{"id":15129,"date":"2025-05-08T23:10:25","date_gmt":"2025-05-08T21:10:25","guid":{"rendered":"https:\/\/themacs-engineering.com\/?p=15129"},"modified":"2026-11-05T13:48:33","modified_gmt":"2026-11-05T13:48:33","slug":"measurement-of-the-thermal-conductivity-of-copper-in-cryogenic-conditions","status":"publish","type":"post","link":"https:\/\/preprod.themacs-engineering.com\/en\/measurement-of-the-thermal-conductivity-of-copper-in-cryogenic-conditions\/","title":{"rendered":"Measurement of the thermal conductivity of copper in cryogenic conditions"},"content":{"rendered":"<h1>Measurement of the thermal conductivity of copper in cryogenic conditions<\/h1>\n<p>We have begun the first measurements under cryogenic conditions of the thermal conductivity of copper samples.<\/p>\n<p>Initial results are conclusive.<\/p>\n<p>&nbsp;<\/p>\n<h3>Article avalable here :<\/h3>\n<p><a href=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/Mesure-de-la-conductivite-thermique-du-cuivre-en-condition-cryogeniques-en-GB.pdf\">Mesure de la conductivit\u00e9 thermique du cuivre en condition cryog\u00e9niques en-GB<\/a><\/p>\n<h2><\/h2>\n<h2><\/h2>\n<h2>Principle of the method<\/h2>\n<p>The method adopted is specific to good conductors like copper.<\/p>\n<h2>experimental set-up<\/h2>\n<p>The experimental set-up is shown below.<\/p>\n<p><a href=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/schema1.png\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-15122 img-responsive aligncenter\" src=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/schema1.png\" alt=\"\" width=\"513\" height=\"358\" srcset=\"https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/schema1.png 758w, https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/schema1-300x209.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/photo1-scaled.jpg\"><img decoding=\"async\" class=\" wp-image-15121 img-responsive aligncenter\" src=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/photo1-scaled.jpg\" alt=\"\" width=\"689\" height=\"310\" \/><\/a><\/p>\n<p>A pulsed heating system is used to continuously calibrate the temperature measurement diodes. A reference temperature sensor is placed on the cold part of the cold head. This sensor is a CERNOX with a calibration certificate.<\/p>\n<p>Pulsed heating creates a heat flow in the sample and measures conductivity:<\/p>\n<p class=\"text-center\"><a href=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/lambda-e1746729797802.png\"><img decoding=\"async\" class=\" wp-image-15123 img-responsive aligncenter\" src=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/lambda-e1746729797802.png\" alt=\"\" width=\"317\" height=\"162\" srcset=\"https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/lambda-e1746729797802.png 520w, https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/lambda-e1746729797802-300x153.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/a><\/p>\n<p>Where \u03bb is the conductivity, P is the injected power, e is the length between the two measurement points, S is the cross-sectional area of the copper bar and \u0394T is the temperature difference between the two measurement points.<\/p>\n<p>During the phases when the heating is switched off, the diodes are calibrated to give the most reliable measurement possible.<\/p>\n<p>An example of temperature measurements is shown below:<\/p>\n<p><a href=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graph1-eng.png\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-15118 img-responsive aligncenter\" src=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graph1-eng.png\" alt=\"\" width=\"726\" height=\"411\" srcset=\"https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graph1-eng.png 980w, https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graph1-eng-300x170.png 300w, https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graph1-eng-768x435.png 768w\" sizes=\"(max-width: 726px) 100vw, 726px\" \/><\/a><\/p>\n<p>As the thermal diffusivity of copper is very high, steady-state conditions can be reached very quickly during both the calibration and conductivity measurement phases.<\/p>\n<p>&nbsp;<\/p>\n<h2>Results<\/h2>\n<p>The measurement results are compared with the NIST values and presented in the graph below:<\/p>\n<p><a href=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graphique-eng.png\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-15120 img-responsive aligncenter\" src=\"http:\/\/themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graphique-eng.png\" alt=\"\" width=\"697\" height=\"402\" srcset=\"https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graphique-eng.png 947w, https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graphique-eng-300x173.png 300w, https:\/\/preprod.themacs-engineering.com\/wp-content\/uploads\/2025\/05\/graphique-eng-768x443.png 768w\" sizes=\"(max-width: 697px) 100vw, 697px\" \/><br \/>\n<\/a><\/p>\n<h2>Conclusion<\/h2>\n<p>The measurement chain has now been validated, but the accuracy of the measurements still needs to be confirmed.<\/p>\n<p>The first measurements below 50K are not currently usable because the cold head was not regulated precisely enough. The measurements were made by letting the temperature rise slowly.<\/p>\n<p>For copper, the next step will be to modify the experimental set-up so as to be able to extract the diffusivity of the pulsed regime and to regulate the temperature with a PID in order to carry out measurements down to 6K.<\/p>\n<p>The measuring device will also be modified to measure the thermal conductivity and heat capacity of epoxy-type polymers.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Measurement of the thermal conductivity of copper in cryogenic conditions We have begun the first measurements under cryogenic conditions of the thermal conductivity of copper samples. Initial results are conclusive. &nbsp; Article avalable here : Mesure de la conductivit\u00e9 thermique du cuivre en condition cryog\u00e9niques en-GB Principle of the method The method adopted is specific [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":15124,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[108],"tags":[],"class_list":["post-15129","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized-en-us"],"_links":{"self":[{"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/posts\/15129","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/comments?post=15129"}],"version-history":[{"count":1,"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/posts\/15129\/revisions"}],"predecessor-version":[{"id":25351,"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/posts\/15129\/revisions\/25351"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/media\/15124"}],"wp:attachment":[{"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/media?parent=15129"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/categories?post=15129"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/preprod.themacs-engineering.com\/en\/wp-json\/wp\/v2\/tags?post=15129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}