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31:
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end of the cooler. By bending the PTR we get a U-shaped cooler. Both hot ends can be mounted on the flange of the vacuum chamber at room temperature. This is the most common shape of PTRs. For some applications it is preferable to have a cylindrical geometry. In that case the PTR can be constructed in a coaxial way so that the regenerator becomes a ring-shaped space surrounding the tube.
1889:
2441:
connects the high-pressure and the low-pressure side of the compressor to the hot end of the regenerator. As the high-temperature part of this type of PTR is the same as of GM-coolers, this type of PTR is called a GM-type PTR. The gas flows through the valves are accompanied by losses which are absent in the
Stirling-type PTR.
2508:, and filters for telecommunication. PTRs are also suitable for cooling MRI-systems and energy-related systems using superconducting magnets. In so-called dry magnets, coolers are used so that no cryoliquid is needed at all or for the recondensation of the evaporated helium. Also the combination of cryocoolers with He-He
2375:
coolers and the popular
Gifford-McMahon coolers have a displacer that ensures that the cooling (due to expansion) takes place in a different region of the machine than the heating (due to compression). Due to its clever design, the PTR does not have such a displacer, making the construction of a PTR
2452:
K. However, one PTR can be used to precool the other. The hot end of the second tube is connected to room temperature and not to the cold end of the first stage. In this clever way it is avoided that the heat, released at the hot end of the second tube, is a load on the first stage. In applications
2444:
PTRs can be classified according to their shape. If the regenerator and the tube are in line (as in fig. 1) we talk about a linear PTR. The disadvantage of the linear PTR is that the cold spot is in the middle of the cooler. For many applications it is preferable that the cooling is produced at the
2035:
Figure 3 shows a coaxial pulse tube, which is a more useful configuration in which the regenerator surrounds the central pulse tube. This is compact and places the cold head at an end, so it is easy to integrate with whatever is to be cooled. The displacer can be passively driven, and this recovers
2044:
The performance of the cooler is determined mainly by the quality of the regenerator. It has to satisfy conflicting requirements: it must have a low flow resistance (so it must be short with wide channels), but the heat exchange should also be good (so it must be long with narrow channels). The
2440:
K usually operate at frequencies of 1 to 2 Hz and with pressure variations from 10 to 25 bar. The swept volume of the compressor would be very high (up to one liter and more). Therefore, the compressor is uncoupled from the cooler. A system of valves (usually a rotating valve) alternately
2531:(STMs) have historically difficult due to the extreme vibration sensitivity of STM. Use of an exchange gas above the vibration sensitive scanning head enabled the first PTR based low temperature STMs. Now, there are commercially available PTR-based, cryogen free scanning probe systems.
1938:
The piston moves periodically from left to right and back. As a result, the gas also moves from left to right and back while the pressure within the system increases and decreases. If the gas from the compressor space moves to the right, it enters the regenerator with temperature
2396:
W. E. Gifford and R. C. Longsworth, in the 1960s, invented the so-called Basic Pulse Tube
Refrigerator. The modern PTR was invented in 1984 by Mikulin who introduced an orifice to the basic pulse tube. He reached a temperature of
1320:
2270:
1934:
is thermally insulated from the surroundings, usually by vacuum. The pressure varies gradually and the velocities of the gas are low. So the name "pulse" tube cooler is misleading, since there are no pulses in the system.
2376:
simpler, cheaper, and more reliable. Furthermore, there are no mechanical vibrations and no electro-magnetic interferences. The basic operation of cryocoolers and related thermal machines is described by De Waele
2345:
1818:
medium with a large specific heat (which can be stainless steel wire mesh, copper wire mesh, phosphor bronze wire mesh, lead balls, lead shot, or rare earth materials) in which the gas flows back and forth
2172:
1995:(at the hot end), which move in and out of the tube through the orifice. Molecules flow into the tube (to the left) when the pressure in the tube is low (it is sucked into the tube via X
2118:
1859:
2401:
K. Soon after that, PTRs became better due to the invention of new variations. This is shown in figure 4, where the lowest temperature for PTRs is plotted as a function of time.
2453:
the first stage also operates as a temperature-anchoring platform for e.g. shield cooling of superconducting-magnet cryostats. Matsubara and Gao were the first to cool below 4
2006:. Later in the cycle, the same mass of gas is pushed out from the tube again when the pressure inside the tube is high. As a consequence, its temperature will be higher than
2288:
However, a pulse-tube refrigerator is not perfectly reversible due to the presence of the orifice, which has flow resistance. Instead, the COP of an ideal PTR is given by
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990:
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489:
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781:
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561:
514:
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The coefficient of performance of PTRs at room temperature is low, so it is not likely that they will play a role in domestic cooling. However, below about 80
2392:
K was reached in a collaboration between the groups of
Giessen and Eindhoven. They used a superfluid vortex cooler as an additional cooling stage to the PTR.
3147:
Gan, Z.H.; Dong, W.Q.; Qiu, L.M.; Zhang, X.B.; Sun, H.; He, Y.L.; Radebaugh, R. (2009). "A single-stage GM-type pulse tube cryocooler operating at 10.6K".
453:
2420:
K by replacing the usual He as refrigerant by its rare isotope He. Later this record was broken by the
Giessen Group that managed to get even below 1.3
2206:
1309:
3022:
2408:
K). Originally this was considered to be impossible. For some time it looked as if it would be impossible to cool below the lambda point of He (2.17
1953:, hence heat is transferred into the regenerator material. On its return, the heat stored within the regenerator is transferred back into the gas.
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1342:
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2550:
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where it is not possible to replenish the cryogens as they are depleted. It has also been suggested that pulse tubes could be used to liquefy
2919:
2855:
2822:
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912:
2489:)) and in the low-temperature region the advantages get the upper hand. PTRs are commercially available for temperatures in the region of 70
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2883:(2). Transactions of the Japan Society of Refrigerating and Air Conditioning Engineers, Volume 11, Issue 2, pp. 89-99: 89–99.
