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Carnot cycle consists of isothermal and adiabatic processes which are reversible. Using analogy in quantum mechanics, these processes can be well explained by replacing variables in classical process with a quantum system. Quantum system which is shown in this paper is a particle that moves under the influence of a cubic potential which is restricted only to the state of the two energy levels. At the end, the efficiency of the system is shown as a function of the width ratio between the initial conditions and the farthest wall while expanding. Furthermore, the system efficiency will be considered 1D and 2D cases. The providing efficiencies are different due to the influence of the degeneration of energy and the degrees of freedom of the system.

Carnot model of heat engine is the most efficient cycle consisting of isothermal and adiabatic processes which are reversible. Although ideal gas usually used as a working fluid in the Carnot engine, Bender used quantum particle confined in 1D potential well as a working fluid. In this paper, by following Bender we generalize the situation to 2D symmetric potential well. The efficiency is express as the ratio of the initial length of the system to the final length of the compressed system. The result then is shown that for the same ratio, 2D potential well is more efficient than 1D potential well.

Cryocoolers with large cooling powers at 80 K are very promising as they could find important applications in superconducting field such as cooling cables, transformers and fault current limiters. The pulse tube cryocooler has attracted attention due to its virtue of no moving components in the cold region. However, as the cooling power increases, problems inside the thermal buffer tube, such as difficulty in obtaining good flow straightening, existence of Rayleigh streaming, the gravity effect etc., present big obstacles to achieving high thermal efficiency. On the other hand, a free piston Stirling cryocooler, though more complicated due to the existence of the displacer, could avoid these problems with the elimination of the thermal buffer tube. Meanwhile, the efficiency is better than the pulse tube cryocooler around 80 K due to its capability of recovering the acoustic work. In this article, a free piston Stirling cryocooler with about 300 W cooling power at 80 K is designed with our simulation based on thermoacoustic theory. The theoretical analysis and numeric model are given in detail. The phase shift effect of the displacer and the internal energy loss mechanism are discussed. From our calculation, a relative Carnot efficiency of about 50% at 80 K has been obtained analytically.

A pulse tube cryocooler with 50 W cooling capacity at 77 K is developed to cool superconducting devices mounted on automobiles. The envisioned cryocooler weight is less than 40 kg, and the input electric power is less than 1 kW. To achieve these requirements, the working frequency is increased to 75 Hz, and the dual-opposed pistons use gas bearings to reduce compressor weight and volume. The heat from the main heat exchanger is rejected by forced convective air instead of water. The compressor and the cold finger are carefully matched to improve the efficiency. The details of these will be presented in this paper. After some adjustment, a no load temperature for the pulse tube cryocooler of 40 K was achieved with 1 kW input electric power in surroundings at 298 K. At 77 K, the cooling capacity is 50 W. If the main heat exchanger is cooled by water at 293 K, the cooling capacity increases to 64 W, corresponding to a relative Carnot efficiency of 18%.

The vapor-compression cycle for refrigeration near ambient temperature achieves high efficiency because the isenthalpic expansion of the condensed liquid is a rather efficient process. However, temperatures are limited to about 200 K with a single-stage system. Temperatures down to 77 K are possible with many stages. In the case of microcryocoolers using microcompressors, pressure ratios are usually limited to about 6 or less. As a result, even more stages are required to reach 77 K. If the microcompressors can be fabricated with low-cost wafer-level techniques, then the use of many stages with separate compressors may become a viable option for achieving temperatures of 77 K with high efficiency. We analyze the ideal thermodynamic efficiency of a cascade Joule-Thomson system for various temperatures down to 77 K and with low pressure ratios. About nine stages are required for 77 K, but fewer stages are also analyzed for operation at higher temperatures. For 77 K, an ideal second-law efficiency of 83 % of Carnot is possible with perfect recuperative heat exchangers and 65 % of Carnot is possible with no recuperative heat exchangers. The results are compared with calculated efficiencies in mixed-refrigerant cryocoolers over the range of 77 K to 200 K. Refrigeration at intermediate temperatures is also available. The use of single-component fluids in each of the stages is expected to eliminate the problem of pulsating flow and temperature oscillations experienced in microcryocoolers using mixed refrigerants.

