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Low liquid helium consumption cryostat for magnetoresistivity measurements in a narrow gap electromagnet
Low liquid helium consumption cryostat for magnetoresistivity measurements in a narrow gap electromagnet H. W h i t e and D. S. McLachlan Department of Physics and Condensed Matter Research Group, University of the Witwatersrand, PO Wits 2050, South Africa
Received 13 September 1989; revised 20 November 1989 A cryostat for measuring the resistivity, magnetoresistivity and Hall coefficient of thin metallic films is described. The cryostat, which is designed to operate between 1.4 and 273 K, is mounted in a 30 mm gap between the poles of an iron-core electromagnet, capable of reaching 1.5 T. Liquid helium consumption is low ( ~ 0.5 dm 3 h - l ) . The cryostat is specifically designed for manufacture in a non-specialist workshop.
Keywords: cryostats; measuring techniques; helium; magnetoresistance The resistivity, magnetoresistance and Hall coefficient of thin sputtered metallic films were measured in a 1.4-273 K cryostat mounted between the poles of a 1.5 T electromagnet 1'2. Conventionally, when measuring the resistivity, magnetoresistance and Hall coefficients of samples in a narrow gap iron-core electromagnet between 1.4 and 273 K, one uses a continuous flow liquid helium (4He) cryostat. The disadvantages of this are the high rate of helium consumption and the difficulties of constructing such a system in a non-specialist workshop. The system utilized here is a low liquid helium (4He) consumption cryostat which can fit into a 30 mm gap. It was specifically designed for easy construction, and makes use of readily available materials. The structure is essentially built up of concentric stainless steel, brass and copper tubes. The unique part of the cryostat is shown in Figure 1. The outer wall (A) of the upper section of the cryostat is a thick walled stainless steel tube (outer diameter 152.4 mm). This wall is separated from the liquid nitrogen reservoir (V) by an evacuated space (E) lined with superinsulation (D). This space is normally pumped to below 0.1 torr* before and during cooling to 77 K. Once * 1 torr = 133.322 Pa
the temperature stabilizes at (or a few degrees above) 77 K, the space is shut off and cryopumped during the liquid helium transfer. An Edwards Penning vacuum gauge is used to monitor the vacuum during cryopumping. The annular liquid nitrogen container (V) has a brass outer wall (F, outer diameter 139.7 mm) and a stainless steel inner wall (G, outer diameter 114.3 mm). The brass tube is the only non-standard item in the system, and it was made to specification in the University plumbing workshop from a brass sheet. Brass was used as it is easier to fabricate than stainless steel. Thermal isolation of the annular liquid nitrogen dewar is obtained by hanging it, in the conventional way, from three stainless steel tubes which pass through the top flange. The bottom of the liquid nitrogen reservoir (H) is a solid brass plate, as shown, lined underneath with a 5 mm thick Teflon ring (I) for insulation. A pumping hole (S) in the brass plate permits evacuation of the space between the liquid nitrogen (V) and liquid helium (L) reservoirs. The base (K) of the outer section of the cryostat is a standard 3 mm thick stainless steel plate, lined on the inside with a 5 mm thick block of Teflon (I). The liquid helium container (L) consists of two concentric stainless steel tubes. The outer wall (B, outer diameter 101.6 mm) is clad with aluminium foil to reduce radiative leakage from the 77 K wall of the liquid nitrogen container, while the inner wall has an outer diameter of 31.75mm. A short copper tube (M, Yorkshire, 38.10mm) rests inside the reservoir and functions to maintain a constant temperature surface (4-5 K) above the helium level. A supporting ring (Z) of 44.45 mm stainless steel tubing is necessary for alignment of the tube (T) because of the small clearances between concentric tubes in the lower section of the cryostat. The shaped copper block (O) on and in which all samples are mounted is thermally linked to the liquid helium reservoir by the exchange gas in a confined space (P) and the thermal conductance of a stainless steel tube (N). The lower section of the sample holder is separated from the 19.05 mm Yorkshire copper tubing (R) by the extension of the exchange space (P). The copper tube (R) is directly mounted on the conical copper supports (Q) and also serves as a constant temperature cap for the sample holder. The tube (R) is sealed at the bottom by a plug (I). A 25.4 mm outer diameter Yorkshire copper tube (T) mounted onto the brass ring (H) acts as a liquid nitrogen radiation shield. This tube is separated from the outer wall (Y, made of thin walled (0.38 mm) stainless steel with outer diameter 31.75 mm) by a continuation of the vacuum chamber and a few layers of superinsulation. Alignment is ensured by a short section of 6.35 mm stainless steel tube attached to a close fitting Teflon spacer (U). The actual length of the lower section is 250 mm (much longer than shown). Another tube (Y) fits with slight distortion between the poles of the electromagnet. The entire assembly hangs from a wall-mounted bracket, with the cryostat being mounted on commercially available antivibration supports, which give slight flexibility in the positioning of the cryostat in the electromagnet. The copper sample holder is coupled to room
