The lowest temperature that has been achieved at the present time is about I x 10-6 K. Lowering a specimen to this temperature requires an additional stage to that described, namely nuclear cooling. This process is similar to magnetic cooling, but it involves the magnetic moment associated with the nucleus rather than that associated with certain ions in the paramagnetic salt. Suppose that 10 J of energy is to be removed from a specimen at an average temperature of 10- 5 K. (Ten joules is about the amount of energy spent by a pin dropping through a distance of 3 mm. Ten joules is also about the amount of energy transferred as heat at this temperature in some experiments.) Consider that a Carnot-cycle refrigerator produces this amount of refrigeration at an average temperature of 10-5 K (for the purpose of determining the theoretical limit). Determine the work input and the coefficient of performance for the refrigeration cycle, assuming that the ambient temperature is 300 K.
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