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FUNDAMENTALS OF THERMOMETRY PART by Henry 1: THE E. I Sostmann ABSOLUTE, OR THERMODYNAMIC KELVIN, TEMPERATURE Temperature is a measure of the hotness of something. be rational (and useful between people), there must scale of numerical values (the most familiar of which Centigrade Scale), and on devices for interpolating temperature scale with a real Kelvin Temperature and Second laws of SCALE For a measure to be agreement on a is the Celsius or between the defining VdUfZS. The only namic First absolute is linear establish TKTS, Zero, by its as Scale (TKTS), Thermodynamics. or zero Kelvin, or definition, only one slope. That reference 273.15K, or basis in nature which can The low OK (without nonzero point is the Thermody- be deduced limit of the from the TKTS is the * mark), and since it reference point is needed to was chosen, in the original 0-C. O’C is a temperature with which we all have a common experience. It is the temperature at which water freezes, or, coming from the other side, ice melts; at which water exists under ideal conditions as both a liquid and a solid under atmospheric pressure. In 1954 the reference point was changed to a much more precisely reproducible point, O.Ol’C. This is known as the triple point of water, and is the temperature at which water exists simultaneously as a liquid and a solid under its own vapor pressure. The triple point of water will be the subject. of extended discussion important in a later reference article in this series point in thermometry. The unit of temperature temperature interval K, and ‘C or K (the indicate a temperature 1K or l’C, but the of articles. It is the most of the TKTS is the kelvin, abbreviated “K”. The ‘C is identically equal to the temperature interval latter without the ’ symbol) may be used also to interval. The difference between 1’C and 2-C is temperature 1-C = the temperature 274.15K. Measurements of temperature employing the TKTS directly are hardly suitable for practicable thermometry. Most easily used thermometers are not based on functions of the First and Second Laws. The practicable thermometers that will be discussed later in this series of articles depend upon some function that is a repeatable and single-valued analog of, or consequence of, temperature, and they are used as devices of utilitarian temperature scales (such as the Temperature Scale) which are themselves artifacts. The main the realisation of the TKTS is to establish relationships Thermodynamic Scale of nature and the practical thermometers of the laboratory or of industry, so that made by non-thermodynamic means can be translated into TKTS, and rational temperature scales can be constructed related to real&able physical phenomena. There points. two or ture is exist in nature a number These are physical states three of the three possible constant. of in what which phases interpolation International purpose between for the scales and measurements terms of the on a basis are called thermometric some pure material simultaneously, and fixed exists in tempera- A two-phase equilibrium is represented by the earlier example of the freezing point of water, or, more properly, the coexistence of liquid and solid water. For this equilibrium to represent a constant temperature, O’C, pressure must be specified, and the specification is a pressure of 1 standard atmosphere, 10 1325 Pascal. (A two-phase fixed point at 1 standard atmosphere is called the “normal” point). The variation due to pressure from the defined temperature of a liquid-solid equilibrium is not large (which is not to say that it may not be significant). The freezing point of water is reduced approximately O.OlK for an increase of pressure of 1 atmosphere. The variation due to pressure for a liquidvapor equilibrium is relatively very large. A three-phase equilibrium is represented by the triple point the coexistence of liquid and solid water under its own vapor at 0.Ol.C. Because all three possible phases are determined physical state, it is generally possible to realise a triple point curately than a two-phase