Uncertainty Analysis of the Thunder Scientific Model 1200 Two-Pressure Humidity Generator

Transcription

1 Uncertainty Analysis of the hnder cientific Model 100 wo-ressre Hmidity Generator 1.0 Introdction escribed here is the generated hmidity ncertainty analysis, following the Gidelines of NI and NL International [1, 6, 7], for a Model 100 Hmidity Generator that tilizes the NI developed and proven two-pressre hmidity generation principle [, 3]. Generation of hmidity in a system of this type does not reqire direct measrements of the water vapor content of the gas. Rather, the generated hmidity is derived from the measrements of satration and chamber pressres, and satration and chamber temperatres. he measrement instrmentation sed in both or in-hose working standards and or manfactred devices are obtained from companies which have demonstrated either NI traceability or traceability to other acceptable standards. In most cases we therefore se the specifications spplied by these manfactrers as the starting point for or ncertainty statements. Over time, check calibrations against a NI traceable pressre gage and NI traceable standard resistance thermometer, as well as the reslts of an on-going intercomparison program of both the individal components and of the otpts of operating generators, have allowed the determination of the ranges of disagreement among the varios temperatres and pressres that enter into the final determination of the otpt ncertainties. he average vales of these disagreements represent the ncertainties from or in-hose processes and things like instrment drift over time, and these are copled with the ncertainties given by the varios instrment manfactrers to give overall ncertainty statements. his docment lists the varios ncertainty sorces, their magnitdes, and their origins over the operating range of the Model 100 generator..0 efining Eqations NI echnical Note 197 [1] states that the ncertainty in a dependent variable, which depends only on ncorrelated inpt variables, is y y xi 1 i xi Relative Hmidity is defined as the amont of water vapor in a sample compared to the maximm amont possible at the given sample s temperatre and pressre. his can be expressed by the following formla e f, % RH e f, Where the f fnctions are enhancement factors, e is the satration vapor pressre, is the % efficiency of satration,, are the chamber and ew/rost point temperatres, and c is the chamber pressre.

2 he ew/rost point temperatres can be expressed by the following formlas W e f f e,, 3 I e f f e,, 4 Where the f fnctions are enhancement factors, e w is the satration vapor pressre over water, e I is the satration vapor pressre over ice,,, are the ew point, rost point and satration temperatres, and c and s are the chamber and satration pressres. Note that the actal ew/rost point temperatre is defined implicitly and mst be obtained throgh iterative solving. ombining eqation 1 with eqations 3 and 4 we can express Relative Hmidity in the terms of satration and chamber temperatres and satration and chamber pressre only by the following formla f e f e RH,, % 5 By incorporating the relationship in eqation into an ncertainty eqation of the form of eqation 5, it can be shown that the total ncertainty in relative hmidity is given by the expression RH RH RH RH RH RH 6 imilarly incorporating the relationship in eqation into an ncertainty eqation of the form of eqation 3 and 4, the ncertainties in dew point and frost point measrement are 7 and 8

3 3 Uncertainty omponents In the mathematical analysis of eqation 6, 7 and 8, we ll analyze the ncertainties de to each of the above components separately and then combine the ncertainties to obtain the total expanded ncertainty. We are therefore concerned with for basic categories of ncertainty, pressre, temperatre, satrator efficiency and the eqations themselves. Each of these categories may also have associated ncertainty components. In determining components of ncertainty, there are several things to consider, sch as measrement ncertainty, measrement hysteresis, and measrement resoltion. Listed below are the identified major ncertainty contribtors and their components for the Model 100 hmidity generator. Uncertainty contribtion from pressre s and c which incldes Measrement ncertainty Measrement resoltion Measrement hysteresis Uncertainty contribtion from temperatre s and c, which incldes Measrement ncertainty Measrement resoltion elf heating Uncertainty contribtion from Eqations e and f,, which incldes atration Vapor ressre Eqation e Enhancement actor Eqation f, Uncertainty contribtion from percent efficiency of the satrator 3.1 ressre Uncertainty ontribtion he pressre terms, c or s, in a two-pressre hmidity generator are major determining factors. he Model 100 hmidity generator ses one pressre transdcer to measres the chamber pressre and the satration pressre. e to this design many pressre ncertainties are shared between the chamber and satration pressre. Any ncertainty contribted by this single transdcer will simltaneosly affect both the chamber and satration pressre readings. he pressre ncertainty contribtion in terms of relative hmidity can be determined by the partial nmeric differential of the RH eqation with respect to pressre, mltiplied by the ncertainty of the pressre component. he eqation for this becomes RH [component ] e f, e f, [component ] RH [component ] = ressre component ncertainty in terms of percent relative hmidity. [component ] = ressre component ncertainty in terms of pressre. 9

