of Chemical Impurities 519 Table C.1.2 (continued) The main chemical impurities are listed and quantified. n.s. = not suitable approach. See Sect. 2.2, Table 2.4a for the approach definitions. See Table C.1.1 for the values of dtliq/dxi and u(dtliq/dxi) of each chemical impurity. Correction Δ = b. n.a. correction not applied a Kf = first cryoscopic constant (values from Pavese 2009). b Total nominal chemical purity. c x = xi, total chemical impurities in amount of substance concentrations. d u(x) = (u(x i)(dtliq/dxi)), in μk, sensitivities from Table C.1.1. e Impurities with no effect on T tp. f Uimp = contribution of chemical impurities only; Utot = by also adding Uobs = U(yobs) in quadrature. g Forced to zero. h Not applicable (see Table 2.4) since U(y obs) <Δ. Other Notes: same as in Table C.1.2(a) above.

25 520 Appendix C Reference Data on Gases Part C.2 Data Sheets of Gases 3-Helium 3 He, Relative Molecular Mass: Critical point parameters T c /K = p c /MPa = ρ c /kg m 3 = 41.3 Vapor properties (see note) ρ v,nbp /kg m 3 c p,v (2 K, 1 bar)/j K 1 mol 1 ρ v,tp /kg m 3 n.a. λ v (2 K, 1 bar)/j K 1 m 1 s w v (3.34 K, 0 Pa)/m s η v (25 C, 1 bar)/10 3 Pa s Liquid properties ρ L,nbp /kg L vap H m,tp /kj mol 1 n.a. ρ L,tp /kg L 1 n.a. c s,l (2 K)/J K 1 mol T nbp /K λ L,nbp /J K 1 m 1 s vap H m,nbp /kj mol 1 30 η L,nbp /10 3 Pa s 6.0 Liquid-vapor pressures (ITS-90; BIPM 1990) dp 1 dp dp 1 dp dp 1 dp T 90 p (kpa) T dt p dt 90 p T dt p dt 90 p (kpa) dt p dt (K) (kpa K 1 ) (%) (K) (kpa) (kpa K 1 ) (%) (K) (kpa K 1 ) (%) Notes and Warnings The use of 3 He is only considered at low temperatures. Therefore here only the some properties of the vapor (i.e., below the critical point) will be indicated. For use of 3 He as a gas in gas thermometry see Chap. 3.

26 Part C.2 Data Sheets of Gases Helium 4 He, Relative Molecular Mass: Critical point parameters T c /K = p c /MPa = ρ c /kg m 3 = Gas properties ρ(300 K, 1 bar)/kg m w g (3.8 K, 0 Pa)/m s ρ(0 C, 1 bar)/kg m c p,g (0 C, 1 bar)/j K 1 mol ρ g,nbp /kg m λ g (0 C, 1 bar)/j K 1 m 1 s ρ g,tp /kg m 3 n.a. η g (25 C, 1 bar)/10 6 Pa s 19.6 Liquid properties ρ L,nbp /kg L vap H m,tp /kj mol 1 n.a. ρ L,tp /kg L 1 n.a. c s,l,nbp /J K 1 mol 1 18 T nbp /K λ L,nbp /J K 1 m 1 s vap H m,nbp /kj mol η L,nbp /10 6 Pa s 3.6 Superfluid properties T λ /K ρ g,λ /kg m p λ /kpa ρ L,λ /kg L Liquid-vapor pressures (ITS-90; BIPM 1990b) dp 1 dp dp 1 dp dp 1 dp T 90 p (kpa) T dt p dt 90 p T dt p dt 90 p (kpa) dt p dt (K) (kpa K 1 ) (%) (K) (kpa) (kpa K 1 ) (%) (K) (kpa K 1 ) (%) Notes and Warnings Thermometric measurements below the λ point are quite specialized.

27 522 Appendix C Reference Data on Gases e-hydrogen H 2, Relative Molecular Mass: (Natural) Critical point parameters T c /K = p c /MPa = ρ c /kg m 3 = n.a. (20.3 K e-h 2 ) T c /K = p c /MPa = ρ c /kg m 3 = (n-h 2 ) ρ c /kg m 3 = 30.6 (e-h 2 ) Gas properties (for n-h 2 : c(o-h 2 ) = 0.749) ρ(300 K, 1 bar)/kg m w g (0 C, 1 bar)/m s ρ(0 C, 1 bar)/kg m c p,g (25 C, 1 bar)/j K 1 mol ρ g,nbp /kg m λ g (0 C, 1 bar)/j K 1 m 1 s ρ g,tp /kg m η g (25 C, 1 bar)/10 6 Pa s 8.9 Liquid properties ρ L,nbp /kg L vap H m,tp /kj mol ρ L,tp /kg L c s,l,nbp /J K 1 mol T nbp /K[c(o-H 2 ) = ] λ L,nbp /J K 1 m 1 s vap H m,nbp /kj mol η L,nbp /10 6 Pa s 13.3 Solid properties ρ s,tp /kg L fus H m,tp /kj mol T tp /K [c(o-h 2 )= ] sub H m,tp /kj mol p tp /kpa 7.03 c t,s,tp /J K 1 mol (dt tp /dp) mc /10 8 KPa 1 34 λ s,tp /J K 1 m 1 s Liquid-vapor and solid-vapor pressures (Pavese 1991: K; BIPM 1983: K; Van Itterbeek et al. 1964) dp 1 dp dp 1 dp dp 1 dp T 90 p (kpa) T dt p dt 68 p T dt p dt 68 p (kpa) dt p dt (K) (kpa K 1 ) (%) (K) (kpa) (kpa K 1 ) (%) (K) (kpa K 1 ) (%) , For ortho-para composition, see Table 2.6 Effect of impurities on T tp,(δt S, δt L )/μk ppm 1 ( =not available) D2: +(5.5, 3.5); HD: +(3.0, 2.5); Ne: (, 2), eutectic point at T = x(ne) = He: (, 11) (on freezing curve mK/MPa = < 0.01mK at t.p.) O 2,N 2 : none.