point. This may be seen from the Phase Rule of water, pressure, by the more ac- of Gibbs: P-C-2=F where P is an integer equal to the number of phases present, C is the number of kinds of molecule present (for an ideally pure material, C = 1) and F is an integer giving the number of degrees of freedom. Obviously, for the two-phase equilibrium there is one degree of freedom, pressure, and for the three-phase equilibrium F = 0; that is, the temperature is independent of any other factor. Fig.1 illustrates one, two and three-phase equilibria. la 2a P=l C=l F=3 3a P=2 C=l F=2 P=3 C=l F=O Fig. 1: The Phase Rule of Gibbs. P = the number of phases C = the number of components (1 for a pure material); degrees of freedom. la is uncontrolled. lb is a melt point. Ic is a triple point. A typical since the (or rather device for realizing the TKTS is vapor pressure of an ideal gas a statistical mechanical function, same thing). The to be the change transfer function in pressure of A rudimentary gas illustrated by using low the temperature Celsius Scale. the helium gas thermometer, is a thermodynamic function which for the purpose is the of a gas a gas kept change in volume of a gas kept at constant to measure accurately change in pressure in volume, constant-volume gas thermometers than constant-pressure gas thermometers. present; F q the or freeze thermometer at constant may be volume, chosen or the pressure. Since it is easier than it is to measure change are more common in use thermometer is shown in it to show that the zero of the normal freezing Fig 2. Its operation will of the TKTS is 273.15K point of water, 0’ on be bethe Fig. 2 shows a cylindrical bulb of constant volume, connected by tubing defined as constant-volume, to a U-tube manometer. A second connection to the manometer leads to a reservoir of mercury, which contains a plunger, P, by means of which the column height of the manometer may be varied. The constant-volume bulb and tubing contain an ideal gas. 4 The bulb is first surrounded by an equilibrium mixture of ice and water (C, in Fig 2a). When the gas is in thermal equilibrium with the slurry in the bath, the pressure of the gas is adjusted by moving the plunger so that both columns of mercury in the U-tube are at the same height, corresponding to an index mark 1. 2a 2b Fig.2: A rudimentary gas thermometer. B = mercury, C = water t ice (O-C), (100’(Z), P = a plunger for adjusting A = helium gas. D = water t steam mercury level. Next, the ice bath is removed and replaced with a bath containing boiling water, or more correctly, an equilibrium mixture of liquid and vapor water at a pressure of 1 standard atmosphere, (D, in Fig 2b). As the manometric gas is heated by the boiling water it expands, and the mercury in the manometer is displaced. The plunger is actuated to reposition the surface of the mercury in the left leg at the index mark 1, restoring the criterion of constant volume in the closed gas system, a condition shown in Fig 2b. However the mercury in the right, open leg is not now at the index mark 1, but measurably higher. In fact, the difference in heights indicates that the pressure of the enclosed gas at the boiling point is 1.366099 times the pressure at the freezing point. We can then calculate: (100-c - O’C)/(1.366099 - I) = 273.15 Eq.2 5 and from pressure reduced zero this we can understand ratio change between by 273.15 Celsius or is Scale reached is which therefore T = t is the 273.15K, zero TKTS. The zero of the gas constant volume the TKTS and t is temperature interval and the zero to the properties of thermometer measurements on the Celsius of the TKTS have any specific sub- can be expressed P2 where the Ts are Scale, and the TOs = 01 - To) / (‘5 - To) temperatures are the relationship assumes the gas thermometer or the volume of the on zero of Eq.4 the that TKTS, the natural temperature Scale. an ideal gas. The reader reflects Charles’ or Boyle’s gas, respectively, be held will have law, if constant. gas is a gas whose behavior can be predicted exactly from Charles’ Law, which obeys it through all ranges of temperature sure, and where the