Uncertainty contribution on the density of liquids due to unknown sinker temperature in hydrostatic weighing apparatus

In this study, the influence of the unknown sinker temperature on the measured density of liquids is evaluated. Generally, due to the intrinsic temperature instability of the heat bath temperature controller, the system will never reach thermal equilibrium but instead will oscillate around a mean temperature. The sinker temperature follows this temperature oscillation with a certain time lag. Since the sinker temperature is not measured directly in a hydrostatic weighing apparatus, the temperature of the sinker, and thus in turn the volume of the sinker, is not known exactly. As a consequence, this leads to uncertainty in the value of the density of the liquid. From an analysis of the volume relaxation of the sinker immersed into a heat bath with time-dependent temperature characteristics, the heat transfer coefficient can be estimated, and thus a characteristic time constant for achieving quasi thermal equilibrium for a hydrostatic weighing apparatus is proposed. Additionally, from a theoretical analysis of the transient behavior of the sinker volume, the systematic deviation of the theoretical to the actual measured liquid density is calculated.