The proposal by NASA to use high-temperature superconducting (HTS) generators and motors on future (~2035) aircraft for turboelectric propulsion imposes difficult requirements for cryocoolers. Net refrigeration powers of about 5 kW to 10 kW at 50 K to 65 K are needed for this application. A 2010 survey by Ladner of published work between 1999 and 2009 on existing Stirling and Stirling-type pulse tube cryocoolers showed efficiencies in the range of 10 to 20 % of Carnot at 50 K, much less than the 30 % of Carnot needed to make the concept feasible. A cryocooler specific mass less than about 3 kg/kW of input power is required to keep the cryocooler mass somewhat less than the mass of the superconducting machinery. Current cryocoolers have specific masses about 3 to 10 times this desired value, even for those designed for airborne or space use. We discuss loss and mass sources and make suggestions where improvements can be made. For Stirling and Stirling-type pulse tube cryocoolers, most of the mass is concen...

This paper analyzes the thermodynamic cycle of oscillating-flow regenerative machines. Unlike the classical analysis of thermodynamic textbooks, the assumptions for pistons' movement limitations are not needed and only ideal flowing and heat transfer should be maintained in our present analysis. Under such simple assumptions, the meso-scale thermodynamic cycles of each gas parcel in typical locations of a regenerator are analyzed. It is observed that the gas parcels in the regenerator undergo Lorentz cycle in different temperature levels, whereas the locus of all gas parcels inside the regenerator is the Ericson-like thermodynamic cycle. Based on this new finding, the author argued that ideal oscillating-flow machines without heat transfer and flowing losses is not the Stirling cycle. However, this new thermodynamic cycle can still achieve the same efficiency of the Carnot heat engine and can be considered a new reversible thermodynamic cycle under two constant-temperature heat sinks.

Industrial Research Ltd has developed a unique diaphragm-based pressure wave generator technology for employment in pulse tube and Stirling cryocoolers. The system uses a pair of metal diaphragms to separate the clean cryocooler gas circuit from a conventionally lubricated mechanical driver, thus producing a clean pressure wave with a long-life drive. We have now extended the same diaphragm concept to support and seal the displacer in a free piston Stirling expander. The diaphragms allow displacer movement without rubbing or clearance gap seals, hence allowing for the development of costeffective long-life and efficient Stirling cryocoolers. Initial modeling, operating in conjunction with a 200 cc swept volume pressure wave generator, predicted in excess of 300 W cooling at 77 K with a Carnot efficiency of over 25%. A proof-of-concept prototype has achieved cryogenic temperatures. Details of the concept, modeling, and testing will be presented.

The reduction of electric power consumption of the cryo-cooler during the working conditions of applied superconducting systems is important, as superconductivity can only be stored at low temperature and the power required for the cooling determines the efficiency of the systems employed. Use of Peltier current leads (PCLs) represents one key solution to effect heat load reduction on the terminals in systems. On the other hand, the performance of cryo-coolers generally increases as the temperature increases given the higher Carnot efficiency. Therefore, combination with suitable mid-stage temperatures represents one possible approach since the thermal anchor can enhance the performance of the system by reducing the electric power consumption of the cryo-coolers. In this paper, we discuss this possibility utilizing an advanced configuration of PCL with a commercially available high temperature cooler. Over 50% enhancement of the performance is estimated.

Industrial Research Ltd (IRL) previously developed a single-stage, inline, pulse tube for use with their metallic-diaphragm pressure wave generator (PWG), achieving 45 W of cooling power at 77 K, with 19.5 % of Carnot efficiency (based on the PV input power). This paper describes the conversion of the inline pulse tube to a co-axial configuration that provides a more accessible cold finger. Sage pulse tube simulation software was used to model the modified pulse tube and predicted 105 W of cooling power at 90 K, with an indicated input power of 1350 W. The pulse tube operated at 50 Hz, with a mean helium working pressure of 2.5 MPa and was closely coupled to a 60 ml swept volume PWG. The experimental results yielded more than 100 W @ 90 K with 2.5 MPa of gas pressure, with a lowest no load temperature of 39.7 K with 1.4 MPa of gas pressure. Details of the development, experimental results and correlations to the Sage model are discussed

