Optimum design of the variable-volume gas pycnometer for determining the volume of solid particles

Little is known about optimum design of gas pycnometers, so that they can determine the volume of solid particles with the greatest accuracy. The purpose of this study was to investigate the optimum design of the 'variable-volume' gas pycnometer, because its ease of handling makes it a good candidate for widespread use. The law of propagation of uncertainty was used to derive a theoretical formula that relates the pycnometer's accuracy to the main sources of random uncertainty (gas-pressure measurements, pycnometer temperature, sample-chamber and piston-chamber volumes). The consequences of this formula in terms of optimizing the geometry and working conditions of the pycnometer are discussed. It was found that some gas pycnometers described in the literature may not have been used under the best conditions. As for the 'constant-volume' gas pycnometer, which was considered in a previous study, it seems possible to use commercially available components for constructing a variable-volume gas pycnometer that can determine the volume of solid particles with a relative standard uncertainty smaller than 0.25%. However, an accurately calibrated pressure transducer is required for the variable-volume gas pycnometer (instead, the only requirement for the constant-volume gas pycnometer is that the transducer's response varies linearly with pressure).