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Are the Heat Capacities of Liquids Calculated from Speeds of Sound and $p_{ρ}T$ Relationships Reliable? A Comparison with the Reference Values and a Discussion of the Uncertainties

Jan Długosz University

Wojciech MARCZAK
Jan Długosz University

Recent advances in the construction of speed of sound meters made high-accuracy routine measurements possible in laboratories non-specialized in physical acoustics. Reliable values of the isentropic compressibility can be obtained from speeds of sound and densities of liquids using the Laplace formula. Strict thermodynamic relationships connect the isentropic compressibility of a medium and its density as a function of temperature and pressure with the heat capacity. These relationships result from the principles of thermodynamics and require no approximations or molecular models. In this study, the heat capacities of twelve liquids: hydrocarbons, acetonitrile, and ionic liquids were calculated from the speeds and densities taken from the literature sources. The agreement of the calculation results with the reference heat capacities, either critical values or measured calorimetrically, was satisfactory. The relative uncertainty of the calculated heat capacities was rather conservatively estimated for 5%. If the measurement procedures were optimized for heat capacity determination, better results would be attained, with the uncertainty probably smaller than 1%. Thus, the speed-and-density method is a potential alternative to classical calorimetry.
Keywords: speed of sound; density; compressibility; expansibility; calorimetry; elevated pressure
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DOI: 10.24425/aoa.2022.142890