Sadi Carnot's ingenious reasoning of reversible cycles (1824) laid foundations for The Second Law before The First Law of energy conservation was even known (Joule 1843) and long before Thermodynamic concepts were established in 1850s. A century later, Bridgman (1941) ‘complained’ that “there are almost as many formulations of The Second Law as there have been discussions of it.” Even today, The Second Law remains so obscure, due to the lack of its comprehension, that it continues to attract new efforts at clarification, including this one.The Laws of Thermodynamics have much wider, including philosophical significance and implication, than their simple expressions based on the experimental observations—they are The Fundamental Laws of Nature: The Zeroth (equilibrium existentialism), The First (conservational transformationalism), The Second (irreversible directional transformationalism), and The Third (unattainability of emptiness). They are defining and unifying our comprehension of all existence and tr...

This paper explores the limiting energy efficiency for the energy uses in a particular office building. This limit might be viewed as the “Carnot efficiency” for the entire building. It assumes that all energy‐consuming services in the building are provided at the minimum energy value that does not violate physical law. Rigorous physical limits such as the Carnot efficiency are used where applicable; in other cases, a plausible approximation has been adopted. Based on the assumptions made, it would be possible to provide all of the energy‐based services currently provided in the building using approximately 0.2 kWh/(ft2−yr). This limiting value is less than 1% of the energy used by a typical office building in the United States. Examination of expected advances in individual technologies suggests that it may be possible to construct a building that uses approximately 0.8 kWh/(ft2−yr) within the next decade.

The constant pressure ratio process, as implemented in the floating pressure—Ganni cycle, is a new variation to prior cryogenic refrigeration and liquefaction cycle designs that allows for optimal operation and design of helium refrigeration systems. This cycle is based upon the traditional equipment used for helium refrigeration system designs, i.e., constant volume displacement compression and critical flow expansion devices. It takes advantage of the fact that for a given load, the expander sets the compressor discharge pressure and the compressor sets its own suction pressure. This cycle not only provides an essentially constant system Carnot efficiency over a wide load range, but invalidates the traditional philosophy that the (‘TS’) design condition is the optimal operating condition for a given load using the as‐built hardware. As such, the Floating Pressure‐Ganni Cycle is a solution to reduce the energy consumption while increasing the reliability, flexibility and stability of these systems over a wide operating range and different operating modes and is applicable to most of the existing plants. This paper explains the basic theory behind this cycle operation and contrasts it to the traditional operational philosophies presently used.

The recent progress of a large Stirling‐type pulse tube cryocooler is reported based on 24/7 operation since August 2008 in a high temperature superconducting (HTS) cable application at American Electric Power’s (AEP) Bixby Road substation in Columbus, OH. The 20‐kW pressure wave generator (PWG) has been upgraded to a second generation design. The in‐line configured pulse tube coldhead, rated at 1 kW at 77 K, was developed by Praxair.The objective of the continued testing at the HTS cable demonstration facility is to accumulate cryocooler operating hours and demonstrate system reliability. The cryocooler uses a parallel flow from the main vacuum subcooling refrigerator then both flows are supplied to the HTS cable inlet. The cryocooler operation has shown consistent results with satisfactory cooling performance. The field demonstrated thermodynamic efficiency is 15% of Carnot at 72 K.

The refrigeration power for large current superconductor systems, such as for electrical power distribution, is dominated by current lead losses. The use of multiple cooling stages between room temperature and ∼70 K is investigated as means to decrease the refrigeration power. We show that it is possible to decrease the electrical power requirements for the refrigerator by about 1/3 through the use of two‐stages current leads; this computed power saving is based on a conservative estimate of refrigerator performance. Using data from real systems, that is, higher temperature refrigerators operating at higher fractions of their Carnot efficiencies we believe that the refrigerator electrical power requirement can actually be decreased by 1/2. Means have been investigated to optimize current lead performance at lower than maximum current operation. Adjustment of the cooling power of the intermediate temperature refrigerators achieves limited success in power consumption minimization. Other means to optimize the performance will be described. The implications of intermediate stages for stability of the current leads following a short overcurrent period will be described.