relationship between concentration (n/V), temperature and (n/V)(T/P) absolute = I/R commonly written pressure observed the presAn ideal Boyle’s or or presabsolute is Eq.5 = a constant as Eq.6 PV = nRT where R is the gas constant, identical for all ideal gases. and is known to about 30ppm. A second condition is that thus the internal energy, intermolecular forces acting, depend on the molecular distances, and (6E Unfortunately is a large / in equation PI / more Celsius Eq.3 All This that sure the + 273.15 on the temperature reference of of as l/273.15 of the if temperature is O’C, an absolute and where T is temperature Scale. Note that the been defined without stance. terms the Celsius degree O’C and 1OO’C. Thus kelvin intervals below 6V)T R = 0.082053, there be no V, does not Eq.7 = 0 there number. is no real ideal gas, Helium comes closest, and the carbon uncertainty dioxide of varies 30ppm most 6 widely sures possible (or the from ideality. are reduced, to measure change However real reflecting the change in volume of gases a in approach reduction pressure a gas at ideality in density. a gas of zero volume) as at the their Since zero pres- it is not pressure requirement for an ideal gas is approached by making a number of measurements at a number of pressures and extrapolating to zero pressure. Such a system of measurements is shown in Fig. 3. Regardless of the nature of the gas, all gas thermometers at the same temperature approach the same reading as the pressure of the gas approaches zero. 374.0 - Fig3: Pressure pressures at Several authors ratios of various the condensation have proposed gases at various point of steam. modifications count for the non-ideality of real gases. of Clausius, is the virial equation, which of the density of the gas, and is written: PV = nRT(1 where the nB, + --” coefficients etc., volume virial given temperature. mometry, it is coefficient. The departure accurate gas n2Cv + ---“2 B, n3Dv + ---“3 C, D, etc., from the ideal One which is a series gas are law is much expansion to used, in ac- that terms Eq.8 +...) coefficients, and Over the usual seldom necessary of real gases thermometry. of called the second, third, fourth, are constants for a given gas at a range of gas densities in gas therto go beyond the second virial ideality is only one of the problems of A second is the purely mechanical matter a real connection to convey the pressure ter. It is inconvenient to locate the bulb thermostatted enclosures, 2 to illustrate enclosure, and a common of dead space. There from the bulb to the and the manometer in practice each carefully thermostatted. this configuration. Fig. Fig.4: Thermostatted gas thermometer. meter and the gas bulb are separately temperature; the (long, perhaps many is not. The length, price which paid is that goes through whose temperature and compromise. is The there the is a capillary wall of each essentially bulb volume is 4 is to use two must be manomethe same separate a modification of Fig. The U-tube manokept at constant meters) capillary tube, generally of of the two thermostats uncontrolled. The solutions can be made as large The temperature distribution as some and are care possible along the relative to the capillary volume. capillary length can be measured at suitable intervals. The capillary volume can be kept small by providing a capillary of small diameter, but not so small as to introduce thermomolecular pressures where the tube a correction for passes through a temperature gradient, or , conversely, thermomolecular pressure can be made. 8 A third obvious problem is that als of construction. An that only the contained ality known correction in the system, A fifth relates or impurities required is including that to the remaining the thermal ideal constant-volume gas is subject to the whole system is subject or estimated, and for which A fourth gas of effects from to for gas thermal temperature correction the of expansion changes, which must be made. gas of sorption, a less than the head column in which ideally materi- thermometer assumes expansion, while in re- hydrostatic the of must pressure of be the