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Exact pressure for the new Kelvin

It is to generate an exactly defined helium absolute pressure within the scope of the Boltzmann project: a pressure balance which mainly consists of a piston-cylinder system. PTB now succeeded in measuring the form and the diameter of these pistons and cylinders exact to a few nanometres and, thus, in remaining below the required accuracies.

The piston of a piston manometer (“pressure standard”) with
the laser interferometer for the 3D form measurement (on the
upper right). The curve on the left shows the diameters at different
measurement positions.

In addition to the "Temperature" Department, other PTB Departments are involved in the socalled Boltzmann project which shall – with the aid of a redefinition of the Boltzmann constant k – lead to a redefinition of the SI unit "kelvin". The precise determination of k by means of dielectricity constant gas thermometry requires, among other things, exactly defined absolute helium pressures of up to 7 MPa. These pressures shall be realized with the aid of a pressure balance, whose most important components are piston-cylinder systems. For the precise calculation of the pressure, the geometry of the piston and of the cylinder at ambient pressure must be known with sufficient accuracy.

Three piston-cylinder systems with a nominal cross-sectional area of 20 cm2, which can be used up to 0.7 Mpa and had been specially purchased for the Boltzmann project, were characterized in the "Coordinate Measuring Technology" Department with respect to their geometric properties. For the form measurements, a cylinder form measuring instrument with very high basic accuracy was used, and the diameters were measured with the comparator for measure and form. This high-precision reference device, which has been operated at PTB for more than one decade, represents the world‘s top for tactile distance and diameter determinations in the measurement range up to 180 mm.

To combine the independently measured form and diameter data of piston and cylinder to a 3D configuration, a least-square fit method has been developed. A first approach for the calculation of the measurement uncertainty of the 3D geometry data generated in this way showed that the dimensional 3D standard measurement uncertainties amount to only 7 nm (piston) and 15 nm (cylinder). From this, a relative measurement uncertainty of 0.7 · 10–6 is derived for the cross-sectional area. Therewith, the objective for this partial tasks of the Boltzmann project has been more than achieved.

In the "Material Properties and Pressure" Department, three additional piston-cylinder systems with a nominal cross-sectional area of 2 cm2, – with the aid of which the required pressures of up to 7 MPa can be achieved – are at present being linked up with the dimensionally measuring 20 cm2 systems by means of pressure measure- ments in a special double piston manometer. By the pressure comparison measure- ments performed up to 7 MPa, proof is finally to be furnished that the cross-sectional areas determined agree in any pair of the six piston-cylinder systems within 1 · 10–6.

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