1655:
is a developing technology that emerged largely in the early 1980s with a series of other innovations in the broader field of
1991:
To understand why the low-pressure gas returns at a lower temperature, look at figure 1 and consider gas molecules close to X
1547:
79:
1956:
In the tube, the gas is thermally isolated (adiabatic), so the temperature of the gas in the tube varies with the pressure.
1442:
3091:. Proceedings of the 17th International Cryogenic Engineering Conference. Institute of Physics Publishing. pp. 11–16.
3809:
3483:
3190:
Matsubara, Y.; Gao, J.L. (1994). "Novel configuration of three-stage pulse tube refrigerator for temperatures below 4 K".
2978:
Matsubara, Y.; Gao, J.L. (1994). "Novel configuration of three-stage pulse tube refrigerator for temperatures below 4 K".
2528:
1782:
Figure 1 represents the
Stirling-type single-orifice pulse-tube refrigerator (PTR), which is filled with a gas, typically
1522:
1295:
272:
3710:
1748:
Figure 1: Schematic drawing of a
Stirling-type single-orifice PTR. From left to right: a compressor, a heat exchanger (X
907:
110:
100:
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on measurement lines, which is a big disadvantage of PTRs. Particularly for scanning probe microscopy uses, PTR-based
1713:
115:
105:
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K practically all materials are suitable. Bronze or stainless steel is often used. For temperatures between 10 and 50
3624:
3514:
2061:
1725:
1437:
1399:
1363:
75:
2935:
Zhu, Shaowei; Wu, Peiyi; Chen, Zhongqi (1990). "Double inlet pulse tube refrigerators: an important improvement".
2784:
2127:
3778:
1192:
940:
386:
199:
189:
3733:
2691:
David, M.; Maréchal, J.-C.; Simon, Y.; Guilpin, C. (1993). "Theory of ideal orifice pulse tube refrigerator".
3758:
3689:
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K. They are applied in infrared detection systems, for reduction of thermal noise in devices based on (high-
1604:
1432:
1229:
932:
871:
407:
396:
62:
2087:
1828:
2838:
Longsworth, R. C. (1967). "An
Experimental Investigation of Pulse Tube Refrigeration Heat Pumping Rates".
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in the low temperature part of the device, making the cooler suitable for a wide variety of applications.
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1254:
338:
92:
67:
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1702:
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362:
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57:
3386:"Development of a near-5-Kelvin, cryogen-free, pulse-tube refrigerator-based scanning probe microscope"
3321:"Development of a near-5-Kelvin, cryogen-free, pulse-tube refrigerator-based scanning probe microscope"
3748:
3407:
3342:
3242:
3156:
3051:
2944:
2902:
Mikulin, E. I.; Tarasov, A. A.; Shkrebyonock, M. P. (1984). "Low-Temperature
Expansion Pulse Tubes".
2884:
2747:
2700:
2545:
1764:), a flow resistance (orifice), and a buffer volume. The cooling is generated at the low temperature
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2436:
For cooling, the source of the pressure variations is unimportant. PTRs for temperatures below 20
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1249:
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1000:
429:
413:
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252:
237:
227:
36:
30:
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Zu, H.; Dai, W.; de Waele, A.T.A.M. (2022). "Development of dilution refrigerators – A review".
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834:
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702:
655:
567:
520:
2606:. Proceedings of the Institute of Refrigeration (London) 1999–2000. Institute of Refrigeration.
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In most coolers gas is compressed and expanded periodically. Well-known coolers such as the
1717:
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1502:
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1422:
1239:
1234:
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884:
352:
217:
3116:. Advances in Cryogenic Engineering: Transactions of the Cryogenic Engineering Conference.
3738:
2372:
2177:
2067:
1999:, coming from the orifice and the buffer). Upon entering the tube, it has the temperature
1721:
1687:
1684:
1656:
1452:
1300:
954:
595:
418:
179:
146:
2516:
mK is attractive since in this way the whole temperature range from room temperature to 2
3411:
3346:
3246:
3160:
3055:
2948:
2888:
2751:
2704:
2424:
K. In a collaboration between the groups from
Giessen and Eindhoven a temperature of 1.2
471:
3705:
3664:
3649:
3634:
3569:
3559:
3554:
3529:
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K, so just above the λ-point of helium, have been obtained. With a three-stage PTR 1.73
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52:
22:
3254:
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Xu, M.Y.; De Waele, A.T.A.M.; Ju, Y.L. (1999). "A pulse tube refrigerator below 2 K".
3063:
3042:
Xu, M.Y.; De Waele, A.T.A.M.; Ju, Y.L. (1999). "A pulse tube refrigerator below 2 K".
2674:
2477:
K the coefficient of performance is comparable with other coolers (compare equations (
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3574:
3544:
3539:
3305:
3289:
3219:
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For many low temperature experiments, mechanical vibrations caused by PTRs can cause
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894:
463:
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136:
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3112:
Tanaeva, I. A.; Lindemann, U.; Jiang, N.; de Waele, A.T.A.M.; Thummes, G. (2004).
2616:
2600:
Development of the Pulse Tube Refrigerator as an Efficient and Reliable Cryocooler
2416:
of the Eindhoven University of Technology managed to cool to a temperature of 1.73
2384:
2057:
K one uses magnetic materials which are specially developed for this application.
2027:
1720:(an interferometer for cosmology studies). Pulse tubes are particularly useful in
2911:
2877:
Transactions of the Japan Society of Refrigerating and Air Conditioning Engineers
2847:
2814:
2265:{\displaystyle \xi _{\text{C}}={\frac {T_{\text{L}}}{T_{\text{H}}-T_{\text{L}}}}}
3024:
Pulsröhrenkühler zur Erzeugung von Temperaturen im Bereich des flüssigen Heliums
1786:
at a pressure varying from 10 to 30 bar. From left to right the components are:
1482:
290:
2570:
Riabzev, S. V.; Pundak, N.; Leshets, A.; Meromi, A.; Veprik, A. M. (2001). "".
