Thermodynamic Behavior and Equation of State for Cryogenic Helium 3-4 Mixtures

Abstract On this study the authors have derived and present an overall Equation of State for Helium 3 and Helium 4 mixtures. The point of the present study is to give equations that are usable for engineering low temperature applications such as dilution or Stirling refrigerators, without the need to make any approximations or having to use different models for different phase regions. The offered model uses all the existing data, experimental and theoretical, describing the different phases of the Helium 3-4 mixture. Additionally, to the pure data, in areas where no direct data exist the presented equations are such that they follow the expected and observed behaviors and in parallel continuously connecting the data refence points while being self-coherent and able to correlate the different thermodynamic values and their derivatives with each other. Furthermore, the effects of mixing properties in the total values have been studied and through the understanding and modeling of their behavior, combined with the equations of state for the pure isotopes the authors have been able to extend the range of the equations outside of any current models by offering a range from near absolute zero to over the lambda line of Helium 4. Because of its importance in applications also the osmotic pressure of the mixture has been included. Lastly in order to make the model more usable for thermodynamic cycles the thermodynamic maps have been created where one can directly foresee the expected behaviors without the need to run the calculations.