This paper is an update of papers written in 1991 and in 1997 by Rod Byrns and this author concerning estimating the cost of refrigeration for superconducting magnets and cavities. The actual costs of helium refrigerators and coolers (escalated to 2007 dollars) are plotted and compared to a correlation function. A correlation function between cost and refrigeration at 4.5 K is given. The capital cost of larger refrigerators (greater than 10 W at 4.5 K) is plotted as a function of 4.5-K cooling. The cost of small coolers is plotted as a function of refrigeration available at 4.2 K. A correlation function for estimating efficiency (percent of Carnot) of both types of refrigerators is also given.

This paper describes the design, development, testing and performance of the Ball Aerospace & Technologies Corp. SB235E, a 2-stage long life space cryocooler optimized for 2 cooling loads. The SB235E model is designed to provide simultaneous cooling at 35 K (typically for HgCdTe detectors) and 85 K (typically for optics). The SB235E is a higher capacity model derivative of the SB235. Initial testing of the SB235E has shown performance of 2.13 W at 35 K and 8.14 W at 85 K for 200 W power at 289 K rejection temperature. These data equate to Carnot efficiency of 0.175 or nearly twice that of other published space cryocooler data. Qualification testing has been completed including full performance mapping and vibration export. Performance mapping with the cold-stage temperature varying from 20 K to 80 K and mid-stage temperature varying from 85 K to 175 K are presented. Two engineering models of the SB235E are currently in build.

This paper describes recent progress on a hydrogen magnetic refrigerator. Magnetic refrigeration makes use of the magnetocaloric effect, and is well known as an efficient method in principal because its cooling cycle can most closely follow the Carnot cycle with appropriate heat switches. A liquefaction principal of our magnetic refrigerator is based on the thermo-siphon method, in which liquid hydrogen is condensed directly on the surface of magnetic refrigerants and drops downward. In liquefaction experiments, we have successfully liquefied hydrogen gas preliminarily cooled to a temperature slightly above the boiling point. To improve liquefaction efficiency, the filling factor and spherical form of the magnetic material have been considered. Increasing the filling factor from 0.34 to 0.45 resulted in increasing %Carnot and cooling power by ∼50%. Spherical magnetic material DGAG with a 0.4 mm diameter was successfully developed. The thermal efficiency during the liquefaction process was increased largely by using the sphere DGAG, but it was observed that the condensed liquid hydrogen was trapped inside the spheres. This disadvantage will not be serious when we use a hybrid cycle consisting of Carnot and AMR.

A brief historical review of the evolution of the Second Law from Sadi Carnot (1824) to present times is presented. The complex nature of irreversibility is used to identify three interrelated domains of thermodynamics, each having a different mathematical form and different types of application. In addition, a proposal is made to bring the nomenclature of the Second Law into parallel alignment with that of the First Law. Some of this material is excerpted from a paper by the author published in the July, 2007 issue of the Mechanical Engineering Magazine.

Increasing levels of certain greenhouse gases (GHGs), most importantly CO2 in the earths atmosphere, lead to climate change and global warming as a result of these gases interacting with thermal infrared (TIR) radiation from earth to space. Here, the option of modifying this radiation is analyzed which would result in modified TIR radiation that would interact less with atmospheric CO2. This alleviates the enhanced greenhouse effect, and at the same time would allow for energy recovery as heat and/or power. Power production is, of course, limited by thermodynamics Second Law. It is shown that various options exist for TIR radiation modification which may be used to generate temperature gradients or temperature differences between volumes of (gases containing) CO2 of sufficient optical thickness. This may be further exploited for power generation: a first, simple case shows power generation of ∼1 W per m2 surface at a Carnot efficiency of ∼7%, using the sky and ground level surroundings as heat reservoirs.

An adiabatic demagnetization refrigerator (ADR) is under development for use in cooling relatively large loads (10–100 mW) at 4 K and rejecting that heat to a cryocooler operating at 10 K. ADRs can operate in this temperature range with an efficiency of 75% of Carnot, saving as much as 2/3 of the required overall input power. In addition this ADR can provide cooling down to 0.4 K. The ADR magnet consists of 8 short coils wired in series and arranged in a toroid to provide self‐shielding of its magnetic field. Eliminating passive or active shields saves 30% of the mass of the system. The average field is 3 Tesla using 5 amps. In the first model the coils are wound with ordinary NbTi superconducting wire and operated at 4 K. A second version will then use fine Nb3Sn wire to provide complete 10 K operation. As a refrigerant for this temperature range we are using readily available gadolinium gallium garnet (GGG) crystals, which provide suitable performance. In the future we will switch to either GdLiF4 or Gd...