4 he pressre ncertainty contribtion in terms of dew or frost point temperatre can be determined by the partial nmeric differential of the iterative dew or frost point eqation with respect to pressre, mltiplied by the ncertainty of the pressre component. he eqations for these become [component ] e W f, f, e [component ] 10 [component ] e I f, f, e [component ] = ressre component ncertainty in terms of dew point temperatre. = ressre component ncertainty in terms of frost point temperatre. [component ] [component ] 11 [component ] = ressre component ncertainty in terms of pressre ressre Measrement Uncertainty omponent ressre Measrement ncertainty of Model 100 hmidity generator s pressre transdcer is specified as 0.04% of the fll scale. Based on a rectanglar distribtion, the ncertainty component of the pressre measrement is then [measrement] = 155 psia fll scale * 0.04% / 3 = ±0.06 psia / 3 O=infinite 3.1. ressre Resoltion Uncertainty omponent he Model 100 hmidity generator ses an Analog to igital device to translate the pressre transdcer s voltage reading into a digital vale. he Analog to igital conversion process resolves over the range of the pressre transdcer. Based on a rectanglar distribtion of the half-interval of resoltion, the ncertainty component of pressre resoltion is then [resoltion] = 155 psia transdcer range / ^15 * 0.5/ 3 = ± psia / 1 O=infinite ressre Hysteresis Uncertainty omponent ince the Model 100 hmidity generator incorporates only one pressre transdcer in a time-shared approach, the transdcer is sbject to some measrement hysteresis. or arond 99.7% of the time, the transdcer monitors the satration pressre. or less than 0.3% of the time once every 30 mintes for approximately 5 seconds, the transdcer monitors the chamber pressre. By this criterion, it is only the chamber pressre, which is affected by hysteresis and therefore only applied to the chamber pressre component. o determine this ncertainty in terms of relative hmidity we have to isolate only the chamber pressre component. his can be determined by the partial nmeric differential of the RH eqation with respect to only the chamber pressre, mltiplied by the ncertainty of the chamber pressre component. he eqation for this becomes.

5 RH [component ] e f, e f, [component ] 1 RH [component ] = ressre component ncertainty in terms of relative hmidity. = hamber ressre component ncertainty in terms of pressre. [component ] he pressre ncertainty contribtion in terms of dew or frost point temperatre can be determined by the partial nmeric differential of the iterative dew or frost point eqation with respect to chamber pressre, mltiplied by the ncertainty of the chamber pressre component. he eqations for these become [component ] e W f, f, e [component ] 13 [component ] e I f, f, e [component ] 14 [component ] = ressre component ncertainty in terms of dew point temperatre. = ressre component ncertainty in terms of frost point temperatre. [component ] = ressre component ncertainty in terms of pressre. [component ] he maximm amont of hysteresis specified for the Model 100 hmidity generator s pressre transdcer is ±0.04% of the measred difference between the satration and chamber pressres, with a rectanglar distribtion. [hysteresis] = ±{0.04% * s - c } psia / 3 O=infinite

6 egrees of reedom Evalation ressre Uncertainty ontribtion mmary he standard ncertainties, RH, components calclated sing eqation 9 and 1 from the associated individal pressre components previosly shown are smmarized in the following table. Note: he Model 100 hmidity generator is limited to a maximm dew point temperatre of 50. Any vale calclated above this limit is grayed ot of the following table. tandard ressre Uncertainty omponents of RH ±% atration ressre Range psia, hamber pressre = 14.7 psia atration emperatre 94.9 %RH 73.6 %RH 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH escription c Hysteresis Infinity ype B Measrement Infinity ype B Resoltion Infinity ype B 94.9 %RH 73.6 %RH 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH c Hysteresis Infinity ype B Measrement Infinity ype B Resoltion Infinity ype B 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH c Hysteresis Infinity ype B Measrement Infinity ype B Resoltion Infinity ype B able 1