0011-2275/90/040365-03 © 1990 Butterworth & Co (Publishers) Ltd
Cryogenics 1990 Vol 30 April
365
Research and technical notes
Sample holder BIII
Sample holder B I I
Copper tags for contact to sample
Temperature control heater Germanium thermometer
/
,
Conduit groove
II IIV
Heater (unused)
Platinum thermometer for T control (under copper block)
250 mm
Heat ( b u f f e r ) I
W Copper thermometer
I
U Heater
X Figure I Liquid helium (4He) cryostat. A, Outer wall of upper part of dewar, thick walled (1.63 mm) stainless steel tubing, outer diameter 152.4 mm (6 in); B, outer wall of liquid helium reservoir, thin walled (0.38mm) stainless steel tubing, outer diameter 101.6 mm, clad on outside with one layer of household aluminium foil; C, brass bottom of liquid helium reservoir; D, superinsulation in vacuum chamber, around the liquid nitrogen reservoir (V); E, vacuum chamber; F, outer wall of liquid nitrogen chamber, outer diameter 139.7 mm brass tubing, manufactured specifically for the cryostat; G, inner wall of liquid nitrogen chamber, outer diameter 114.30 mm thin walled stainless steel tubing; H, brass bottom of liquid nitrogen reservoir and thermal contact to liquid nitrogen radiation shield (T); I, Teflon insulating layer, screwed onto brass floor; J, household aluminium foil; K, 3 mm stainless steel base; L, liquid helium reservoir; M, short 38.10 mm Yorkshire copper tubing; N, thin walled stainless steel tubing, outer diameter 31.75 mm; O, copper sample holder on and in which all samples, thermometers and heaters are mounted; P, exchange gas space; Q, copper cone on which sample holder (0) rests; R, 19.05 mm outer diameter Yorkshire copper tubing, silver soldered to Q, forming constant temperature chamber around O; S, pumping hole to evacuate space between liquid nitrogen and liquid helium reservoirs; T, liquid nitrogen radiation shield, 25.4 mm outer diameter Yorkshire copper tubing; U, Teflon spacer on 6.35 mm stainless steel tubing; V, liquid nitrogen reservoir; W, copper base; X, 2 mm stainless steel plate to seal vacuum chamber; Y, outer wall of lower part of cryostat, thin walled stainless steel tubing, outer diameter 31.75 mm (the actual length of the lower section is 250 mm); Z, stainless steel ring for support of tube R in the 77 K shield
temperature through a 1 m long, 12.5 mm stainless steel tube. The stainless steel tube ends on a quick-coupling connector. The tube also supports all the leads to the sample holder. All electrical wiring terminates on vacuum tight Oxford 10 pin connectors mounted on the quick-coupler head. All leads in and out of the system are twisted pairs of 42 gauge insulated wire. Copper was used for the current
Platinum thermometer Carbon thermometer for T control I T o stainless steel tube
Figure 2 Copper sample holder upon and in which all samples, thermometers and heaters are mounted. Only sample holder with BJ was utilized (/being the current through the sample)
carrying leads, and manganin for the voltage monitoring leads. The leads are wrapped around the 1 m long stainless steel tube and thermally anchored to the copper sample holder by tightly clamping them to the block between cigarette papers covered in thermal grease. The rest of the construction and layout are fairly standard. The cryostat is cooled in the usual way, with at most 100/~m of air in the (rotary-pumped) insulation space and close to 1 atm t of helium gas in the exchange space. The small liquid nitrogen chamber and poor insulation during cool-down necessitated an automatic liquid nitrogen filling device. Cooling the cryostat from 77 K requires ~ 3 dm 3 liquid helium. A more than adequate liquid helium level detector utilizing four independent Wheatstone bridges with four Allen-Bradley resistors mounted at different depths in the helium reservoir was built. Transfer of 4 dm 3, after cool-down, enables 4 h of measurements to be made between 4 and 20 K, after t 1 atm = 101.325 kPa
Research and technical notes which the system is pumped down to 1.4 K, with roughly 3 h of measurements being done below 4 K. This is to be compared with the ,~ 1 dm a h- 1 needed to maintain a continuous flow cryostat at or near 4.2 K or ~ 2 dm 3 h - 1 at temperatures approaching 1.5 K. Above 20 K, a powerful heater (300 mW) is required, which results in increased helium consumption. The higher specific heats of materials at these temperatures causes longer waiting periods before temperature stabilization occurs, and hence the design is not really suited to fixed temperature measurements between 20 and 80 K. The temperature below 4 K was controlled to _ 0.02 K, during the 15 min period needed for 26 magnetoresistance points, using a Lake Shore manostat controller on the pumping line. Between 4 and 20 K the temperature was controlled using an electronic temperature controller 3, with which the temperature drift during a 15 min period was also + 0.02 K. Prolonged measurements above 80 K can be done, of course, by filling the liquid helium chamber with liquid nitrogen.