Conversion into Hydrogen Energy Society is advanced focusing on the application to a fuel cell electric vehicle. As volume and weight density of liquid hydrogen are large, it is the method which was most excellent as the storage method of hydrogen. However, in order to store liquid hydrogen stably over a long period of time, decreasing the loss of energy, development of an efficient small cryocooler becomes important. This paper reports the research about improvement in the refrigeration efficiency of a two‐stage GM cryocooler.In order that the GM cryocooler may operate by the Simon expansion, it carries out asymptotic of the COP of the GM cryocooler to the Carnot COP as a compression ratio is lowered. When experimented based on this view, it was checked that refrigeration efficiency rises with reduction in a compression ratio. Furthermore, if the compression ratio is lowered, refrigeration efficiency will fall rapidly. The peak value of the refrigeration efficiency in 20K level attained 28%Carnot.It was ...

An analysis of the Claude form of an idealized helium liquefier for the minimum input work reveals the ‘Carnot Step’ for helium refrigerator cycles. As the ‘Carnot Step’ for a multi‐stage polytropic compression process consists of equal pressure ratio stages; similarly for an idealized helium liquefier the ‘Carnot Step’ consists of equal temperature ratio stages for a given number of expansion stages. This paper presents the analytical basis and some useful equations for the preliminary examination of existing and new Claude helium refrigeration cycles.

The Stirling convertor concept continues to be a viable potential candidate for various space power applications at electrical power levels ranging from greater than 100 KW to on the order of 10+watts. Various development efforts, both in the past and currently underway, have clearly demonstrated the potential for long operating life of this concept, its high efficiency in comparison to alternative power systems (>50% of Carnot based on electric power out to heat in), and its excellent specific power characteristics. A truly unique attribute of the Stirling convertor is the ability to maintain many of these same advantages at significantly lower electrical power levels (on the order of 1 watt and below). This provides the opportunity for a wider range of potential space power applications and the use of alternative heat sources operating at dramatically lower hot‐end temperatures (about 250 °C vs. current values of about 650 °C). An overview of low‐power Stirling convertors and related Stirling cooler tec...

A new heat engine concept has been invented that operates on a new two‐phase thermodynamic power conversion cycle. This device exploits the space flight proven technique of using a porous capillary structure to separate liquid from vapor through heat addition. This new thermodynamic cycle, the Baker cycle, is different from the existing Rankine because liquid and vapor are at different pressures and are separated during the phase change heat addition process as opposed to the Rankine cycle where liquid and vapor are at the same pressure and mixed during phase change heat addition. This new cycle also differs from Rankine because the heat addition process occurs at varying pressures and temperatures, where as in a Rankine cycle heat addition occurs at constant pressure. It is advantageous to apply this new cycle to space applications because management of the two‐phase working fluid in micro gravity can be accomplished as never before using space flight proven Loop Heat Pipe and Capillary Pumped Loop technology. This new power system contains many components with significant flight heritage. Thermodynamic performance calculations are presented for several design cases. The new power cycle and system is inherently more efficient than single‐phase systems because minimal compression power is required. One case shows 31.1% overall efficiency with a maximum working fluid temperature of 637.4 K. Since the heat addition process occurs at varying temperatures, waste heat from the spacecraft could be tapped and recovered to supply a large portion of the input energy. For the example cases discussed, between 63.1 to 84.4% of the total input energy could be waste heat. This new system could be used in conjunction with phase change thermal energy storage to supplement power production replacing batteries for solar low‐earth‐orbit applications. It could also be used as a power converter with a radioisotope heat source yielding efficiencies over 30% while requiring a maximum temperature well below that of single‐phase dynamic converters. Because this new power system is capable of operating at high efficiency at relatively low temperatures it could also be used as the bottoming cycle of a space based cogeneration power system with a single‐phase or static power converter being the top cycle.