2404:
At the moment, the lowest temperature is below the boiling point of helium (4.2
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1664:
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1517:
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169:
3427:
3370:
3319:
Kasai, Jun; Koyama, Tomoki; Yokota, Munenori; Iwaya, Katsuya (2022-04-01).
3029:
Pulse tube cooler for generating temperatures in the range of liquid helium
1691:
1679:
Pulse tube cryocoolers are used in niche industrial applications such as
1285:
1202:
994:
402:
174:
3470:
2638:
2388:
Figure 4: The temperature of PTRs over the years. The temperature of 1.2
1888:
1884:
a buffer volume (a large closed volume at practically constant pressure)
3475:
391:
3419:
3354:
3125:
3031:]. DKV-Tagungsbericht (in German). Vol. 23. pp. 147–159.
2448:
The lowest temperature reached with single-stage PTRs is just above 10
2340:{\displaystyle \xi _{\text{PTR}}={\frac {T_{\text{L}}}{T_{\text{H}}}}}
3384:
Kasai, Jun; Koyama, Tomoki; Yokota, Munenori; Iwaya, Katsuya (2022).
1815:
1791:
1783:
1729:
3320:
3402:
3337:
2805:
Gifford, W. E.; Longsworth, R. C. (1965). "Surface Heat Pumping".
2505:
2428:
K was reached by combining a PTR with a superfluid vortex cooler.
2045:
material must have a large heat capacity. At temperatures above 50
2026:
1887:
2457:
K with a three-stage PTR. With two-stage PTRs temperatures of 2.1
3455:
1878:
near room temperature where heat is released to the surroundings
1733:
367:
3479:
2084:) of coolers is defined as the ratio between the cooling power
1811:
where heat is released to the surroundings at room temperature
2736:"Basic Operation of Cryocoolers and Related Thermal Machines"
2663:. Vol. 45A. Montreal, Quebec, Canada. pp. 457–464.
2017:, it releases heat and cools down to the ambient temperature
2628:
QUBIC Bolometric interferometry: the concept (official site)
1946:
and leaves the regenerator at the cold end with temperature
3460:
2906:. Vol. 29. Boston, MA: Springer US. pp. 629–637.
2572:
Journal of Superconductivity: Incorporating Novel Magnetism
1959:
At the cold end of the tube, the gas enters the tube via X
2746:(5–6). Springer Science and Business Media LLC: 179–236.
2627:
2036:
work that would otherwise be dissipated in the orifice.
1970:
and returns when the pressure is low with a temperature
2659:. Proceedings of the Cryogenic Engineering Conference.
3021:
Thummes, G.; Wang, C.; Bender, S.; Heiden, C. (1996).
1712:
where liquid cryogens are typically used, such as the
3471:
The James Webb Space Telescope Cryocooler (JWST/NASA)
2639:
The James Webb Space Telescope Cryocooler (JWST/NASA)
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1825:, cooled by the gas, where the useful cooling power
3724:
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3623:
3583:
3524:
3513:
3451:A Short History of Pulse Tube Refrigerators (NASA)
2465:K has been reached using He as the working fluid.
2339:
2264:
2186:
2166:
2112:
2076:
1915:): a gas element enters the tube with temperature
1900:): a gas element enters the tube with temperature
1853:
1701:In research, PTRs are often used as precoolers of
1149:
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1039:
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1705:. They are also being developed for cooling of
3491:
2031:Figure 3: Coaxial pulse tube with a displacer
1624:
8:
2167:{\displaystyle \xi ={\dot {Q}}_{\text{L}}/P}
1984:: this gives the desired cooling effect at X
1871:a tube in which the gas is pushed and pulled
3118:Unsolved Problems of Noise and Fluctuations
2363:which is lower than that of ideal coolers.
1963:when the pressure is high with temperature
1659:. In contrast with other cryocoolers (e.g.
3521:
3498:
3484:
3476:
3120:. Vol. 49B. AIP. pp. 1906–1913.
2783:Gifford, W. E.; Longsworth, R. C. (1964).
1794:moving back and forth at room temperature
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1617:
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29:
18:
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1002:
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522:
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3466:Pulse-tube animation (Thales Cryogenics)
3088:Classification of pulse tube cryocoolers
2650:Marquardt, E.D.; Radebaugh, Ray (2000).
2383:
1922:and leaves it with a higher temperature.
1907:and leaves it with a lower temperature.
1881:a flow resistance (often called orifice)
1743:
1694:applications such as for the cooling of
3660:Homogeneous charge compression ignition
2562:
1667:), this cryocooler can be made without
1377:
1354:
1308:
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1218:
1183:
376:
351:
280:
207:
154:
21:
16:Device using sound waves to reduce heat
2734:de Waele, A. T. A. M. (10 June 2011).
2551:Timeline of low-temperature technology
2174:. For a perfectly reversible cooler,
2113:{\displaystyle {\dot {Q}}_{\text{L}}}
1854:{\displaystyle {\dot {Q}}_{\text{L}}}
1752:), a regenerator, a heat exchanger (X
7:
2512:for the temperature region down to 2
2290:
2200:
1868:, taken from the object to be cooled
1861:is delivered at the low temperature
2785:"Pulse Tube Refrigeration Progress"
2842:. Vol. 12. pp. 608–618.
2809:. Vol. 11. pp. 171–179.