S a m p l e holder The lower part of the sample holder which is mounted
Computer animation as a teaching aid: the Stirling cycle A. Laesecke* University of Siegen, Department of Mechanical Engineering, Institute for Fluid- and Thermodynamics, PO Box 10 12 40, 5900 Siegen, FRG Received 25 September 1989
An instructional program has been developed for personal computers to visualize the motion inside a Stirling cryocooler. Used to supplement an experimental laboratory course, the program has turned out as a valuable pedagogical tool, greatly facilitating the understanding of this important thermodynamic cycle by the students.
Keywords: thermodynamics; Stirling coolers; models; computer animation
cryo-
* Present address: National Institute of Standards and Technology, Thermophysics Division, 325 Broadway, Boulder, CO 80303-3328, USA 0011-2275/90/040367-04 1 ¢1ClORHttArworth & Co (Publishers~ Ltd
within the helium (4He) cryostat is shown in Figure 2. The sample holder is constructed from a solid copper rod, extended a short distance above (below in the figure) where it joins the previously mentioned 12.5 mm stainless steel tubing. The sample holder is designed to hold two thin film samples (on glass substrates); one perpendicular to the applied magnetic field and one parallel. Contact to the sample is made by bridging the gap between the copper contact tags and the sample with a short coiled wire and then painting over this with conductive silver paint. To determine the temperature, a calibrated platinum thermometer was used for T > 20 K and a calibrated germanium thermometer for 1.4 < T < 20 K. The thermometers and heaters were kept in good thermal contact with the copper block by means of Apiezon M grease.
References 1 White, H. and McLacldan, D.S. JPhys C SolidState Phys(1986)19 5414 2 White, H. and McLachlan, D.S. J PhysCondensedMatter(1989)1 6665 3 Newrock, R.S.,Wagner, D.K. andStanley, H.E. JPhysEScilnstrum (1977) 10 934
Thermodynamics is one of the more difficult fields in engineering, although it does not require an extensive mathematical framework. To illustrate the abstract matter, lecture courses in thermodynamics are always accompanied by laboratory tutorials. Graduate students in the Department of Mechanical Engineering of Siegen University are offered the chance to participate in a laboratory experiment which deals with the liquefaction of ambient air by means of a Stifling cryocooler. The objectives of the experiment are: first, to perform a complete analysis of the energy conversion and thermodynamic efficiency of a real Stirling cycle as opposed to the ideal process1; and second, to perform a comparison between the ideal and real behaviour of the working gas, hydrogen, in the Stirling cryocooler using the equation of state of Bender 2. The experiments are conducted with a Philips PLA 107 engine** which is used in the department on a regular basis to produce liquid air as a coolant for material science research. The set-up is almost identical to the one shown in the article of Krhler 3. For the measurements, it has been equipped with additional instrumentation. The electrical energy consumption of the driving electric motor is measured with a wattmeter. The volume flow rate of the cooling water is determined with a flowmeter while two thermocouples measure its inlet and outlet temperature. The produced mass of liquid air is measured with a balance. Thermocouples are also used to determine the temperatures close to the expansion and compression space of the Stirling engine. A pressure transducer has been mounted to measure the pressure in the compression space. Its signal is amplified
** Philips GmbH, Scientific Instruments, Kassel, FRG
Received 13 September 1989; revised 20 November 1989 A cryostat for measuring the resistivity, magnetoresistivity and Hall coefficient of thin metallic films is described. The cryostat, which is designed to operate between 1.4 and 273 K, is mounted in a 30 mm gap between the poles of an iron-core electromagnet, capable of reaching 1.5 T. Liquid helium consumption is low ( ~ 0.5 dm 3 h - l ) . The cryostat is specifically designed for manufacture in a non-specialist workshop.
