Volume calibration of a 100 ml Gay-Lussac Pycnometer

1. EUROMET Project 692 Volume calibration of a 100 ml Gay-Lussac Pycnometer Presentation of final results EUROMET Flow Meeting 2005/Thessaloniki

2. Summary • The Project started on September 2002; • Fifteen participating countries, one as redraw from the comparison; • Seventeen results presented (IPQ has 3 measurement results and PTB has 2 results); • A draft B report has been sent to all participants. EUROMET Flow Meeting 2005/Thessaloniki

3. Participating countries • Slovakia/SLM • Turkey/UME • Spain/CEM • Italy/IMGC • Hungary/OMH • Greece/EIM • Austria/BEV • Sweden/SP • Portugal/IPQ • Czech Republic/CMI • Switzerland/METAS • France/BNM-LNE • Denmark/FORCE • Germany/PTB • Netherlands/NMI EUROMET Flow Meeting 2005/Thessaloniki

4. The method and instrument Pycnometer nº 62 Pycnometer nº 144 EUROMET Flow Meeting 2005/Thessaloniki

5. Results Pycnometer nº62 Pycnometer nº144 EUROMET Flow Meeting 2005/Thessaloniki

6. Difference (ml) Weighted mean (ml) Uncertainty (ml) with k=2 IPQ 0,1109 (IPQ-1 – IPQ-2) 0,1118 0,0016 PTB 0,1120 (PTB-1 – PTB-2) Correction of results EUROMET Flow Meeting 2005/Thessaloniki

7. Final results EUROMET Flow Meeting 2005/Thessaloniki

8. Reference value calculations (1) Weighted mean Weighted mean uncertainty • M. G. Cox, “The evaluation of key comparisons”, Metrologia, 39, p.589-595, 2002 EUROMET Flow Meeting 2005/Thessaloniki

9. Reference value calculations Consistency statistical test - Chi-square test Where the degrees of freedom are :  = N -1 Regard the consistency check as failing if: EUROMET Flow Meeting 2005/Thessaloniki

10. > > Reference value calculations The obtained weighted mean using the 14 results (one for each laboratory) is: y = 100,0917 ml with a u(y) = 0,0007 ml with k=2 The chi-square test gives the following results: The consistency test fails. The volume value for the SLM is then removed. EUROMET Flow Meeting 2005/Thessaloniki

11. > Reference value calculations A new consistent test is preformed and the results are now the following: We conclude that the results are consistent. xref = 100,0914 ml, u(xref) = 0,0006 ml with k=2 EUROMET Flow Meeting 2005/Thessaloniki

12. Results with the reference value EUROMET Flow Meeting 2005/Thessaloniki

13. Degree of equivalence EUROMET Flow Meeting 2005/Thessaloniki

14. Uncertainty presentation EUROMET Flow Meeting 2005/Thessaloniki

15. Uncertainty components The major uncertainty components presented were: • The Mass filled • Mass pieces density • Water density • Air density • Expansion Coefficient • Water temperature EUROMET Flow Meeting 2005/Thessaloniki

16. Uncertainty components results Mass filled - These uncertainties values probably include the whole of the weighing procedure for the mass filled, so the major difference between the results may be due to several components like the used mass standards or the static electricity. EUROMET Flow Meeting 2005/Thessaloniki

17. Uncertainty components results Mass pieces density - Some laboratories do not consider this uncertainty, probably this component is added into the mass filled uncertainty. EUROMET Flow Meeting 2005/Thessaloniki

18. Uncertainty components results Water density - All the laboratories have specified a value; the lower values probably are due to the purity of the water or some different way of determining the density of the water. Also some laboratories may have put this contribution into the temperature uncertainty. EUROMET Flow Meeting 2005/Thessaloniki

19. Uncertainty components results Air density - The uncertainties between the laboratories are quite similar only one laboratory has stated a very high value compared to the others. EUROMET Flow Meeting 2005/Thessaloniki

20. Uncertainty components results Expansion Coefficient - Several laboratories do not question the expansion coefficient and others have very low values. EUROMET Flow Meeting 2005/Thessaloniki

21. Uncertainty components results Water temperature -The uncertainty of the water temperature is very similar between the laboratories; only SP has a large uncertainty because they use a standard value for all the volume standards that they calibrate. EUROMET Flow Meeting 2005/Thessaloniki

22. Uncertainty components results Some laboratories presented uncertainties components in addition to those proposed in the spreadsheet by the pilot laboratory. Some different components are: the pycnometer temperature, the cleaning of the remaining water of the stopper, or the static electricity, weight differences, mass empty, etc. EUROMET Flow Meeting 2005/Thessaloniki

23. Major source of uncertainty IPQ-1 - Water density CMI - Water density BNM-LNE- Water temperature FORCE - Water density PTB-1 - Water density IPQ-2 - Water density PTB-2 - Water density NMi-VSL - Water density SLM - Water density UME – Mass CEM – Evaporeted Mass IMGC - Water temperature OMH -Water density EIM - Water density BEV - Water density SP - Water temperature on water density IPQ-3 - Water density EUROMET Flow Meeting 2005/Thessaloniki

24. Average of the components for the standard uncertainties EUROMET Flow Meeting 2005/Thessaloniki

25. Conclusions • Globally the results are quite satisfactory. Except for one or two participants, the laboratories volume results are quite consistent with the reference value, and with each other. • The uncertainty budgets are very similar and the major uncertainty component to the final uncertainty is, for the majority of the participants, the water density. • There is a difference in the determination of the total uncertainty in some of the laboratories. It is probably due to the repeatability of the measurements, problems with the ambient conditions, the use of different mass standards and the use of different formulas for the volume calculation. EUROMET Flow Meeting 2005/Thessaloniki