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Lecture 12. Refrigerators. Toward Absolute Zero (Ch. 4)

Center of hottest stars. 10 9. Center of Sun, nuclear reactions. Lecture 12. Refrigerators. Toward Absolute Zero (Ch. 4). 10 7. 10 5. Electronic/chemical energy. Surface of Sun, hottest boiling points. 10 3. Temperature, K. Organic life. Liquid air. 10 1. Liquid 4 He.

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Lecture 12. Refrigerators. Toward Absolute Zero (Ch. 4)

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  1. Center of hottest stars 109 Center of Sun, nuclear reactions Lecture 12. Refrigerators. Toward Absolute Zero (Ch. 4) 107 105 Electronic/chemical energy Surface of Sun, hottest boiling points 103 Temperature, K Organic life Liquid air 101 Liquid 4He Electronic magnetism Universe Superfluid 4He 10-1 Superconductivity Superfluid 3He 10-3 Nuclear magnetism 10-5 Lowest T of condensed matter

  2. How Low Temperatures Are Produced Although the efficiency of an “ideal” refrigerator does not depend on the working substance, in practice the choice of working substance is very important because Qfrom the environment Qto the fridge cooling volume “cold reservoir” At the lowest T, these two flows of thermal energy compensate each other.

  3. Recall: More on Enthalpy The latent heatL of phase transformation at P = const:

  4. Cooling of Gases constant P = P1 - P2 . V1 T1 V2 T2 P1 P2 • an “expansion engine” • ( W  0); • (b) a porous membrane or a constriction. • ( W = 0).  W  W

  5. Compressor Simple Expansion Refrigerator Heat ejection This process works for both ideal and real gases. Heat exchanger Expansion engine For an ideal monatomic gas: Cooling volume

  6. The Joule-Thomson Process (b) Throttling process • Irreversible!! • Real gases only Isenthalpic expansion: For an ideal gas, :

  7. The JT Process in Real Gases(low density) Upot vdW gas x expansion

  8. The JT Process in Real Gases (high density) Upot x At high densities, the effect is reversed: the sign of T depends on initial T and P. expansion

  9. The JT Process in Real Gases (cont.) All gases have two inversion temperatures: in the range between the upper and lower inversion temperatures, the JT process cools the gas, outside this range it heats the gas. heating cooling

  10. Liquefaction of Gases For air, the inversion T is above RT. In 1885, Carl von Linde liquefied air in a liquefier based solely on the JT process: Linde refrigerator

  11. “Efficiency” of liquefaction Estimate of efficiency: let 1 mole of gas enter the liquefier, suppose that the fraction  is liquefied. Liquefaction takes place if

  12. Example (Pr. 4.34, Pg 143) The fraction of N2 liquefied on each pass through a Linde cycle operating between Pin = 100 bar and Pout = 1 bar at Tin = 200 K:

  13. Historical Development of Refrigeration 103 Faraday, chlorine 1823 02 N2 102 H2 101 Kamerlingh- Onnes 4He Low T 3He 100 10-1 Magnetic refrigeration, electronic mag. moments 10-2 3He-4He, Ultra-low T 10-3 Magnetic refrigeration, nuclear mag. moments 10-4 10-5 1840 1860 1880 1980 1900 1920 1940 1960 2000

  14. Cooling by Evaporation of Liquids  Q – the cooling power, dn/dt – the number of molecules moved across the liquid/vapor interface Usually a pump with a constant-volume pumping speed is used, and thus the mass flow dn/dt is proportional to the vapor pressure. Pr. 5.35

  15. Cryoliquids the cooling power diminishes rapidly with decreasing T (at T0, S becomes small for all processes) the evaporation cooling of Liquid Helium

  16. A liquid with suitable characteristics (e.g., Freon) circulates through the system. The compressor pushes the liquid through the condenser coil at a high pressure (~ 10 atm). The liquid sprays through a throttling valve into the evaporation coil which is maintained by the compressor at a low pressure (~ 2 atm). Kitchen Refrigerator condenser P processes at P = const, Q=dH 2 3 liquid throttling valve compressor 1 4 cold reservoir (fridge interior) T=50C gas liquid+gas V evaporator The enthalpies Hi can be found in tables. hot reservoir (fridge exterior) T=250C

  17. Dilution Refrigerator (down to a few mK) evaporation cooling with a non-exponential dependence Pvap(T) H – the enthalpy difference between the 3He-rich and dilute phases

  18. B1 S/NkB 1 B2>B1 3 2 Tf Ti kBT/ B the slope ~ T 1 Ei Cooling by Adiabatic Demagnetization Let’s consider a quantum system with Boltzmann distribution of population probabilities for two discrete levels: B1 - lnni 1 – 2- Isothermal increase of B from B1 to B2 . The upper energy level rises because W has been done by external forces. If T = const, the work performed must be followed by population rearrangement, so that the red line is shifted, but its slope ~ T remains the same: e.g., if the magnetic field is increased, the population must decrease at the highest level and increase at the lowest – S decreases! Ei 2 B2 - lnni 2 – 3- Adiabatic decrease of B(the specimen is thermally isolated). S = const: the population of each level must be kept constant, while its Ei varies. The red line slope decreases – T decreases! 3 Ei B3 - lnni

  19. Nobel Prize in Physics 1997 Laser cooling • Very dilute gas (avoid condensing) • Momentum transfer from photons  slowing down of molecules  TK.E. decrease http://www.colorado.edu/physics/2000/bec/lascool1.html

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