Keywords: cryostats; measuring techniques; helium; magnetoresistance The resistivity, magnetoresistance and Hall coefficient of thin sputtered metallic films were measured in a 1.4-273 K cryostat mounted between the poles of a 1.5 T electromagnet 1'2. Conventionally, when measuring the resistivity, magnetoresistance and Hall coefficients of samples in a narrow gap iron-core electromagnet between 1.4 and 273 K, one uses a continuous flow liquid helium (4He) cryostat. The disadvantages of this are the high rate of helium consumption and the difficulties of constructing such a system in a non-specialist workshop. The system utilized here is a low liquid helium (4He) consumption cryostat which can fit into a 30 mm gap. It was specifically designed for easy construction, and makes use of readily available materials. The structure is essentially built up of concentric stainless steel, brass and copper tubes. The unique part of the cryostat is shown in Figure 1. The outer wall (A) of the upper section of the cryostat is a thick walled stainless steel tube (outer diameter 152.4 mm). This wall is separated from the liquid nitrogen reservoir (V) by an evacuated space (E) lined with superinsulation (D). This space is normally pumped to below 0.1 torr* before and during cooling to 77 K. Once * 1 torr = 133.322 Pa
the temperature stabilizes at (or a few degrees above) 77 K, the space is shut off and cryopumped during the liquid helium transfer. An Edwards Penning vacuum gauge is used to monitor the vacuum during cryopumping. The annular liquid nitrogen container (V) has a brass outer wall (F, outer diameter 139.7 mm) and a stainless steel inner wall (G, outer diameter 114.3 mm). The brass tube is the only non-standard item in the system, and it was made to specification in the University plumbing workshop from a brass sheet. Brass was used as it is easier to fabricate than stainless steel. Thermal isolation of the annular liquid nitrogen dewar is obtained by hanging it, in the conventional way, from three stainless steel tubes which pass through the top flange. The bottom of the liquid nitrogen reservoir (H) is a solid brass plate, as shown, lined underneath with a 5 mm thick Teflon ring (I) for insulation. A pumping hole (S) in the brass plate permits evacuation of the space between the liquid nitrogen (V) and liquid helium (L) reservoirs. The base (K) of the outer section of the cryostat is a standard 3 mm thick stainless steel plate, lined on the inside with a 5 mm thick block of Teflon (I). The liquid helium container (L) consists of two concentric stainless steel tubes. The outer wall (B, outer diameter 101.6 mm) is clad with aluminium foil to reduce radiative leakage from the 77 K wall of the liquid nitrogen container, while the inner wall has an outer diameter of 31.75mm. A short copper tube (M, Yorkshire, 38.10mm) rests inside the reservoir and functions to maintain a constant temperature surface (4-5 K) above the helium level. A supporting ring (Z) of 44.45 mm stainless steel tubing is necessary for alignment of the tube (T) because of the small clearances between concentric tubes in the lower section of the cryostat. The shaped copper block (O) on and in which all samples are mounted is thermally linked to the liquid helium reservoir by the exchange gas in a confined space (P) and the thermal conductance of a stainless steel tube (N). The lower section of the sample holder is separated from the 19.05 mm Yorkshire copper tubing (R) by the extension of the exchange space (P). The copper tube (R) is directly mounted on the conical copper supports (Q) and also serves as a constant temperature cap for the sample holder. The tube (R) is sealed at the bottom by a plug (I). A 25.4 mm outer diameter Yorkshire copper tube (T) mounted onto the brass ring (H) acts as a liquid nitrogen radiation shield. This tube is separated from the outer wall (Y, made of thin walled (0.38 mm) stainless steel with outer diameter 31.75 mm) by a continuation of the vacuum chamber and a few layers of superinsulation. Alignment is ensured by a short section of 6.35 mm stainless steel tube attached to a close fitting Teflon spacer (U). The actual length of the lower section is 250 mm (much longer than shown). Another tube (Y) fits with slight distortion between the poles of the electromagnet. The entire assembly hangs from a wall-mounted bracket, with the cryostat being mounted on commercially available antivibration supports, which give slight flexibility in the positioning of the cryostat in the electromagnet. The copper sample holder is coupled to room
0011-2275/90/040365-03 © 1990 Butterworth & Co (Publishers) Ltd
Cryogenics 1990 Vol 30 April
365
Research and technical notes
Sample holder BIII
Sample holder B I I
Copper tags for contact to sample
