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Why can't I reach 4K with the Siemens-cycle?
It appears that He liquification systems use the Siemens cycle upfront in the high temperature range, and the last stage is Hampson-Linde cycle.The Hampson-Linde cycle ( independently patented by W. Hampson and C. von Linde 1895) is very similar to the Siemens cycle, except that the expansion-machine is replaced by a Joule-Thomson orifice in [D]. First a few words about the Joule-Thomson effect. A gas could be cooled by letting it expand freely against the atmosphere. This could be explained by that the gas was doing a work against the atmosphere by lifting and/or heating it, and thereby loosing energy in form of heat. 1852 Joule and Thomson did some experiments to observe a gas, expanding without any work to be done. They let the gas flow through a pipe with a porous plug to restrict the flow. To their surprise the gas was cooled by passing the plug. This could first be explained twenty years later by van der Waals. The gas was not doing an external work, but an internal against the forces between the molecules. What Hampson and von Linde did was to combine Siemens cooling machine with Joules and Thomsons expansion plug, and put together a complete gas liquefication cycle.
The Siemens-cycle is a process used to produce liquid helium from gaseous helium by compressing and cooling it in multiple stages. It is named after the German scientist Ernst Werner von Siemens who first described the process in 1894.
The Siemens-cycle involves compressing gaseous helium to a high pressure, then cooling it to a temperature of about 15 K (-258.5 °C or -433.3 °F) using a series of heat exchangers and expansion valves. This causes the helium to liquefy. The liquid helium is then further cooled and purified through a series of additional stages.
Liquid helium produced through the Siemens-cycle is used in a variety of scientific and industrial applications, including superconducting magnets for MRI machines, particle accelerators, and nuclear magnetic resonance (NMR) spectroscopy. It is also used in cryogenic research and in the production of superconducting materials.
Liquid helium is typically stored in specialized containers called cryostats, which are designed to maintain the extremely low temperatures required to keep the helium in its liquid state. These containers are usually made of highly insulated materials such as stainless steel or glass, and they may also include a vacuum layer to further reduce heat transfer.
The main challenges in producing liquid helium through the Siemens-cycle are related to the extremely low temperatures and high pressures involved in the process. These conditions require specialized equipment and materials that can withstand the harsh environment. Additionally, helium is a rare and non-renewable resource, so there are concerns about its availability and sustainability in the future.