7 egrees of reedom Evalation he standard ncertainties,, components calclated sing eqation 10 and 13 from the associated individal pressre components previosly shown are smmarized in the following table. Note: he Model 100 hmidity generator is limited to a maximm dew point temperatre of 50. Any vale calclated above this limit is grayed ot of the following table. atration emperatre tandard ressre Uncertainty omponents of ew oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia d 5.5 d -0. d -4.0 d -6.9 d -1.0 d d -0. d escription c Hysteresis Infinity ype B Measrement Infinity ype B Resoltion Infinity ype B 34.0 d 9.6 d.7 d 18.1 d 14.6 d 8.6 d 4.5 d -1.1 d c Hysteresis Infinity ype B Measrement Infinity ype B Resoltion Infinity ype B 45.4 d 40.0 d 35.9 d 8.8 d 3.4 d 17.5 d c Hysteresis Infinity ype B Measrement Infinity ype B Resoltion Infinity ype B able

8 egrees of reedom Evalation he standard ncertainties,, components calclated sing eqation 11 and 14 from the associated individal pressre components previosly shown are smmarized in the following table. Note: Any frost point vale that is theoretically not possible is grayed ot of the following table. atration emperatre tandard ressre Uncertainty omponents of rost oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia f -3.6 f -6. f f f f escription c Hysteresis Infinity ype B Measrement Infinity ype B Resoltion Infinity ype B -0.9 f c Hysteresis Infinity ype B Measrement Infinity ype B Resoltion Infinity ype B c Hysteresis Infinity ype B Measrement Infinity ype B Resoltion Infinity ype B able 3 3. emperatre Uncertainty ontribtion he temperatre terms, c or s, in a two-pressre hmidity generator are another major contribtor of ncertainty and are sed mathematically to calclate satration vapor pressres. he Model 100 hmidity generator ses two temperatre probes to measres the chamber temperatre and the satration temperatre. e to this design each temperatre probe contribtes its own ncertainty to the over all system and will be addressed independent of one another atration emperatre Uncertainty ontribtion he satration temperatre ncertainty contribtion in terms of relative hmidity can be determined by the partial nmeric differential of the RH eqation with respect to satration temperatre, mltiplied by the ncertainty of the satration temperatre component. he eqation for this becomes RH [component ] e f, e f, [component ] 15 RH [component ] = at emperatre component ncertainty in terms of percent relative hmidity. = at emperatre component ncertainty in terms of pressre. [component ]

9 he satration temperatre ncertainty contribtion in terms of dew or frost point temperatre can be determined by the partial nmeric differential of the iterative dew or frost point eqation with respect to satration temperatre, mltiplied by the ncertainty of the satration temperatre component. he eqations for these become [component ] e W f, f, e [component ] 16 [component ] e I f, f, e [component ] 17 [component ] = ressre component ncertainty in terms of dew point temperatre. = ressre component ncertainty in terms of frost point temperatre [component ] = ressre component ncertainty in terms of pressre. [component ] atration emperatre Measrement Uncertainty omponent emperatre measrement ncertainty of Model 100 hmidity generator s satration temperatre probe is specified as Based on a rectanglar distribtion, the ncertainty component of satration temperatre measrement is then [measrement] = ±0.05 / 3 O=infinite atration emperatre Resoltion Uncertainty omponent he Model 100 hmidity generator ses a compter modle to translate the satration temperatre probe readings into digital vales. he compter modle has a specified resoltion of Based on a rectanglar distribtion of the half-interval of resoltion, the ncertainty component of satration temperatre resoltion is then [resoltion] = 0.01 * 0.5/ 3 = ±0.01 / 1 O=infinite atration emperatre elf-heating Uncertainty omponent he satration temperatre probe is installed in a thermo-well, affixed with heat sink compond, within the flid jacket at the otlet of the Model 100 s satrator. his design is similar to a well-stirred flid bath and since the probe is not in air, the effects of self-heating associated with its measrement are considered insignificant and will not be considered.

