Correlating the Speed of Sound with the Gibbs Energy and Estimating the Speed of Sound in Fatty Acid Methyl Ester and Biodiesel

Abstract

The relationship between the speed of sound (u) in biodiesel and the change in Gibbs energy (ΔG) has not been described in the literature. With the Gibbs energy additivity method, the relationship between u and ΔG can be expressed as ln(u2) = ΔG/RT + A, where R is the universal gas constant, T is the absolute temperature, and A is a constant. The molecule of fatty acid methyl ester (FAME) was arbitrarily sub-divided into groups of atoms and a ΔG was assigned to each group of atoms. A new model correlating the speed of sound to the structure of fatty acid was derived. The proposed model was good for estimation of the speed of sound in both FAME and biodiesel at various temperatures with good accuracy. The absolute average deviations for the speed of sound in FAME (65 data points) and in biodiesel (175 data points) were 0.23% and 0.36%, respectively. Only the number of double bonds and carbon atoms of the fatty acid are required for the calculation.