Determination of isothermal secant and tangent bulk modules

In a system for measuring the isothermal adiabatic bulk modulus {overscore (BS+L )} of a liquid in a vessel on a pressure-volume-temperature relationship at a constant volume corrected for changes in vessel volume due to elevated pressure and temperature, a method comprising the steps of:

• entirely filling said vessel with said liquid;
• degassing said vessel
• calibrating the volume of the vessel at various pressures and temperatures from atmospheric pressure and ambient temperature to various elevated temperatures and pressures to determine data relative to the final volume VT,Pf, at any given pressure and temperature, and using said data to establish a calibration curve;
• determining the volume VT of the vessel at atmospheric pressure and temperature T;
• determining the weight WT of the liquids at temperature T and 1 atmosphere;
• determining the density DT of the liquid at temperature T and 1 atmosphere;
• determining the volume determining the volume VT,Pf, where VT,Pf, is the volume of the liquid at temperature T;
• determining the volume VT1 of the vessel at temperature T and 1 atmosphere;
• solve the equation
• {overscore (BS+L )}=−[VT,Pf ∂P/∂T]S
• where ∂P is equal to the difference in pressure P between 1 atmosphere and a specified pressure;
• and ∂T is a change in temperature;
• calibrating the volume of the vessel at various pressures and temperatures from atmospheric pressure and ambient temperature to various elevated temperature and pressures to determine the volume, and establishing a calibration curve.