2740:Journal of Low Temperature Physics
838:
791:
706:
659:
571:
524:
344:Intensive and extensive properties
14:
2904:Advances in Cryogenic Engineering
2840:Advances in Cryogenic Engineering
2807:Advances in Cryogenic Engineering
2661:Advances in Cryogenic Engineering
2053:K lead is most suitable. Below 10
3390:Review of Scientific Instruments
3325:Review of Scientific Instruments
3290:10.1016/j.cryogenics.2021.103390
3169:10.1016/j.cryogenics.2009.01.004
2792:Cryogenic Engineering Conference
1690:circuits. They are also used in
1600:
1599:
919:Table of thermodynamic equations
1395:Maxwell's thermodynamic surface
2529:scanning tunneling microscopes
1814:a regenerator consisting of a
1129:
1117:
1074:
1062:
1019:
1007:
979:
967:
1:
3255:10.1016/s0011-2275(99)00101-0
3064:10.1016/s0011-2275(99)00101-0
2794:. University of Pennsylvania.
2367:Comparison with other coolers
1980:, hence taking up heat from X
1296:Mechanical equivalent of heat
3241:(10). Elsevier BV: 865–869.
3204:10.1016/0011-2275(94)90104-x
3050:(10). Elsevier BV: 865–869.
2992:10.1016/0011-2275(94)90104-x
2957:10.1016/0011-2275(90)90051-d
2912:10.1007/978-1-4613-9865-3_72
2848:10.1007/978-1-4757-0489-1_63
2815:10.1007/978-1-4757-0522-5_18
2713:10.1016/0011-2275(93)90129-c
2504:) superconductivity such as
908:Onsager reciprocal relations
3565:Stirling (pseudo/adiabatic)
3198:(4). Elsevier BV: 259–262.
3155:(5). Elsevier BV: 198–201.
2986:(4). Elsevier BV: 259–262.
2943:(6). Elsevier BV: 514–520.
2699:(2). Elsevier BV: 154–161.
2653:Pulse Tube Oxygen Liquefier
2485:
2479:
1714:Atacama Cosmology Telescope
1400:Entropy as energy dispersal
1211:"Perpetual motion" machines
1150:{\displaystyle G(T,p)=H-TS}
1095:{\displaystyle A(T,V)=U-TS}
1040:{\displaystyle H(S,p)=U+pV}
3826:
2871:Matsubara, Yoichi (1994).
2062:coefficient of performance
1726:James Webb Space Telescope
847:{\displaystyle \partial T}
800:{\displaystyle \partial V}
715:{\displaystyle \partial p}
668:{\displaystyle \partial V}
580:{\displaystyle \partial T}
533:{\displaystyle \partial S}
3456:SHI Cryogenics Group Home
2873:"Pulse Tube Refrigerator"
2761:10.1007/s10909-011-0373-x
2617:About ACT (official site)
2120:and the compressor power
2013:. In the heat exchanger X
1321:An Inquiry Concerning the
3114:Superfluid Vortex Cooler
2520:mK is easier to access.
1756:), a tube (often called
1334:Heterogeneous Substances
751:{\displaystyle \alpha =}
619:{\displaystyle \beta =-}
2597:Radebough, Ray (1999).
2584:10.1023/A:1007876004471
1645:pulse tube refrigerator
3085:Matsubara, Y. (1998).
2510:dilution refrigerators
2393:
2341:
2266:
2188:
2168:
2114:
2078:
2032:
1923:
1855:
1779:
1771:. Room temperature is
1760:), a heat exchanger (X
1740:Principle of operation
1722:space-based telescopes
1703:dilution refrigerators
1151:
1096:
1041:
986:
985:{\displaystyle U(S,V)}
848:
824:
801:
777:
752:
716:
692:
669:
645:
620:
581:
557:
534:
510:
485:
464:Specific heat capacity
68:Quantum thermodynamics
2414:low-temperature group
2387:
2342:
2267:
2189:
2169:
2115:
2079:
2030:
1926:The part in between X
1891:
1856:
1790:a compressor, with a
1747:
1653:pulse tube cryocooler
1332:On the Equilibrium of
1152:
1097:
1050:Helmholtz free energy
1042:
987:
849:
825:
802:
778:
753:
717:
693:
670:
646:
621:
582:
558:
535:
511:
486:
3810:Thermodynamic cycles
3749:Regenerative cooling
3627:combustion / thermal
3526:Without phase change
3517:combustion / thermal
3507:Thermodynamic cycles
2680:on 18 November 2017.
