Thermodynamic properties of He3-He4 solutions with applications to the He3-He4 dilution refrigerator

Ultimate Temperature of Pulse Tube Cryocoolers

“…Such low concentrations limits the mass flow and the cooling achievable in a practical sized cooler. This type of cooler has not seen further development nor has it seen any practical application The present thermodynamic model of dilute 3 He in 4 He [16][17][18] shows no evidence of a low temperature limit of a pulse tube cryocooler.…”

“…In the pulse tube, the constraint that ∇P = 0 is replaced by ∇µ 4 = 0, where µ 4 is the chemical potential of the 4 He. Several loci of ∇µ 4 = 0 (from data in reference [16]) are shown in FIGURE 5 from which one sees that in the pulse tube x 3 increases as the temperature decreases. The cold end temperature is limited by phase separation.…”

“…A full treatment of the thermodynamics in this regime is beyond the scope of this paper. Reviews of the thermodynamics of dilute 3 He in 4 He solutions have been given elsewhere [16][17][18].…”

THERMODYNAMIC PROPERTIES OF LIQUID [sup 3]He-[sup 4]He MIXTURES BETWEEN 0.15 K AND 1.5 K

“…The primary sources of data are Alvesalo et al [11] and de Bruyn Ouboter et al [15], which are the only sources at values of x greater than about 0.2. Radebaugh's calculated specific heats [1] are also used, albeit only at low 3 He concentrations, where they are expected to be good. The deviation terms are written as: …”

“…As a result, thermodynamic property tables for these mixtures, developed from the late 1960s through to the early 1980s, are restricted to property regions where dilution refrigerators typically operate -low pressures and dilute solutions of 3 He in 4 He. The most extensive set of thermodynamic property tables for 3 He- 4 He mixtures was developed by Radebaugh [1] in 1967. He calculated properties at saturated pressure, at temperatures below 1.5 K and 3 He mole fractions of only less than 30%.…”