The use and misuse of pure water PVT properties for lake waters

Abstract

ALTHOUGH dissolved substances affect the thermodynamic properties of lake waters,^1,2 many limnologists still consider lake water as pure water^3–8. This can be a good assumption if used with caution: lake water is by no means pure water, especially when the precise pressure, volume, temperature (PVT) properties are considered. PVT properties of lake water can be determined from an equation of state for sea water provided that the total mass fraction of dissolved salts in seawater and lake water are equated⁹. In addition, the total mass fraction of dissolved salts affects calculations concerning the temperature of maximum density and thus stability¹⁰. Therefore, in the absence of direct PVT measurements on a particular lake, it is at present most appropriate to use an equation of state for seawater when examining effects of PVT properties in lakes. We present here a short equation of state determined with a precision of 2 × 10⁻⁶ g cm⁻³ in density over the appropriate range for most fresh water lakes, 0–0.6‰ salinity, 0–30 °C, and 0–180 bar. The equation of state is based on the 1 atm pure water density and compressibility equations of Kell¹¹, the pure water temperature and pressure effects of Fine and Millero¹², and the effects of dissolved salts of Millero et al.¹³ and Chen and Millero¹⁴: where d^p and d⁰ are the densities of lake water at applied pressures P and 0 (sea level), respectively, t is the temperature in °C, S(‰) is the salinity: where g_T is the total grams of dissolved salt in 1 kg of lake water¹⁵. The values of g_T usually increase with depth due to the increase of HCO₃⁻, Ca²⁺ and nutrients¹⁶. The small changes in composition in a lake can be accounted for by making the appropriate changes in gt. Further, Millero⁹ and Millero et al.¹⁷ showed that the densities calculated from the seawater equation of state for Lake Tanganyika water and artificial river water agree with the measured values to within ±2×10⁻⁶g cm⁻³ despite the large composition difference between the two waters. This verifies the validity of our equation of state for fresh waters.