2546:Regenerative cooling
2297:
2207:
2187:{\displaystyle \xi }
2178:
2128:
2088:
2077:{\displaystyle \xi }
2068:
1829:
1345:Motive Power of Fire
1111:
1056:
1001:
961:
913:Bridgman's equations
890:Fundamental relation
835:
814:
788:
767:
739:
703:
682:
656:
635:
604:
568:
547:
521:
500:
472:
3412:2022RScI...93d3711K
3347:2022RScI...93d3711K
3247:1999Cryo...39..865X
3161:2009Cryo...49..198G
3056:1999Cryo...39..865X
2949:1990Cryo...30..514S
2889:2011TRACE..11...89M
2752:2011JLTP..164..179D
2705:1993Cryo...33..154D
1661:Stirling cryocooler
1323:Source ... Friction
1255:Loschmidt's paradox
447:Material properties
325:Conjugate variables
3800:Cooling technology
2394:
2337:
2262:
2184:
2164:
2110:
2074:
2033:
1924:
1874:a heat exchanger X
1851:
1821:a heat exchanger X
1780:
1587:Order and disorder
1343:Reflections on the
1250:Heat death paradox
1147:
1092:
1037:
982:
844:
820:
797:
773:
748:
712:
688:
665:
641:
616:
577:
553:
530:
506:
484:{\displaystyle c=}
481:
454:Property databases
430:Reduced properties
414:Chemical potential
378:Functions of state
301:Thermal efficiency
37:Carnot heat engine
3787:
3786:
3764:Vapor-compression
3690:Staged combustion
3619:
3618:
3584:With phase change
3420:10.1063/5.0084888
3355:10.1063/5.0084888
3126:10.1063/1.1774894
2921:978-1-4613-9867-7
2857:978-1-4757-0491-4
2824:978-1-4757-0524-9
2670:978-0-306-46443-0
2361:
2360:
2335:
2332:
2322:
2307:
2286:
2285:
2260:
2256:
2243:
2232:
2217:
2153:
2147:
2107:
2101:
1848:
1842:
1641:
1640:
1582:Self-organization
1407:
1406:
1105:Gibbs free energy
903:Maxwell relations
861:
860:
857:
856:
823:{\displaystyle V}
776:{\displaystyle 1}
731:Thermal expansion
725:
724:
691:{\displaystyle V}
644:{\displaystyle 1}
590:
589:
556:{\displaystyle N}
509:{\displaystyle T}
437:
436:
353:Process functions
339:Property diagrams
318:System properties
308:
307:
273:Endoreversibility
165:Equation of state
3817:
3759:Vapor absorption
3522:
3500:
3493:
3486:
3477:
3438:
3437:
3435:
3434:
3405:
3381:
3375:
3374:
3340:
3316:
3310:
3309:
3273:
3267:
3266:
3230:
3224:
3223:
3187:
3181:
3180:
3144:
3138:
3137:
3109:
3103:
3102:
3082:
3076:
3075:
3039:
3033:
3032:
3018:
3012:
3011:
2975:
2969:
2968:
2932:
2926:
2925:
2899:
2893:
2892:
2868:
2862:
2861:
2835:
2829:
2828:
2802:
2796:
2795:
2789:
2780:
2774:
2773:
2763:
2731:
2725:
2724:
2688:
2682:
2681:
2679:
2673:. Archived from
2658:
2647:
2641:
2636:
2630:
2625:
2619:
2614:
2608:
2607:
2605:
2594:
2588:
2587:
2567:
2519:
2515:
2496:
2492:
2476:
2464:
2460:
2456:
2451:
2439:
2427:
2423:
2419:
2411:
2407:
2400:
2391:
2355:
2346:
2344:
2343:
2338:
2336:
2334:
2333:
2330:
2324:
2323:
2320:
2314:
2309:
2308:
2305:
2291:
2280:
2271:
2269:
2268:
2263:
2261:
2259:
2258:
2257:
2254:
2245:
2244:
2241:
2234:
2233:
2230:
2224:
2219:
2218:
2215:
2201:
2196:Carnot's theorem
2193:
2191:
2190:
2185:
2173:
2171:
2170:
2165:
2160:
2155:
2154:
2151:
2149:
2148:
2140:
2119:
2117:
2116:
2111:
2109:
2108:
2105:
2103:
2102:
2094:
2083:
2081:
2080:
2075:
2056:
2052:
2048:
1860:
1858:
1857:
1852:
1850:
1849:
1846:
1844:
1843:
1835:
1718:Qubic experiment
1696:infrared sensors
1683:fabrication and
1665:GM-refrigerators
1633:
1626:
1619:
1603:
1602:
1310:Key publications
1291:
1290:("living force")
1240:Brownian ratchet
1235:Entropy and life
1230:Entropy and time
1181:
1156:
1154:
1153:
1148:
1101:
1099:
1098:
1093:
1046:
1044:
1043:
1038:
991:
989:
988:
983:
885:Clausius theorem
880:Carnot's theorem
853:
851:
850:
845:
829:
827:
826:
821:
806:
804:
803:
798:
782:
780:
779:
774:
761:
760:
757:
755:
754:
749:
721:
719:
718:
713:
697:
695:
694:
689:
674:
672:
671:
666:
650:
648:
647:
642:
629:
628:
625:
623:
622:
617:
586:
584:
583:
578:
562:
560:
559:
554:
539:
537:
536:
531:
515:
513:
512:
507:
494:
493:
490:
488:
487:
482:
460:
459:
333:
152:
33:
19:
3825:
3824:
3820:
3819:
3818:
3816:
3815:
3814:
3790:
3789:
3788:
3783:
3720:
3694:
3626:
3615:
3605:Organic Rankine
3579:
3533:
3530:hot air engines
3527:
3516:
3509:
3504:
3447:
3442:
3441:
3432:
3430:
3383:
3382:
3378:
3318:
3317:
3313:
3275:
3274:
3270:
3232:
3231:
3227:
3189:
3188:
3184:
3146:
3145:
3141:
3111:
3110:
3106:
3099:
3084:
3083:
3079:
3041:
3040:
3036:
3020:
3019:
3015:
2977:
2976:
2972:
2934:
2933:
2929:
2922:
2901:
2900:
2896:
2870:
2869:
2865:
2858:
2837:
2836:
2832:
2825:
2804:
2803:
2799:
2787:
2782:
2781:
2777:
2733:
2732:
2728:
2690:
2689:
2685:
2677:
2671:
2656:
2649:
2648:
2644:
2637:
2633:
2626:
2622:
2615:
2611:
2603:
2596:
2595:
2591:
2569:
2568:
2564:
2559:
2537:
2517:
2513:
2503:
2494:
2490:
2474:
2471:
2462:
2458:
2454:
2449:
