Thermodynamic anomalies of water near its singular temperature of 42 °C

Abstract

The anomalous behavior of such thermodynamic responses of water as isothermal compressibility, isobaric thermal expansion coefficient and isobaric heat capacity have been analyzed using reliable physical–chemical databases. The “thermodynamic tree of derivatives” has been introduced for the thermodynamic potential, being the Gibbs free energy, with a chemical potential at the vertex. The expressions for thermodynamic responses were obtained containing three contributions that are related to the derivatives of entropy, volume and internal energy with respect to thermodynamic variables. It was proved that the volume contribution could be neglected in the temperature range θ≈(0÷200) °C for water in the liquid state. The calculations also showed that the temperature dependence of the derivative -(∂V/∂P)T, which determined the isothermal water compressibility, reached its minimum value in the vicinity of a singular temperature of θ=(42.2±0.2) °C. On the basis of experimental data, a comparison of the proposed expressions for water and argon was carried out, confirming that the anomalous behavior of isothermal compressibility, isobaric expansion coefficient, and isobaric heat capacity turned out to be associated precisely with the entropy contribution in the vicinity of a singular water temperature of θ=(42.2±0.2) °C.