itself. impurities in clean system, the are gas, ab- sorbed on the walls of the bulb and other parts of the thermometer system at the reference temperature, desorbed at a higher temperature, with the effect of elevating the measured gas pressure, and then reabsorbed as the temperature approaches the references temperature. Attention to the elimination of sorption has resulted in gas thermometry measurement Gas of the thermometry menters ner and normal has for some Edsinger, boiling claimed generations, followed the point of attention the most by Schooley, dards. This work forms much of the Practical Temperature Scale of 1968 Scale of 1990, in an effort to more water of as a 99.975-C! number recent of whom at the National thrust to replace with the International closely approximate temperatures in a practicable Scale. A concise mometer and gas thermometry at the NBS is should be consulted by anyone interested Schooley provides an example of the accuracy of fine experi- have been GuildBureau of Stanthe International Temperature thermodynamic account of the gas therand given by Schooley, in experimental elegance. and precision of this work: Fixed Steam point Gas therm IPTS-68 Uncertainty IC IC 3 pt 99.975 231.924 419.514 231.9681 419.58 Tin pt Zinc pt 100.000 M.005 f0.015 io.03 With the conclusion of work in preparation for ITS-90, is considered to be a finished matter at the NBS. The itself, which should have been preserved as a national ment, is now in the process of dismemberment. As a generality, namic values methods have of gas the been thermometry thermometric used largely has led the fixed points, to check its gas thermometry gas thermometer shrine or monu- development of and a variety accuracy and thermodyof other consistency. 9 These include noise portion thermometry of the range 2: THE INTERNATIONAL On October accepted for a Practical cession acoustic 5, thermometry, and of the OF International in place as the tr,O/‘C = TgO/K temperatures - are thermometry, appropriate to a (ITS-90) on Weights Committee and on Measures Thermometry to replace the International had replaced, in turn, a suc1927, etc. The official text of from the official the first quarter international As in previous “practical” used in the title of the fined as each Committee the ITS-90, in English translation lished in Metrologia, probably in and 1990 a recommendation of its Consultative new “practical” temperature scale, Temperature Scale of 1968, which of previous Scales, those of 1948, officially gas radiation thermometry, the temperature Scale. SCALE 1989, dielectric-constant legal of Scale as Scales (although the new Scale) the relationship French, 1990. of word will The be pubITS-90 is 1 January, 1990. “practical” to the TKTS is is not de- 273.15 defined in terms of the equilibrium states of pure substances (defining~ fixed points), interpolating instruments, and equations which relate the measured property to T(90). The defining fixed points and the values assigned to them are listed in Table 1, and the values which were assigned on IPTS(68) are listed also, for comparison. It is to be remembered that, while the Scale values assigned to a fixed point may have been changed, the fixed point has the identical hotness it always Several had. deep From cryogenic 0.65K ranges to 5.OK are using provided. a These helium vapor are: pressure interpolation device From 3.OK to the triple volume gas thermometer point of neon From point of neon 4.2K to the triple (24.5561K) with 4He using as the a constant- thermometric gas From 3.OK thermometric to the gas triple point of neon with 3He or 4He as the 10 These ranges cialists, and thermometer from 13.8033K of subranges. slightly The are probably of interest to only a limited number of spewill not be dealt with in detail in this paper. The resistance portion of the Scale is divided into two major ranges, one to 0-C and the other from O’C to 961,68’C, with a number There below Scale to is ranges are The interpolations platinum resistance the resistance a change O’C, and one range O’C, summarised the triple in which embraces specifically Table from 