A 4 kW electrical input Linear Motor driven pulse tube cryocooler has successfully been designed, built and tested. The optimum operation frequency is 60 Hz with a design refrigeration of >200 W at 80 K. The design exercise involved modeling and optimization in DeltaE software. Load matching between the cold head and linear motor was achieved by careful sizing of the transfer tube. The cryocooler makes use of a dual orifice inertance network and a single compliance tank for phase optimization and streaming suppression in the pulse tube. The in‐line cold head design is modular in structure for convenient change‐out and re‐assembly of various components. The Regenerator consists of layers of two different grades of wire‐mesh. The Linear motor is a clearance seal, dual opposed piston design from CFIC Inc. Initial results have demonstrated the refrigeration target of 200 W by liquefying Nitrogen from an ambient temperature and pressure. Overall Carnot efficiencies of 13% have been achieved and efforts to furt...

The flow through the regenerator of a Stirling cryocooler is driven by differences in pressure at the warm and cold sides. These differences lead to power dissipation in the regenerator. The pressure distribution in the regenerator is found using linearized theory. Expressions are derived for the rate of refrigeration and for the coefficient of performance (COP) at fixed amplitude of the piston at the warm side. The rate of refrigeration is optimized with respect to the amplitude and the phase of the piston on the cold side. The maximum rate of refrigeration and the corresponding COP are subject to severe limitations. These limitations are independent of the value of the regenerator conductance. In the limit of zero frequency and zero regenerator void volume, the COP at maximum rate of refrigeration is less than half of the Carnot value. The COP decreases as frequency and void volume increase. Results are presented for the piston amplitude ratio and phase difference corresponding to the maximum rate of refrigeration.

We have recently assembled a 4‐stage continuous adiabatic demagnetization refrigerator (CADR) that provides continuous cooling at 50 mK and below, while rejecting heat to a 4.2 K helium bath. Temperature control and cycling of the ADR is fully automated, making it simple to operate and stable. Temperature fluctuations of the cold stage are typically less than 10 μK rms (at 100 mK). The cooling power of 20 μW at 100 mK is comparable to that of small dilution refrigerators, but because its efficiency is so much higher (50% of Carnot), the peak heat rejection rate is less than 10 mW. This is significant in allowing the ADR to be cooled by relatively low‐power cryocoolers. In addition to commercial pulse‐tube and Gifford McMahon (GM) coolers, this potentially includes small GM systems that run on 120 V power and do not need water cooling. The present focus is to design and fabricate a small dewar to house the CADR and a cryocooler, in anticipation of making a cryogen‐free, low cost CADR commercially available. Performance of the prototype CADR and the complete system are discussed.

This paper reports on the current status of an advanced 35 We free‐piston Stirling convertor currently being developed under NASA SBIR Phase II funding. Also described is a further advanced and higher performance ∼80 watt free‐piston convertor being developed by Sunpower and Boeing/Rocketdyne for NASA under NRA funding. Exceptional overall convertor (engine plus linear alternator) thermodynamic performance (greater than 50% of Carnot) with specific powers around 100 We /kg appear reasonable at these low power levels.

Requirements for cooling and power consumption in space platforms are subject to significantly greater constraints than the requirements for terrestrial applications. Existing cooling systems incorporate various mechanisms including thermoelectric (Peltier) cooling elements, radiative cooling, and phase‐change compressor‐based systems. This paper outlines an alternative mechanism currently in development called “thermotunneling”. This mechanism exploits electron tunneling across a vacuum gap of ∼10nm to effect a temperature differential with high efficiency. When complete, these devices (“Cool Chips”) are expected to offer a compact, lightweight, low maintenance and highly efficient (in excess of 50% of Carnot Efficiency) thermal management solution ideally suited for the needs of aerospace applications. This article was originally published with an incorrect list of authors which is now corrected.

This paper presents the projected performance and overall design characteristics of a high efficiency, low mass 35 W free‐piston Stirling engine design. Overall (engine plus linear alternator) thermodynamic performance greater than 50% of Carnot, with a specific power close to 100 W/kg appears to be a reasonable goal at this small power level. Supporting test data and analysis results from exiting engines are presented. Design implications of high specific power in relatively low power engines is presented and discussed.