10 3.. hamber emperatre Uncertainty ontribtion he chamber temperatre ncertainty contribtion in terms of relative hmidity can be determined by the partial nmeric differential of the RH eqation with respect to chamber temperatre, mltiplied by the ncertainty of the chamber temperatre component. he eqation for this becomes RH [component ] e f, e f, [component ] 18 RH [component ] = hamber emperatre component ncertainty in terms of percent relative hmidity. = hamber emperatre component ncertainty in terms of pressre. [component ] Examining eqations 3 and 4, dew and frost point eqations, we see that the chamber temperatre has no component and therefore no ncertainty contribtion to the generated dew or frost point temperatres hamber emperatre Measrement Uncertainty omponent emperatre measrement ncertainty of Model 100 hmidity generator s chamber temperatre probe is specified as Based on a rectanglar distribtion, the ncertainty component of chamber temperatre measrement is then [measrement] = ±0.05 / 3 O=infinite 3... hamber emperatre Resoltion Uncertainty omponent he Model 100 hmidity generator ses a 16 Bit compter modle to translate the chamber temperatre probe readings into digital vales. he compter modle has a specified resoltion of Based on a rectanglar distribtion of the half-interval of resoltion, the ncertainty component of chamber temperatre resoltion is then [resoltion] = 0.01 * 0.5/ 3 = ±0.01 / 1 O=infinite hamber emperatre elf-heating Uncertainty omponent Unlike the satration temperatre probe, the chamber temperatre probe is sed in air and there is the possibility of some self-heating associated with this measrement that mst be considered. he selfheating, with temperatre measrements in, is estimated to be 0.05% of reading. he eqation for the chamber temperatre ncertainty of self-heating is then [self-heating] = ± 0.05% * c / 3 O=infinite

11 egrees of reedom Evalation 3..3 emperatre Uncertainty ontribtion mmary he standard ncertainties, RH, components calclated sing eqation 15 and 18 from the associated individal temperatre components previosly shown are smmarized in the following table. Note: he Model 100 hmidity generator is limited to a maximm dew point temperatre of 50. Any vale calclated above this limit is grayed ot of the following table. tandard emperatre Uncertainty omponents of RH ±% atration ressre Range psia, hamber pressre = 14.7 psia atration emperatre 94.9 %RH 73.6 %RH 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH escription s Measrement Infinity ype B c Measrement Infinity ype B c elf Heating Infinity ype B c Resoltion Infinity ype B s Resoltion Infinity ype B 94.9 %RH 73.6 %RH 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH s Measrement Infinity ype B c Measrement Infinity ype B c elf Heating Infinity ype B c Resoltion Infinity ype B s Resoltion Infinity ype B 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH s Measrement Infinity ype B c Measrement Infinity ype B c elf Heating Infinity ype B c Resoltion Infinity ype B s Resoltion Infinity ype B able 4

12 egrees of reedom Evalation he standard ncertainties,, components calclated sing eqation 16 from the associated individal temperatre components previosly shown are smmarized in the following table. Note: he Model 100 hmidity generator is limited to a maximm dew point temperatre of 50. Any vale calclated above this limit is grayed ot of the following table. atration emperatre tandard emperatre Uncertainty omponents of ew oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia d 5.5 d -0. d -4.0 d -6.9 d -1.0 d d -0. d escription s Measrement Infinity ype B s Resoltion Infinity ype B 34.0 d 9.6 d.7 d 18.1 d 14.6 d 8.6 d 4.5 d -1.1 d s Measrement Infinity ype B s Resoltion Infinity ype B 45.4 d 40.0 d 35.9 d 8.8 d 3.4 d 17.5 d s Measrement Infinity ype B s Resoltion Infinity ype B able 5

