Statistical and Low Temperature Physics - University of Liverpool

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Exercises When the nuclear magnetic interaction energy µbi becomes comparable to the thermal energy k BTn, we have The magnetic moment is Substituting this, we get Solving for Tn, k BTn = µbi. µ = gµn. k BTn = gµnbi. Tn = gµnbi . kB Substituting the given values of g and bi, we get Tn = 3.66 µT. Statistical Physics 87 Oct - Dec 2009
Exercise 5 Exercises How long would it take a 3 He- 4 He dilution refrigerator with a circulation rate of 1 mmole 3 He/s to precool 20 mole of copper in 8 T to 15 mK from a higher temperature? How does this compare with cooling it isothermally at 15 mK with the same dilution refrigeraton? You may use the high temperature approximation for the entropy per mole: Sn = R ln(2I + 1) − λnB 2 2µ0T 2 n where λn = N AI(I + 1)µ0µ 2 ng 2 n/3k B, and gn is the g-factor for the nucleus. [You are given that copper has a nuclear spin I of 3/2 and a nuclear g-factor of 2.22. The nuclear magneton µn = 5.051 × 10 −27 J T −1 .] Statistical Physics 88 Oct - Dec 2009
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Statistical and Low Temperature Phy
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Sections The magnetic refrigerator
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9.1 The Principle of Magnetic Cooli
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The Principle of Magnetic Cooling T
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The Principle of Magnetic Cooling A
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The Principle of Magnetic Cooling N
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The Principle of Magnetic Cooling P
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How does it work? We have seen how
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An adiabatic, constant entropy chan
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9.2 Thermodynamics of Magnetic Cool
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Thermodynamics of Magnetic Cooling
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The new temperature is Thermodynami
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Interaction between magnetic dipole
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Interaction between magnetic dipole
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Magnetic disorder entropy Previousl
Page 37 and 38: Magnetic disorder entropy Substitut
Page 39 and 40: Magnetic disorder entropy The expan
Page 41 and 42: Magnetic Refrigerators The performa
Page 43 and 44: Magnetic Refrigerators The follow g
Page 45 and 46: Magnetic Refrigerators These are ex
Page 47 and 48: 9.6 Nuclear Refrigeration Statistic
Page 49 and 50: Nuclear Refrigeration To get some i
Page 51 and 52: Nuclear Refrigeration From the entr
Page 53 and 54: Nuclear Refrigeration Because the s
Page 55 and 56: Nuclear Refrigeration One disadvant
Page 57 and 58: Nuclear Refrigeration The copper bl
Page 59 and 60: Nuclear Refrigeration The copper bl
Page 61 and 62: Nuclear Refrigeration The small nuc
Page 63 and 64: From the entropy formula, Nuclear R
Page 65 and 66: Nuclear Refrigeration To see how we
Page 67 and 68: Nuclear Refrigeration The other way
Page 69 and 70: Nuclear Refrigeration Note that usi
Page 71 and 72: Nuclear Refrigeration (a) The nucle
Page 73 and 74: Nuclear Refrigeration Notice from t
Page 75 and 76: 9.7 Exercises Statistical Physics 7
Page 77 and 78: Define Exercises x = µ BB k BT . R
Page 79 and 80: Exercise 2 Exercises CMN is a spin-
Page 81 and 82: Exercises where C is the heat capac
Page 83 and 84: Exercises The entropy change refers
Page 85 and 86: Exercises A spin 1/2 salt would hav
Page 87: Exercise 4 Exercises At which nucle
Page 91 and 92: Exercises We also need to assume th
Page 93 and 94: n = 20, B = 8 T, Ti = 0.015 K and n
Page 95: then Exercises nλnB 2 ∆Q = T ∆
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Statistical and Low Temperature Physics - University of Liverpool

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