Alkali Metal Thermal‐to‐Electric Conversion (AMTEC), although currently at a Technology Readiness Level‐3 (TRL‐3), has an excellent potential for use in Space Nuclear Reactor Power (SNRP) systems for NASA’s deep‐space exploration missions. In addition to operating at a conversion efficiency > 20%, representing the highest fraction (> 60%) of Carnot efficiency of all other static and dynamic conversion technology options, the relatively high heat rejection radiator temperature (650–700 K) reduces the size and mass of the radiator and of the SNRP system. A high‐power AMTEC unit design has been developed and optimized for operating at reactor exit temperatures ⩽ 1180 K and radiator temperature ⩽ 680 K. Depending on the reactor exit temperature, the nominal electrical power of the AMTEC unit, measuring 594 mm × 410 mm × 115 mm and weighting 44.3 kg, could be as high as 5.6 kWe, with a margin of ⩾ 5% for an additional load‐following increase. A conceptual design of a 100 kWe SNRP system with these high‐power AMTEC units is developed and presented in this paper. The total mass of major subsystems, including the converters, nuclear reactor, shadow radiation shield, and radiator, is calculated and compared with that for the SP‐100. Despite the large specific mass of the AMTEC units compared to the SiGe thermoelectrics in the SP‐100 system, the lower masses of the reactor, radiation shield, and radiator make the present AMTEC‐SNRP system > 26% lighter, for the same electrical power. An optimized AMTEC‐SNRP system could potentially operate at a specific power > 30 We/kg (or specific mass < 33 kg/kWe), use non‐refractory structures of super‐steel alloys with well‐know properties, relatively low density, low Ductile‐To‐Brittle (DTB) transition temperatures, and good compatibility with space and planetary environments containing CO2 and oxygen. The radiator area for the baseline 100 kWe AMTEC SNRP system is < 27 m2, which, together with operating the potassium heat pipes in the radiator sonic limited shortly after a reactor shutdown, would extensively prolong the cool‐down time of the reactor from several days to many months, before freezing the sodium in the reactor’s heat pipes (371 K).

We consider a Carnot cycle engine in which the working medium is a photon gas inside a cavity with perfectly reflecting walls. The thermal baths responsible for supplying heat to the radiation field is a stream of three‐level atoms. The phase of the atomic coherence provides a new and interesting control parameter. Here we discuss the questions pertaining to the preparation energy of atomic coherence with an explicit calculation of the associated entropy change.

The efficiency of coolers designed to provide refrigeration for industrial equipment is discussed. Experience accumulated during more than twenty years of manufacturing shows that multistage auto-cascade coolers provide high refrigeration performance along with rapid cool down and defrost. Both single-stage and two-stage throttle cycles have been analyzed. Comparative data on the performance of the cycles are obtained with a computer model that includes an equation of state to calculate thermodynamic properties of mixed refrigerants. Both flammable argon-hydrocarbon- and nonflammable argon-hydrofluorocarbon-based mixed refrigerants have been considered. Non-flammable environmentally friendly mixed refrigerants include commercially available components. The experimental data were obtained for coolers based on a single-stage compressor. The tested systems provided refrigeration capacity from 500 to 3600 W depending on the compressor displacement volume. A Carnot efficiency coefficient as high as 0.21 was achieved. This corresponds to the efficiency of conventional freezers operating at temperatures above 230 K.

The science of Thermodynamics was founded by Sadi Carnot; his Reflections on the Motive Power of Fire was published in 1824. Carnot’s work was based on the incorrect principle of Conservation of Heat. The concept of entropy was first adumbrated by Rankine, in 1850, 18 years after Carnot’s death. An explicit statement of a “Second Law” was first given four years later by Clausius. It is sometimes said, nevertheless, that “Carnot knew the Second Law without knowing the First”. In this talk we will examine Carnot’s actual argument, in order to determine whether, or to what extent, Carnot “knew the Second Law”.

A thermoacoustic engine is a new type of pressure-wave generator that possibly has a very long lifetime because of no mechanical moving parts. A thermoacoustic engine operating in standing wave mode is also called a natural engine with intrinsic thermodynamic irreversibility, so it shows a poor thermodynamic performance in converting thermal energy to acoustic energy. The conversion efficiency is around 10 to 25 percent of Carnot. By analyzing the generation rate of acoustic workflow and the local critical temperature gradient in the traveling-wave and standing wave modes, a thermoacoustic engine with local traveling-wave loop was designed, built and studied. In addition, a miniature coaxial pulse tube refrigerator was attached to the engine, and about 80 K temperature difference was achieved with nitrogen in preliminary tests.