2437:
2434:
2425:
2421:
2417:
2409:
2405:
2398:
2389:
2382:
2373:Stirling engine
2369:
2353:
2325:
2315:
2300:
2295:
2294:
2278:
2249:
2236:
2235:
2225:
2210:
2205:
2204:
2176:
2175:
2137:
2126:
2125:
2091:
2086:
2085:
2066:
2065:
2054:
2050:
2046:
2042:
2023:
2016:
2012:
2005:
1998:
1994:
1987:
1983:
1979:
1969:
1962:
1952:
1945:
1933:
1929:
1921:
1914:
1906:
1899:
1877:
1867:
1832:
1827:
1826:
1824:
1810:
1800:
1777:
1770:
1763:
1755:
1751:
1742:
1688:radio-frequency
1685:superconducting
1677:
1657:thermoacoustics
1637:
1592:
1591:
1567:
1559:
1558:
1557:
1417:
1409:
1408:
1387:
1373:
1348:
1344:
1337:
1333:
1326:
1322:
1289:
1282:
1264:
1245:Maxwell's demon
1207:
1178:
1177:
1161:
1160:
1159:
1109:
1108:
1107:
1054:
1053:
1052:
999:
998:
997:
959:
958:
957:
955:Internal energy
950:
935:
925:
924:
899:
874:
864:
863:
862:
833:
832:
812:
811:
786:
785:
765:
764:
737:
736:
701:
700:
680:
679:
654:
653:
633:
632:
602:
601:
596:Compressibility
566:
565:
545:
544:
519:
518:
498:
497:
470:
469:
449:
439:
438:
419:Particle number
372:
331:
320:
310:
309:
268:Irreversibility
180:State of matter
147:Isolated system
132:
122:
121:
120:
95:
85:
84:
80:Non-equilibrium
72:
47:
39:
17:
12:
11:
5:
3823:
3821:
3813:
3812:
3807:
3802:
3792:
3791:
3785:
3784:
3782:
3781:
3776:
3771:
3766:
3761:
3756:
3751:
3746:
3741:
3736:
3730:
3728:
3722:
3721:
3719:
3718:
3713:
3708:
3702:
3700:
3696:
3695:
3693:
3692:
3687:
3682:
3677:
3672:
3667:
3662:
3657:
3652:
3647:
3642:
3637:
3631:
3629:
3621:
3620:
3617:
3616:
3614:
3613:
3608:
3598:
3593:
3587:
3585:
3581:
3580:
3578:
3577:
3572:
3567:
3562:
3557:
3552:
3547:
3542:
3536:
3534:
3525:
3519:
3511:
3510:
3505:
3503:
3502:
3495:
3488:
3480:
3474:
3473:
3468:
3463:
3458:
3453:
3446:
3445:External links
3443:
3440:
3439:
3376:
3311:
3268:
3225:
3182:
3139:
3104:
3097:
3077:
3034:
3013:
2970:
2927:
2920:
2894:
2863:
2856:
2830:
2823:
2797:
2775:
2726:
2683:
2669:
2642:
2631:
2620:
2609:
2589:
2561:
2560:
2558:
2555:
2554:
2553:
2548:
2543:
2536:
2533:
2501:
2470:
2467:
2433:
2430:
2381:
2378:
2368:
2365:
2359:
2358:
2349:
2347:
2328:
2318:
2312:
2303:
2284:
2283:
2274:
2272:
2252:
2248:
2239:
2228:
2222:
2213:
2183:
2163:
2159:
2146:
2143:
2136:
2133:
2124:. In formula:
2100:
2097:
2073:
2064:(COP; denoted
2060:The so-called
2041:
2038:
2021:
2014:
2010:
2003:
1996:
1992:
1985:
1981:
1977:
1967:
1960:
1950:
1943:
1931:
1927:
1919:
1912:
1904:
1897:
1886:
1885:
1882:
1879:
1875:
1872:
1869:
1865:
1841:
1838:
1822:
1819:
1812:
1808:
1805:heat exchanger
1801:
1798:
1775:
1768:
1761:
1758:the pulse tube
1753:
1749:
1741:
1738:
1676:
1673:
1639:
1638:
1636:
1635:
1628:
1621:
1613:
1610:
1609:
1608:
1607:
1594:
1593:
1590:
1589:
1584:
1579:
1574:
1568:
1565:
1564:
1561:
1560:
1556:
1555:
1550:
1545:
1540:
1535:
1530:
1525:
1520:
1515:
1510:
1505:
1500:
1495:
1490:
1485:
1480:
1475:
1470:
1465:
1460:
1455:
1450:
1445:
1440:
1435:
1430:
1425:
1419:
1418:
1415:
1414:
1411:
1410:
1405:
1404:
1403:
1402:
1397:
1389:
1388:
1386:
1385:
1382:
1378:
1375:
1374:
1372:
1371:
1366:
1364:Thermodynamics
1360:
1357:
1356:
1352:
1351:
1350:
1349:
1340:
1338:
1329:
1327:
1318:
1313:
1312:
1306:
1305:
1304:
1303:
1298:
1293:
1281:
1280:
1278:Caloric theory
1274:
1271:
1270:
1266:
1265:
1263:
1262:
1257:
1252:
1247:
1242:
1237:
1232:
1226:
1223:
1222:
1216:
1215:
1214:
1213:
1206:
1205:
1200:
1195:
1189:
1186:
1185:
1179:
1176:
1175:
1172:
1168:
1167:
1166:
1163:
1162:
1158:
1157:
1146:
1143:
1140:
1137:
1134:
1131:
1128:
1125:
1122:
1119:
1116:
1102:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1061:
1047:
1036:
1033:
1030:
1027:
1024:
1021:
1018:
1015:
1012:
1009:
1006:
992:
981:
978:
975:
972:
969:
966:
951:
949:
948:
943:
937:
936:
931:
930:
927:
926:
923:
922:
915:
910:
905:
898:
897:
892:
887:
882:
876:
875:
870:
869:
866:
865:
859:
858:
855:
854:
843:
840:
830:
819:
808:
807:
796:
793:
783:
772:
758:
747:
744:
734:
727:
726:
723:
722:
711:
708:
698:
687:
676:
675:
664:
661:
651:
640:
626:
615:
612:
609:
599:
592:
591:
588:
587:
576:
573:
563:
552:
541:
540:
529:
526:
516:
505:
491:
480:
477:
467:
458:
457:
456:
450:
445:
444:
441:
440:
435:
434:
433:
432:
427:
422:
411:
400:
381:
380:
374:
373:
371:
370:
365:
359:
356:
355:
349:
348:
347:
346:
341:
322:
321:
316:
315:
312:
311:
306:
305:
304:
303:
298:
293:
285:
284:
278:
277:
276:
275:
270:
265:
260:
258:Free expansion
255:
250:
245:
240:
235:
230:
225:
220:
212:
211:
205:
204:
203:
202:
197:
195:Control volume
192:
187:
185:Phase (matter)
182:
177:
172:
167:
159:
158:
150:
149:
144:
139:
133:
128:
127:
124:
