Highly Accurate Densities and Isobaric and Isochoric Heat Capacities of Compressed Liquid Water Derived from New Speed of Sound Measurements

Abstract

Comprehensive and accurate measurements of the speed of sound in liquid water are reported. The measurements were carried out by a double-path-length pulse-echo technique and cover the temperature range from 273.65 K to 368.15 K with pressures up to 100 MPa. The relative expanded (k=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${ k}=2$$\\end{document}) uncertainties are 2.1 mK in temperature, 45 parts-per-million (ppm) in pressure, and between 40 ppm and 70 ppm in speed of sound. Furthermore, values for the density and specific isobaric and isochoric heat capacities were derived from the speed of sound data in the measured temperature range up to 100 MPa by the method of thermodynamic integration. Very accurate values for the derived properties were obtained by using density data of Takenaka and Masui (Metrologia 27:165–171, 1990) and isobaric heat capacity data of Osborne et al. (J Res Natl Bur Stand 23:197, 1939) at ambient pressure as initial values in combination with an accurate correlation of our speed of sound. The relative expanded (k=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${ k}=2$$\\end{document}) uncertainties of the derived properties are 2 ppm in density, 0.11% in isobaric heat capacity, and 0.12% in isochoric heat capacity. The experimental speeds of sound and derived properties are compared with experimental data of other authors from the literature, the IAPWS-95 (International Association of the Properties of Water and Steam) formulation for the thermodynamic properties of water, and a recent equation of state for supercooled water.