273.15K, be strain of these the as the ratios of the (PRTs) at temperatures point of water; that definition of IPTS(68) (gallium melt W(234.3156K) L 0.844235 (mercury triple WT(90) - where WT(90) the reference use to W,T(90) is the (silver Z 4.2844 T(90) calculated used be of and point) from of point) the at Eq.12 point freeze resistance Eq.11 point) freezing the made of pure platinum of these requirements if silver must also Eq.13 resistance ratio relation- Eq.14 = dWT(90) is the observed function, and resistance of T(90) is: which L 1.11807 temperature +29.7646-C. Eq.10 W(302.9146K) W(1234.93K) to 2. as denominator. The PRT must free; it is considered a measure two constrains are met: for temperatures -38.8344’ = RT(90)/R(273.16K) and a PRT acceptable meet this requirement: The ship: short above are expressed thermometers at WT(90) third slightly value, dWT(90) W,T(90) is the is the deviation value calculated value of the from spe- cific PRT from the reference function at T(90). (The reference functions represent the characteristics of a fictitious “standard” thermometer; the deviation function represents the difference between that thermometer and an individual real thermometer). The deviation function is obtained by calibration at the specified fixed points, and its mathematical form depends THE upon RANGE the FROM temperature 13.8033k range TO 273.16K of calibration. 11 The reference function for this range is 12 ln[WrT(90)] = A, where the If PRT the + K Ai{[ln(T(90)/273.16K)+1.5]/1.5)i i=l values is to of A, and Ai be calibrated are given over 83.8058K not to (-189.3442-C), triple the entire or include details, the primary the in the it must be calibrated at specified fixed tures determined by vapor pressure mometers will most likely be calibrated and this paper will of general interest Kq.15 of The deviation function dW = aCW(T(90)) THE RANGE FROM For the freezing range point WrT(90) = C, and coefficients the I] 0-C TO from O’C of silver, - dWT(90) + c[WT(90) - II3 two temperaSuch therLaboratories, that the laboratory subranges begin at requires calibration at the triple point of mercury (obtain the coefficients a and Eq.16 the over this entire range must be calibrated at and the freezing points of tin, zinc, aluminum a, b and c are derived from the tin, zinc the and and - the freezing function is: Ci are 11 + b[WT(90) + dCWt(90) point 754.15)/4811i specified and the reference measurements function is - 13.8033K, to Co and = a[WT(90) to argon. lllnW(T(90)) to 961.78-C, the reference 9 + I: Ci [(T(90)/K i=l temperature deviation down 961.76.C aluminum calibrations respectively, the deviation of WT(90) from the silver. For d = 0. The Scale. is: + blW(T(90)) The PRT to be used triple point of water silver. The coefficients the and also at thermometry. by National but assume calibration point of range, points gas only The subrange from -189.3442’ to 273.16-C triple point of argon (-189.3442’C), the 38.8344-C) and the triple point of water to b. text below - of water Eq.17 in the coefficient value at the II2 - W(933.473KE2 text of the Scale. d is derived from the freezing point of freezing point Eq. 18 of silver, 12 PRTs may be terminating ranges of calibrated over the at the freezing points Eq. 18, the equation is jJoner whole range For the dT(90) For still limit the indium, freezing range from calibrations point of dWT(90) the are indium. range from calibrations the are equation is as range from the - a most useful calibrations are gallium melting dT(90) = aCHT(90) However the portion 0-c. For of a relatively - - Scale of water the to water triple function II2 point shorter the freezing point and Eq.19 of water the triple function to the freezing point is: of point water and Eq.20 except for triple point range for function O’C, must and the the “Realising the melting and the point of deviation coefficients. of mercury to near-environmental and water equation is the melting point thermometry triple points and of the Eq.21 112 be calculated from Eq.17 polynomial approximation to +600-C, accurate -200’ thermometer range from 1.5mK below, see the article Isotech