13 egrees of reedom Evalation he standard ncertainties,, components calclated sing eqation 17 from the associated individal temperatre components previosly shown are smmarized in the following table. Note: Any frost point vale that is theoretically not possible is grayed ot of the following table. atration emperatre tandard emperatre Uncertainty omponents of rost oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia f -3.6 f -6. f f f f escription s Measrement Infinity ype B s Resoltion Infinity ype B -0.9 f s Measrement Infinity ype B s Resoltion Infinity ype B s Measrement Infinity ype B s Resoltion Infinity ype B able Eqation Uncertainty ontribtion he eqations sed to calclate the satration vapor pressre at a given temperatre and its enhancement factor at the same temperatre and given pressre have pblished ncertainties as determined by the athor or athors of the eqations. hese eqations are sed throghot the Relative Hmidity, ew point and rost point eqations and therefore contribte their own ncertainty to the over all system atration Vapor ressre Eqation Uncertainty omponent he satration vapor pressre is the partial pressre of the water vapor at a given temperatre with respect to ice or water. he satration vapor pressre is dependent on temperatre only and is compted with the Wexler s [4] satration vapor pressre eqation. Wexler [4] also list a table of ncertainties at varios temperatres for his satration vapor pressre eqation. hese ncertainty vales are interpolated to determine the satration vapor pressre eqation ncertainty component for a given temperatre Enhancement actor Eqation Uncertainty omponent Enhancement factors are slight correction factors sed to accont for the non-ideal behavior of water vapor when admixed with other gases. he enhancement factor is dependent on both temperatre and pressre and is compted with Greenspan s [5] enhancement factor eqation. Wexler and R.W. Hyland [8] list a table of ncertainties for varios temperatres and pressres for the enhancement factor eqation. hese ncertainty vales are interpolated to determine the enhancement factors eqation ncertainty component for a given temperatre and pressre.

14 egrees of reedom Evalation Eqation Uncertainty ontribtion mmary he standard ncertainties, RH, components calclated sing the associated eqation ncertainty tables mentioned above are smmarized in the following table. Note: he Model 100 hmidity generator is limited to a maximm dew point temperatre of 50. Any vale calclated above this limit is grayed ot of the following table. tandard Eqation Uncertainty omponents of RH ±% atration ressre Range psia, hamber pressre = 14.7 psia atration emperatre 94.9 %RH 73.6 %RH 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH escription V@t Infinity ype B V@s Infinity ype Infinity ype Infinity ype B 94.9 %RH 73.6 %RH 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH V@t Infinity ype B V@s Infinity ype Infinity ype Infinity ype B 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH V@t Infinity ype B V@s Infinity ype Infinity ype Infinity ype B able 7

15 egrees of reedom Evalation he standard ncertainties,, components calclated sing the associated eqation ncertainty tables mentioned above are smmarized in the following table. Note: he Model 100 hmidity generator is limited to a maximm dew point temperatre of 50. Any vale calclated above this limit is grayed ot of the following table. atration emperatre escription tandard Eqation Uncertainty omponents of ew oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia d 5.5 d -0. d -4.0 d -6.9 d -1.0 d d -0. d V@s Infinity ype B V@d Infinity ype Infinity ype Infinity ype B 34.0 d 9.6 d.7 d 18.1 d 14.6 d 8.6 d 4.5 d -1.1 d V@s Infinity ype B V@d Infinity ype Infinity ype Infinity ype B 45.4 d 40.0 d 35.9 d 8.8 d 3.4 d 17.5 d V@s Infinity ype B V@d Infinity ype Infinity ype Infinity ype B able 8

16 egrees of reedom Evalation he standard ncertainties,, components calclated sing the associated eqation ncertainty tables mentioned above are smmarized in the following table. Note: Any frost point vale that is theoretically not possible is grayed ot of the following table. atration emperatre escription tandard Eqation Uncertainty omponents of rost oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia f -3.6 f -6. f f f f V@s Infinity ype B V@d Infinity ype Infinity ype Infinity ype B -0.9 f V@s Infinity ype B V@d Infinity ype Infinity ype Infinity ype B V@s Infinity ype B V@d Infinity ype Infinity ype Infinity ype B able atrator Efficiency Uncertainty ontribtion All two-pressre hmidity generators rely on the ability of the satrator to flly satrate the gas with water vapor as it passes from inlet to otlet. he Model 100 hmidity generator incorporates a presatrator device along with the satrator to assre the fll satration of the gas with water vapor. Why this design helps assre 100% satration of the gas, there may still be small amonts of ncertainty with regards to satrator efficiency, bt they are considered insignificant and will not be considered. his analysis assmes 100% satrator efficiency.

