Cooling Power
At not too low temperatures the cooling power at the mixing chamber is approximately given by
where is the 3He molar circulation rate, Tm is the mixing-chamber temperature, and Ti the temperature of the 3He entering the mixing chamber. In the case of zero heat load there is a fixed ratio between the two temperatures
From this relation it is clear that a low Tm can only be reached if Ti is low. In dilution refrigerators Ti is reduced by using heat exchangers as shown in Fig.2. However, at very low temperatures this becomes more and more difficult due to the so-called Kapitza resistance. This is a heat resistance at the surface between the helium liquids and the solid body of the heat exchanger. It is inversely proportional to T4 and the heat-exchanging surface area A. In other words: to get the same heat resistance one needs to increase the surface by a factor 10,000 if the temperature goes down by a factor 10. In order to get a low thermal resistance at low temperatures (below about 30 mK) a large surface area is needed. The lower the temperature, the larger the area. In practice one uses very fine silver powder.
Read more about this topic: Dilution Refrigerator
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