Journal. of Eq.20 triple point of water to required at these points, below the is: 11 11 + bCWT(90) simple point at the deviation required at the mercury point, and the deviation reference the triple required at The reference - same the triple For the gallium, For the gallium from are required and tin. The 11 + bCWT(90) = a[WT(90) the For ranges d=O c=d=O shorter range shorter Coefficient tin, calibrations points of indium = aCWT(90) for of aluminum or zinc. truncated as follows: Aluminum Zinc point of freezing or the ITS(90)” for from the over to 1mK in this Eq.15 portion for the above the resistance above O’C and issue of the 13 The temperature radiation is: range above thermometer as L X(TYD)/LX(TYO(X) the freezing interpolating = (expCc2/ L X(T90) and XT90(X)] LX(TSO(X)) ance of a blackbody TSO(X) may be the 0.014388 m’K. at silver 3: THE OF 1990 VALUE The National The change international representations was made standard of not insignificant various national resistors following Germany: are 1) - 1) employs the a relationship Eq.22 OHM of the because resistance, differences laboratories, which were adjustments - and silver the spectral concentrations of radix in vacuum at TSO and at TSO(X). gold point or the copper point. C2 = wavelength point, the THE of instrument, /(eXP[C2/hT901 where point standard also the quantum Hall permits correction in the value due to drift kept as were made ohm effect, of the assigned to over years National standards by England, the change of United in 1990. the slight new but the ohm by the of the standard The resistance. States and West NPL (England) increased the value of their ohm by t1.61 ppm. Thus a perfectly stable 1 ohm resistor calibrated at NPL prior to January 1, 1990, has a new value of 0.99999839 ohm. A 10 ohm resistor has a new value of 9.9999839 ohm. 1Q (NPL 1Q (NPL NIST ppm. 1990, value 90) 89) (United A drift-free has a new of 1Q (NBS 89) ppm. 1990, value of 9.9999944 increased 89) SO) the value of at NIST A 10 ohm their ohm prior to resistor by +I.69 January 1, has a new ohm. so) PTB (West A drift-free has a new States) (NPL (NPL 1 ohm resistor calibrated value of 0.99999831 ohm. 9.9999831 1~ (NIST = 1.00000161Q = 0.99999839Q = 1.00000169s2 = 0.99999831Q (NBS (NIST 89) 90) Germany) increased the 1 ohm resistor calibrated value of 0.99999944 ohm. ohm. value of their ohm by to.56 at PTB prior to January 1, A 10 ohm resistor has a new 14 90) = 1.00000056 Q (PTB 89) 89) = 0.999999944 Q (PTB 90) 1~ (PTB 1Q (PTB Other laboratories adjusted the ohm (a decrease); France, +O.?lppm; BIPM, The effects mometer on the calibration calibrated (for example follows: t(89) 0-c 650-C where d(Q) and d(t) is by 25.5249052) is the decrease the increase in = Ro 1 1 t a(tl a and 13 are given is = 24.994-C The change in thermometry. It ence temperature the value is unlikely for the 13 term can platinum typical (f or 90 Q (USSR) resistance resistance example -0.15ppm value d(t) 25.52486 -0.00004 to.000393 85.28828 -0.00014 +0.001705 standards but real at 85.28842~) d(Q) in resistance measured hotness represented by ther- for the O’C are as the same hotness same resistance. as maintained in most resistance dependance therupon as (t68) the a 650-C resistance have a small The value of resistance tinue to be. However 25-C at 25.52490 85.28842 written of and VNIIM a standard with NIST temperature, (values resistor). 1989, NBS 89 Q In addition, practicable mometry laboratories Rl in of as follows: tL92ppm. be to) t in 6(tl - to)2l the calibration conventionally reported Eq.23 report at for 25-C, the individual and will con- Eq.24 t(90) of the ohm may be significant that the difference in the value resistor will require consideration. in precision of the referCertainly ignored. ************************************+***%%%%%%%%%%%%%%%%%%%% In our next issue, the fixed points realising them. we and will of discuss in detail the the equipment and physical operations embodiment involved of in TABLE 1 15 FIXED POINTS OF THE IPTS-68 AND OF THE ITS(90) AS ADOPTED BY CIPM, OCTOBER 5 1989 SUBSTANCE STATE CELSIUS TEMP. IPTS-68 e-H2 Trip -259.34 -259.3467 02 