17 10 egrees of reedom Evalation 4.0 ombined tandard and Expanded Uncertainty he combined standard ncertainty is obtained by the statistical combination of the individal standard ncertainty components of pressre, temperatre, and eqation in terms of relative hmidity, dew point or frost point. Utilizing a confidence level of 95.45% and a coverage factor k=, the expanded ncertainty, U, is expressed by mltiplying the combined standard ncertainty by the coverage factor as show in the following formla U = k * c 19 Using eqation 6 and 19, the following tables reflect the standard ncertainty components, RH, the combined standard ncertainty, c RH, and the combined expanded ncertainty, URH, at varios temperatres and pressres. Note: he Model 100 hmidity generator is limited to a maximm dew point temperatre of 50. Any vale calclated above this limit is grayed ot of the following tables. Uncertainty omponents of RH ±% atration ressre Range psia, hamber pressre = 14.7 psia atration emperatre escription 94.9 %RH 73.6 %RH 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH s Measrement Infinity ype B c Measrement Infinity ype B c Resoltion Infinity ype B c elf Heating Infinity ype B s Resoltion Infinity ype B Measrement Infinity ype Infinity ype Infinity ype B V@t Infinity ype B V@s Infinity ype B c Hysteresis Infinity ype B Resoltion Infinity ype B ombined tandard Uncertainty Infinity Expanded Uncertainty k= able 10

18 60 egrees of reedom Evalation 35 egrees of reedom Evalation atration emperatre escription Uncertainty omponents of RH ±% atration ressre Range psia, hamber pressre = 14.7 psia %RH 73.6 %RH 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH s Measrement Infinity ype B c Measrement Infinity ype B c elf Heating Infinity ype B c Resoltion Infinity ype B s Resoltion Infinity ype B Measrement Infinity ype B V@t Infinity ype B V@s Infinity ype Infinity ype Infinity ype B c Hysteresis Infinity ype B Resoltion Infinity ype B ombined tandard Uncertainty Infinity Expanded Uncertainty k= able 11 atration emperatre escription Uncertainty omponents of RH ±% atration ressre Range psia, hamber pressre = 14.7 psia %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH s Measrement Infinity ype B c Measrement Infinity ype B c elf Heating Infinity ype B c Resoltion Infinity ype B s Resoltion Infinity ype B Measrement Infinity ype Infinity ype Infinity ype B V@t Infinity ype B V@s Infinity ype B c Hysteresis Infinity ype B Resoltion Infinity ype B ombined tandard Uncertainty Infinity Expanded Uncertainty k= able 1

19 35 egrees of reedom Evalation 10 egrees of reedom Evalation Using eqation 7 and 19, the following tables reflect the standard ncertainty components,, the combined standard ncertainty, c, and the combined expanded ncertainty, U, at varios temperatres and pressres. Note: he Model 100 hmidity generator is limited to a maximm dew point temperatre of 50. Any vale calclated above this limit is grayed ot of the following tables. atration emperatre escription Uncertainty omponents of ew oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia d 5.5 d -0. d -4.0 d -6.9 d -1.0 d d -0. d s Measrement Infinity ype B s Resoltion Infinity ype B Measrement Infinity ype Infinity ype Infinity ype B V@s Infinity ype B V@d Infinity ype B c Hysteresis Infinity ype B Resoltion Infinity ype B ombined tandard Uncertainty Infinity Expanded Uncertainty k= able 13 atration emperatre escription Uncertainty omponents of ew oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia d 9.6 d.7 d 18.1 d 14.6 d 8.6 d 4.5 d -1.1 d s Measrement Infinity ype B s Resoltion Infinity ype B Measrement Infinity ype Infinity ype Infinity ype B V@s Infinity ype B V@d Infinity ype B c Hysteresis Infinity ype B Resoltion Infinity ype B ombined tandard Uncertainty Infinity Expanded Uncertainty k= able 14

20 60 egrees of reedom Evalation atration emperatre escription Uncertainty omponents of ew oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia d 40.0 d 35.9 d 8.8 d 3.4 d 17.5 d s Measrement Infinity ype B s Resoltion Infinity ype B Measrement Infinity ype Infinity ype Infinity ype B V@s Infinity ype B V@d Infinity ype B c Hysteresis Infinity ype B Resoltion Infinity ype B ombined tandard Uncertainty Infinity Expanded Uncertainty k= able 15