Temperature control heater Germanium thermometer
/
,
Conduit groove
II IIV
Heater (unused)
Platinum thermometer for T control (under copper block)
250 mm
Heat ( b u f f e r ) I
W Copper thermometer
I
U Heater
X Figure I Liquid helium (4He) cryostat. A, Outer wall of upper part of dewar, thick walled (1.63 mm) stainless steel tubing, outer diameter 152.4 mm (6 in); B, outer wall of liquid helium reservoir, thin walled (0.38mm) stainless steel tubing, outer diameter 101.6 mm, clad on outside with one layer of household aluminium foil; C, brass bottom of liquid helium reservoir; D, superinsulation in vacuum chamber, around the liquid nitrogen reservoir (V); E, vacuum chamber; F, outer wall of liquid nitrogen chamber, outer diameter 139.7 mm brass tubing, manufactured specifically for the cryostat; G, inner wall of liquid nitrogen chamber, outer diameter 114.30 mm thin walled stainless steel tubing; H, brass bottom of liquid nitrogen reservoir and thermal contact to liquid nitrogen radiation shield (T); I, Teflon insulating layer, screwed onto brass floor; J, household aluminium foil; K, 3 mm stainless steel base; L, liquid helium reservoir; M, short 38.10 mm Yorkshire copper tubing; N, thin walled stainless steel tubing, outer diameter 31.75 mm; O, copper sample holder on and in which all samples, thermometers and heaters are mounted; P, exchange gas space; Q, copper cone on which sample holder (0) rests; R, 19.05 mm outer diameter Yorkshire copper tubing, silver soldered to Q, forming constant temperature chamber around O; S, pumping hole to evacuate space between liquid nitrogen and liquid helium reservoirs; T, liquid nitrogen radiation shield, 25.4 mm outer diameter Yorkshire copper tubing; U, Teflon spacer on 6.35 mm stainless steel tubing; V, liquid nitrogen reservoir; W, copper base; X, 2 mm stainless steel plate to seal vacuum chamber; Y, outer wall of lower part of cryostat, thin walled stainless steel tubing, outer diameter 31.75 mm (the actual length of the lower section is 250 mm); Z, stainless steel ring for support of tube R in the 77 K shield
temperature through a 1 m long, 12.5 mm stainless steel tube. The stainless steel tube ends on a quick-coupling connector. The tube also supports all the leads to the sample holder. All electrical wiring terminates on vacuum tight Oxford 10 pin connectors mounted on the quick-coupler head. All leads in and out of the system are twisted pairs of 42 gauge insulated wire. Copper was used for the current
Platinum thermometer Carbon thermometer for T control I T o stainless steel tube
Figure 2 Copper sample holder upon and in which all samples, thermometers and heaters are mounted. Only sample holder with BJ was utilized (/being the current through the sample)
carrying leads, and manganin for the voltage monitoring leads. The leads are wrapped around the 1 m long stainless steel tube and thermally anchored to the copper sample holder by tightly clamping them to the block between cigarette papers covered in thermal grease. The rest of the construction and layout are fairly standard. The cryostat is cooled in the usual way, with at most 100/~m of air in the (rotary-pumped) insulation space and close to 1 atm t of helium gas in the exchange space. The small liquid nitrogen chamber and poor insulation during cool-down necessitated an automatic liquid nitrogen filling device. Cooling the cryostat from 77 K requires ~ 3 dm 3 liquid helium. A more than adequate liquid helium level detector utilizing four independent Wheatstone bridges with four Allen-Bradley resistors mounted at different depths in the helium reservoir was built. Transfer of 4 dm 3, after cool-down, enables 4 h of measurements to be made between 4 and 20 K, after t 1 atm = 101.325 kPa
Research and technical notes which the system is pumped down to 1.4 K, with roughly 3 h of measurements being done below 4 K. This is to be compared with the ,~ 1 dm a h- 1 needed to maintain a continuous flow cryostat at or near 4.2 K or ~ 2 dm 3 h - 1 at temperatures approaching 1.5 K. Above 20 K, a powerful heater (300 mW) is required, which results in increased helium consumption. The higher specific heats of materials at these temperatures causes longer waiting periods before temperature stabilization occurs, and hence the design is not really suited to fixed temperature measurements between 20 and 80 K. The temperature below 4 K was controlled to _ 0.02 K, during the 15 min period needed for 26 magnetoresistance points, using a Lake Shore manostat controller on the pumping line. Between 4 and 20 K the temperature was controlled using an electronic temperature controller 3, with which the temperature drift during a 15 min period was also + 0.02 K. Prolonged measurements above 80 K can be done, of course, by filling the liquid helium chamber with liquid nitrogen.