123:
119:
118:
113:
108:
103:
97:
96:
91:
90:
87:
86:
83:
82:
71:
70:
65:
60:
55:
49:
48:
45:
44:
41:
40:
35:The classical
34:
26:
25:
23:Thermodynamics
15:
13:
10:
9:
6:
4:
3:
2:
3822:
3811:
3808:
3806:
3803:
3801:
3798:
3797:
3795:
3780:
3777:
3775:
3772:
3770:
3767:
3765:
3762:
3760:
3757:
3755:
3754:Transcritical
3752:
3750:
3747:
3745:
3742:
3740:
3737:
3735:
3734:Hampson–Linde
3732:
3731:
3729:
3727:
3726:Refrigeration
3723:
3717:
3714:
3712:
3709:
3707:
3704:
3703:
3701:
3697:
3691:
3688:
3686:
3683:
3681:
3678:
3676:
3673:
3671:
3668:
3666:
3663:
3661:
3658:
3656:
3655:Gas-generator
3653:
3651:
3648:
3646:
3643:
3641:
3640:Brayton/Joule
3638:
3636:
3633:
3632:
3630:
3628:
3622:
3612:
3609:
3606:
3602:
3599:
3597:
3594:
3592:
3589:
3588:
3586:
3582:
3576:
3573:
3571:
3568:
3566:
3563:
3561:
3558:
3556:
3553:
3551:
3548:
3546:
3545:Brayton/Joule
3543:
3541:
3538:
3537:
3535:
3531:
3523:
3520:
3518:
3512:
3508:
3501:
3496:
3494:
3489:
3487:
3482:
3481:
3478:
3472:
3469:
3467:
3464:
3462:
3461:Cryomech Home
3459:
3457:
3454:
3452:
3449:
3448:
3444:
3429:
3425:
3421:
3417:
3413:
3409:
3404:
3399:
3396:(4): 043711.
3395:
3391:
3387:
3380:
3377:
3372:
3368:
3364:
3360:
3356:
3352:
3348:
3344:
3339:
3334:
3331:(4): 043711.
3330:
3326:
3322:
3315:
3312:
3307:
3303:
3299:
3295:
3291:
3287:
3283:
3279:
3272:
3269:
3264:
3260:
3256:
3252:
3248:
3244:
3240:
3236:
3229:
3226:
3221:
3217:
3213:
3209:
3205:
3201:
3197:
3193:
3186:
3183:
3178:
3174:
3170:
3166:
3162:
3158:
3154:
3150:
3143:
3140:
3135:
3131:
3127:
3123:
3119:
3115:
3108:
3105:
3100:
3098:0-7503-0597-5
3094:
3090:
3089:
3081:
3078:
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2131:
2123:
2098:
2095:
2071:
2063:
2058:
2039:
2037:
2029:
2025:
2020:
2009:
2002:
1989:
1976:
1973:
1966:
1957:
1954:
1949:
1942:
1936:
1918:
1910:
1903:
1895:
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1693:
1689:
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1681:semiconductor
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1611:
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1598:
1597:
1596:
1595:
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1578:
1577:Self-assembly
1575:
1573:
1570:
1569:
1563:
1562:
1554:
1551:
1549:
1548:van der Waals
1546:
1544:
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1499:
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1481:
1479:
1476:
1474:
1473:von Helmholtz
1471:
1469:
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1464:
1461:
1459:
1456:
1454:
1451:
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1123:
1120:
1114:
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1103:
1089:
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1080:
1077:
1071:
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928:
921:
920:
916:
914:
911:
909:
906:
904:
901:
900:
896:
895:Ideal gas law
893:
891:
888:
886:
883:
881:
878:
877:
873:
868:
867:
841:
831:
817:
810:
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745:
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728:
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543:
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527:
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478:
475:
468:
465:
462:
461:
455:
452:
451:
448:
443:
442:
431:
428:
426:
425:Vapor quality
423:
421:
420:
415:
412:
410:
409:
404:
401:
398:
394:
393:
388:
385:
384:
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292:
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286:
283:
279:
274:
271:
269:
266:
264:
263:Reversibility
261:
259:
256:
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251:
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246:
244:
241:
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148:
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137:Closed system
135:
134:
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117:
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109:
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102:
99:
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51:
50:
43:
42:
38:
32:
28:
27:
24:
20:
3743:
3611:Regenerative
3540:Bell Coleman
3431:. Retrieved
3393:
3389:
3379:
3328:
3324:
3314:
3281:
3277:
3271:
3238:
3234:
3228:
3195:
3191:
3185:
3152:
3148:
3142:
3117:
3113:
3107:
3087:
3080:
3047:
3043:
3037:
3028:
3023:
3016:
2983:
2979:
2973:
2940:
2936:
2930:
2903:
2897:
2880:
2876:
2866:
2839:
2833:
2806:
2800:
2791:
2778:
2743:
2739:
2729:
2696:
2692:
2686:
2675:the original
2660:
2652:
2645:
2634:
2623:
2612:
2599:
2592:
2578:(1): 35–39.
