A new theoretical method for calculating temperature and water vapor saturation ratio in an expansion cloud chamber

Abstract

The expansion cloud chamber is a widely used apparatus for investigating the dynamics of condensational growth of aerosols and clouds. Theoretical calculations of temperature T and water vapor saturation ratio S are necessary for quantitative interpretations of experimental data obtained from the expansion cloud chamber. In this paper, we revisit the thermodynamics associated with the underlying assumptions for calculating the time‐dependent temperature T(t) and saturation ratio S(t) in an expansion chamber as a function of experimentally observable parameters. We introduce an intuitive and robust method, the virtual path (VP) method, by which changes in the thermodynamic state of a moist air parcel containing cloud droplets are schematically represented on a thermodynamic diagram. The validity of the VP method is confirmed by comparisons with the differential equation (DE) method, which is a numerical simulation of real physical processes according to the time evolution equations involving T and S. In contrast to the conventional DE method, the governing equations of the VP method do not involve time t, an irrelevant parameter in the framework of classical thermodynamics. The VP method is advantageous compared to the DE method because the former is applicable to the raw experimental data acquired with a finite time resolution, allowing a robust calculation of the T and S values and the errors that are only caused by the measurement errors of the input data.