Trip -218.789 -218.7916 Ar Trip -189.352 -189.3442 N2 Boil -195.802 -195.794 Hg Trip -38.842 -38.8344 H20 Trip 0.01 Ga Melt 29.772 29.7646 In Freeze 156.634 156.5985 Sn Freeze 231.9681 231.928 Zn Freeze 419.58 419.527 Al Freeze 660.46 660.323 Ag Freeze 961.93 961.78 AU Freeze 1064.43 1064.18 CU Freeze 1084.88 1084.62 CELSIUS TEMP. ITS-90 0.01 Notes: e-H2 represents molecular forms Boiling, Pa. melt hydrogen and freeze in points equilibrium are between at 1 standard the ortho atmosphere and para = 101 325 TABLE 2 16 RANGES OF THE ITS-90 THE PURCHASEROF A CALIBRATION MUST STATE THE RANGE REQUIRED* LOW LIMIT -259.3467 HIGH LIMIT FIXED POINTS REOUIRED 0.01 e-H (TP), e-H2 (VP), ?TP), Ar (TP). (TP). 50 (TP) ‘32 -218.7916 0.01 02 Ne (TP), Hg (TP), Ar (TP). Hg (TP), (TP), b OF’), Hz0 H20 (TP) -189.3442 0.01 Ar 0.01 29.7646 H$ 0.01 156.5985 H20 (TP). Ga (HP). In (FP) 0.01 231.928 H20 (TP’), Ga (HP), Sn (FP) 0.01 419.527 H20 (TP). Sn (FP), Zn (FP) 660.323 H20 (TP), (FP) Sn (FP), 2n (FP), Al 961.78 H20 (TP), Sn (FP), (FP). A8 (FP) Zn (FP), Al Hg (TP). Ga (MP) 0.01 -38.8344 29.7646 (TP), Ga (ME’) H20 (TP). pressure determination, (TP) = triple point. (VP) = a vapor (MP) = melting freezing point at 1 standard atmosphere, standard atmosphere *The purchaser may choose to specify -189.3442’ to +419.527’, for example, -200’ to +500’. example, (TP) point a combination of several or some extrapolation, (FP) at = 1 ranges, for 17 TABLE 3 THE COEFFICIENTS OF THE REFERENCE The values of the coefficients Eq. 15 and 17 FUNCTIONS Ai and Ci of the reference Eq.15 functions of Eq.17 CONSTANT OR COEFFICIENT VALUE CONSTANT OR COEFFICIENT VALUE A0 -2.135 Al A2 3.183 -1.801 247 20 435 97 A3 A4 A5 0.717 0.503 -0.618 -0.053 0..280 272 04 440 27 993 95 323 22 213 62 0.107 -0.293 152 24 028 65 0.044 0.118 -0.052 598 72 686 32 481 34 A6 A? A8 A9 A10 All A12 347 co 29 Cl c2 c3 c4 c5 c6 c7 c8 C¶ 2.781 572 54 1.646 -0.137 -0.006 -0.002 0.005 0.001 -0.002 509 16 143 90 497 67 344 44 118 68 879 82 044 72 -0.000 0.000 461 22 457 24 TABLE 4 VALUES OF W,(t90) AT THE RESISTANCE THERHOUETW FIXED POINTS FIXED POINT Wr(T901 FIXED POINT iJr(T(90) e-H2 (TP) Ne UP) 02 (TP) Ar (TP) Hg (TP) Hz0 (TP) 0.001 0.008 0.091 0.215 0.844 1.000 190 449 718 859 142 000 07 74 04 75 11 00 Ga (MP) In (MP) Sn (FP) Zn (FP) Al (FP) nP (FP) 1.118 1.609 1.892 2.568 3.376 4.286 138 801 797 917 008 420 89 85 68 30 60 53 18 FUNDAMENTALS GAS THERMOMRTRY, THERMCMETRY James F. especially T. J. OF AND Schooley, on gas Quinn, THE 1, REFERENCES THERMODYNAMIC Th-o&y, thermometry Twnpm PART SCALE CRC Press, the NBS at a, Academic Press, London F. Henning, H. Maser, Twnpucatuwn &wag, New York, 3rd edition (1977). German pressure thermometry by W. Thomas THE INTERNATIONAL t&&a Preston-Thomas 06 19 68 TEMPERATURE The (~e:ev-i-&on Raton, and I Metrologia 4oa Poids valuable, Changea .taomotive Teddington, York (1986) (1873) Berlin and on vapor- P.wzc-GcaX Tanpeaduae 12, 1 (1976) tie et IPTS-68 and Mesures, Sevres, but will be revised e Scu& The Iti.awat.Lod TempcauUu/t official text of the new Scale, and it will Metrologia advises that it will be published 1990). 1990 New Springer-Verlag, text; fine section R. E. Bedford, G. Bonnier, H. Maas, F. Pavese, appeoximetlng .#LQ I-tied Temp wt.aauAe BIMP, when published; no projected date is known. unofficial copies of a late draft indicate that this will THE Florida SCALE Ira.tea~od 04 1975 Supp&mentcMy Inbomon Bureau International des publication continues to be date to include ITS-90 Boca 06 be in the EPT-76, France. This at some future Techniquea dolr sceee 04 1990, Our reading of be of great value. 1990 is the title of the published in Metrologia. Vol. 27 No. 1 (February OHM Ln tie Vdue 04 the UK Force and Redistance, England (1989) N. Belecki at Imp&zmenting Ohm, U.S.Department V. Kose, H. WeCteagabe Bundesanstalt al, the Bachmair, &e-w PTB-E-35, NIST Technical New Rep~eaentetLon-6 of Commerce (1989) Neue Re&xence National Note S+and4nda Physical 1263, &.idl.h&Sn, Braunschweig FRG Gu.id.a-f-ines Vo-C-t and 40’~ .the Fe&t.egungen blk Physikalisch-Technische d.-k 04 Iwoti (1989) 06 &&QCLaboratory, .the