21 35 egrees of reedom Evalation 10 egrees of reedom Evalation Using eqation 8 and 19, the following tables reflect the standard ncertainty components,, the combined standard ncertainty, c, and the combined expanded ncertainty, U, at varios temperatres and pressres. Note: Any frost point vale that is theoretically not possible is grayed ot of the following tables. atration emperatre escription Uncertainty omponents of rost oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia f -3.6 f -6. f f f f Measrement Infinity ype B c Hysteresis Infinity ype B s Measrement Infinity ype B V@d Infinity ype Infinity ype Infinity ype B s Resoltion Infinity ype B Resoltion Infinity ype B V@s Infinity ype B ombined tandard Uncertainty Infinity Expanded Uncertainty k= able 16 atration emperatre escription Uncertainty omponents of rost oint emperatre ± atration ressre Range psia, hamber pressre = 14.7 psia f Measrement Infinity ype B c Hysteresis Infinity ype B s Measrement Infinity ype Infinity ype B s Resoltion Infinity ype Infinity ype B Resoltion Infinity ype B V@s Infinity ype B V@d Infinity ype B ombined tandard Uncertainty Infinity Expanded Uncertainty k= able 17

22 5.0 mmary A smmary of the final combined expanded ncertainty is smmarized in the following tables. Note: he Model 100 hmidity generator is limited to a maximm dew point temperatre of 50. Any vale calclated above this limit or that is theoretically not possible, is grayed ot of the following tables. atration emperatre Expanded %RH Uncertainty k= atration ressre Range psia, hamber pressre = 14.7 psia %RH 73.6 %RH 49.1 %RH 36.9 %RH 9.6 %RH 19.9 %RH 14.9 %RH 10.0 %RH 10 ±0.58 ±0.41 ±0.301 ±0.37 ±0.197 ±0.141 ±0.113 ± ±0.448 ±0.360 ±0.64 ±0.11 ±0.177 ±0.18 ±0.103 ± ±0.39 ±0.194 ±0.164 ±0.10 ±0.098 ±0.076 able 18 atration emperatre Expanded ew oint emperatre Uncertainty k= atration ressre Range psia, hamber pressre = 14.7 psia d 5.5 d -0. d -4.0 d -6.9 d -1.0 d d -0. d 10 ±0.058 ±0.059 ±0.064 ±0.067 ±0.070 ±0.074 ±0.077 ± d 9.6 d.7 d 18.1 d 14.6 d 8.6 d 4.5 d -1.1 d 35 ±0.058 ±0.060 ±0.068 ±0.07 ±0.075 ±0.081 ±0.086 ± d 40.0 d 35.9 d 8.8 d 3.4 d 17.5 d 60 ±0.07 ±0.079 ±0.083 ±0.089 ±0.095 ±0.109 able 19 atration emperatre Expanded rost oint emperatre Uncertainty k= atration ressre Range psia, hamber pressre = 14.7 psia f -3.6 f -6. f f f f 10 ±0.057 ±0.060 ±0.063 ±0.068 ±0.07 ± f 35 ±0.086 able 0

23 6.0 References 1. aylor, Barry N. and Kyatt, hris E., Gidelines for Evalating and Expressing the Uncertainty of NI Measrement Reslts, NI echnical Note 197, 1994 Edition. Wexler, Arnold and aniels, Raymond, ressre-hmidity Apparats, Jornal of Research of the National Brea of tandards, April 195, Vol. 48, No. 4, Hasagawa,. and Little, J.W., he NB wo-ressre Hmidity Generator, Mark, Jornal of Research of the National Brea of tandards A. hysics and hemistry, Janary-ebrary 1977, Vol. 81A, No. 1, Wexler, Arnold, Vapor ressre ormlations for Water in Range 0 to 100. A Revision, Jornal of Research of the National Brea of tandards - A. hysics and hemistry, eptember-ecember 1976, Vol. 80A, Nos. 5 and 6, , Eqation Greenspan, L., nctional Eqations for the Enhancement actors for O -ree Moist Air, Jornal of Research of the National Brea of tandards A. hysics and hemistry, Janary-ebrary 1976, Vol. 80A, No.1, Kyatt, hris, et al., etermining and Reporting Measrement Uncertainties, Recommended ractice R-1, National onference of tandards Laboratories, April NL International RI-5, wo-ressre, wo-emperatre Hmidity Generator, Recommended Intrinsic/erived tandards ractice, Janary A. Wexler and R.W. Hyland, In hermodynamic properties of dry air, moist air and water and I psychrometric charts, 1983 AHRAE roject 16 R, able 0.