Decomposition of effective specific heat of molecular relaxation for gas detection in a mixture

The effective specific heat (ESH) is the "footprint" of acoustic relaxation processes in gases, and is characterized by a semicircle curve that is dependent on the acoustic frequency in the complex plane. In this paper, the ESH of the molecular relaxation process of a gas mixture is decomposed to obtain the relaxation contributions of the individual gas components. The decomposed ESHs obtained by the proposed method have the same complex-plane curves as the ESHs of the corresponding pure gases; thus, the ESH curve of the mixture can be obtained by the sum of the ESH curves of the corresponding pure gases. This conclusion not only provides a theoretical foundation for the existing gas sensing method based on acoustic spectral peaks, but can also be used to identify gas components in mixtures. The connecting lines of the minimum points of the ESH curves were used to quantitatively detect carbon dioxide and methane in dry air, and to monitor contaminant gases in natural gas.