2575:
2571:
2565:
2525:microphonics
2522:
2498:
2484:
2478:
2472:
2447:
2443:
2435:
2413:
2412:K), but the
2403:
2395:
2370:
2362:
2351:
2287:
2276:
2194:is given by
2121:
2059:
2043:
2034:
2018:
2007:
2000:
1990:
1974:
1971:
1964:
1958:
1955:
1947:
1940:
1937:
1925:
1916:
1908:
1901:
1893:
1862:
1795:
1781:
1772:
1765:
1757:
1724:such as the
1707:astronomical
1700:
1678:
1669:moving parts
1652:
1648:
1644:
1642:
1438:Carathéodory
1369:Heat engines
1341:
1330:
1319:
1301:Motive power
1286:
946:Free entropy
917:
417:
416: /
406:
405: /
397:introduction
390:
389: /
328:
291:Heat engines
78: /
3779:Ionocaloric
3774:Vuilleumier
3596:Hygroscopic
2040:Performance
1260:Synergetics
941:Free energy
387:Temperature
248:Quasistatic
243:Isenthalpic
200:Instruments
190:Equilibrium
142:Open system
76:Equilibrium
58:Statistical
3805:Cryogenics
3794:Categories
3744:Pulse tube
3716:Mixed/dual
3433:2024-04-03
3403:2204.01195
3338:2204.01195
3278:Cryogenics
3235:Cryogenics
3192:Cryogenics
3149:Cryogenics
3044:Cryogenics
2980:Cryogenics
2937:Cryogenics
2693:Cryogenics
2557:References
2541:Cryocooler
1892:Figure 2:
1572:Nucleation
1416:Scientists
1220:Philosophy
933:Potentials
296:Heat pumps
253:Polytropic
238:Isentropic
228:Isothermal
3739:Kleemenko
3625:Internal
3363:0034-6748
3306:244005391
3298:0011-2275
3263:0011-2275
3220:122086143
3212:0011-2275
3177:0011-2275
3134:0094-243X
3072:0011-2275
3008:122086143
3000:0011-2275
2965:0011-2275
2770:0022-2291
2721:0011-2275
2469:Prospects
2302:ξ
2247:−
2212:ξ
2182:ξ
2145:˙
2132:ξ
2099:˙
2072:ξ
1911:: (near X
1896:: (near X
1840:˙
1710:detectors
1553:Waterston
1503:von Mayer
1458:de Donder
1448:Clapeyron
1428:Boltzmann
1423:Bernoulli
1384:Education
1355:Timelines
1139:−
1084:−
872:Equations
839:∂
792:∂
743:α
707:∂
660:∂
614:−
608:β
572:∂
525:∂
233:Adiabatic
223:Isochoric
209:Processes
170:Ideal gas
53:Classical
3706:Combined
3665:Humphrey
3650:Expander
3635:Atkinson
3570:Stoddard
3560:Stirling
3555:Ericsson
3515:External
3428:35489903
3371:35489903
2535:See also
1692:military
1605:Category
1543:Thompson
1453:Clausius
1433:Bridgman
1287:Vis viva
1269:Theories
1203:Gas laws
995:Enthalpy
403:Pressure
218:Isobaric
175:Real gas
63:Chemical
46:Branches
3769:Siemens
3685:Scuderi
3601:Rankine
3408:Bibcode
3343:Bibcode
3243:Bibcode
3157:Bibcode
3052:Bibcode
2945:Bibcode
2885:Bibcode
2748:Bibcode
2701:Bibcode
2493:K and 4
2483:) and (
2380:History
1716:or the
1528:Smeaton
1523:Rankine
1513:Onsager
1498:Maxwell
1493:Massieu
1198:Entropy
1193:General
1184:History
1174:Culture
1171:History
395: (
392:Entropy
329:italics
130:Systems
3675:Miller
3670:Lenoir
3645:Diesel
3591:Kalina
3575:Manson
3550:Carnot
3426:
3369:
3361:
3304:
3296:
3261:
3218:
3210:
3175:
3132:
3095:
3070:
3006:
2998:
2963:
2918:
2854:
2821:
2768:
2719:
2667:
2518:
2514:
2506:SQUIDs
2495:
2491:
2475:
2463:
2459:
2455:
2450:
2438:
2426:
2422:
2418:
2410:
2406:
2399:
2390:
2055:
2051:
2047:
1816:porous
1792:piston
1784:helium
1730:oxygen
1518:Planck
1508:Nernst
1483:Kelvin
1443:Carnot
733:
598:
466:
408:Volume
323:Note:
282:Cycles
111:Second
101:Zeroth
3699:Mixed
3398:arXiv
3333:arXiv
3302:S2CID
3216:S2CID
3027:[
3004:S2CID
2788:(PDF)
2678:(PDF)
2657:(PDF)
2604:(PDF)
2432:Types
1972:below
1930:and X
1909:Right
1651:) or
1566:Other
1533:Stahl
1488:Lewis
1478:Joule
1468:Gibbs
1463:Duhem
156:State
116:Third
106:First
3711:HEHC
3680:Otto
3424:PMID
3367:PMID
3359:ISSN
3294:ISSN
3259:ISSN
3208:ISSN
3173:ISSN
3130:ISSN
3093:ISBN
3068:ISSN
2996:ISSN
2961:ISSN
2916:ISBN
2852:ISBN
2819:ISBN
2766:ISSN
2717:ISSN
2665:ISBN
1894:Left
1734:Mars
1675:Uses
1663:and
1643:The
1538:Tait
368:Heat
363:Work
93:Laws
3416:doi
3351:doi
3286:doi
3282:121
3251:doi
3200:doi
3165:doi
3122:doi
3060:doi
2988:doi
2953:doi
2908:doi
2844:doi
2811:doi
2756:doi
2744:164
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2580:doi
2397:105
2306:PTR
1732:on
1649:PTR
1381:Art
327:in
3796::
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3066:.
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2959:.
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2875:.
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2790:.
2764:.
2754:.
2742:.
2738:.
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1988:.
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2711::
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2586:.
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2502:c
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2122:P
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2096:Q
2022:H
2019:T
2015:3
2011:H
2008:T
2004:H
2001:T
1997:3
1993:3
1986:2
1982:2
1978:L
1975:T
1968:L
1965:T
1961:2
1951:L
1948:T
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1932:3
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