S a m p l e holder The lower part of the sample holder which is mounted
Computer animation as a teaching aid: the Stirling cycle A. Laesecke* University of Siegen, Department of Mechanical Engineering, Institute for Fluid- and Thermodynamics, PO Box 10 12 40, 5900 Siegen, FRG Received 25 September 1989
An instructional program has been developed for personal computers to visualize the motion inside a Stirling cryocooler. Used to supplement an experimental laboratory course, the program has turned out as a valuable pedagogical tool, greatly facilitating the understanding of this important thermodynamic cycle by the students.
Keywords: thermodynamics; Stirling coolers; models; computer animation
cryo-
* Present address: National Institute of Standards and Technology, Thermophysics Division, 325 Broadway, Boulder, CO 80303-3328, USA 0011-2275/90/040367-04 1 ¢1ClORHttArworth & Co (Publishers~ Ltd
within the helium (4He) cryostat is shown in Figure 2. The sample holder is constructed from a solid copper rod, extended a short distance above (below in the figure) where it joins the previously mentioned 12.5 mm stainless steel tubing. The sample holder is designed to hold two thin film samples (on glass substrates); one perpendicular to the applied magnetic field and one parallel. Contact to the sample is made by bridging the gap between the copper contact tags and the sample with a short coiled wire and then painting over this with conductive silver paint. To determine the temperature, a calibrated platinum thermometer was used for T > 20 K and a calibrated germanium thermometer for 1.4 < T < 20 K. The thermometers and heaters were kept in good thermal contact with the copper block by means of Apiezon M grease.
References 1 White, H. and McLacldan, D.S. JPhys C SolidState Phys(1986)19 5414 2 White, H. and McLachlan, D.S. J PhysCondensedMatter(1989)1 6665 3 Newrock, R.S.,Wagner, D.K. andStanley, H.E. JPhysEScilnstrum (1977) 10 934
Thermodynamics is one of the more difficult fields in engineering, although it does not require an extensive mathematical framework. To illustrate the abstract matter, lecture courses in thermodynamics are always accompanied by laboratory tutorials. Graduate students in the Department of Mechanical Engineering of Siegen University are offered the chance to participate in a laboratory experiment which deals with the liquefaction of ambient air by means of a Stifling cryocooler. The objectives of the experiment are: first, to perform a complete analysis of the energy conversion and thermodynamic efficiency of a real Stirling cycle as opposed to the ideal process1; and second, to perform a comparison between the ideal and real behaviour of the working gas, hydrogen, in the Stirling cryocooler using the equation of state of Bender 2. The experiments are conducted with a Philips PLA 107 engine** which is used in the department on a regular basis to produce liquid air as a coolant for material science research. The set-up is almost identical to the one shown in the article of Krhler 3. For the measurements, it has been equipped with additional instrumentation. The electrical energy consumption of the driving electric motor is measured with a wattmeter. The volume flow rate of the cooling water is determined with a flowmeter while two thermocouples measure its inlet and outlet temperature. The produced mass of liquid air is measured with a balance. Thermocouples are also used to determine the temperatures close to the expansion and compression space of the Stirling engine. A pressure transducer has been mounted to measure the pressure in the compression space. Its signal is amplified
** Philips GmbH, Scientific Instruments, Kassel, FRG