{"id":101640,"date":"2024-07-22T10:17:07","date_gmt":"2024-07-22T08:17:07","guid":{"rendered":"https:\/\/www.linseis.com\/bez-kategorii\/pomiar-pojemnosci-cieplnej-wlasciwej-cp-przy-uzyciu-metody-nieustalonego-drutu-grzejnego\/"},"modified":"2026-01-16T10:04:16","modified_gmt":"2026-01-16T09:04:16","slug":"pomiar-pojemnosci-cieplnej-wlasciwej-cp-przy-uzyciu-metody-nieustalonego-drutu-grzejnego","status":"publish","type":"post","link":"https:\/\/www.linseis.com\/pl\/wiedza\/pomiar-pojemnosci-cieplnej-wlasciwej-cp-przy-uzyciu-metody-nieustalonego-drutu-grzejnego\/","title":{"rendered":"Pomiar pojemno\u015bci cieplnej w\u0142a\u015bciwej (Cp) przy u\u017cyciu metody nieustalonego drutu grzejnego"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"101640\" class=\"elementor elementor-101640 elementor-15038\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9eb8745 e-flex e-con-boxed e-con e-parent\" data-id=\"9eb8745\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-be9105e elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"be9105e\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Pojemno\u015b\u0107 cieplna w\u0142a\u015bciwa jest podstawow\u0105 termofizyczn\u0105 w\u0142a\u015bciwo\u015bci\u0105 materia\u0142u i jest przydatna do oceny materia\u0142\u00f3w i obszar\u00f3w ich zastosowania. Mo\u017cna j\u0105 okre\u015bli\u0107 za pomoc\u0105 <a href=\"https:\/\/www.linseis.com\/startseite\/methoden\/dynamische-differenz-kalorimetrie\/\">\n  <strong>dynamicznej r\u00f3\u017cnicowej kalorymetrii skaningowej (DSC)<\/strong>\n<\/a> mo\u017cna okre\u015bli\u0107. <\/p><p>Innym sposobem okre\u015blenia pojemno\u015bci cieplnej w\u0142a\u015bciwej jest zastosowanie metody przej\u015bciowego nagrzewania drutu (<a href=\"https:\/\/www.astm.org\/c1113_c1113m-09r19.html\" target=\"_blank\" rel=\"noopener\">\n  <strong>ASTM C1113-99<\/strong>\n<\/a>). Metoda zale\u017cna od czasu zapewnia dok\u0142adne i precyzyjne wyniki okre\u015blania warto\u015bci termofizycznych <a href=\"https:\/\/www.linseis.com\/messgeraete\/waermeleitfaehigkeit\/\">\n  <strong>Przewodno\u015b\u0107 cieplna \u03bb<\/strong>\n<\/a>, <a href=\"https:\/\/www.linseis.com\/startseite\/messgroessen\/temperaturleitfaehigkeit\/\">\n  <strong>dyfuzyjno\u015b\u0107 cieplna<\/strong>\n<\/a> <strong>a<\/strong> i <a href=\"https:\/\/www.linseis.com\/wissen\/spezifische-waermekapazitaet\/\">\n  <strong>pojemno\u015bci cieplnej w\u0142a\u015bciwej cp<\/strong>\n<\/a> gaz\u00f3w i cieczy. Wzrost temperatury jest mierzony w pr\u00f3bce, kt\u00f3ra jest ogrzewana przez cienki drut grzejny w znanej odleg\u0142o\u015bci. Drut s\u0142u\u017cy jako \u017ar\u00f3d\u0142o ciep\u0142a Joule&#8217;a i jednocze\u015bnie jako termometr oporowy. Wraz ze wzrostem temperatury zmienia si\u0119 rezystancja drutu, co pozwala na pomiar temperatury.    <\/p><p>Ju\u017c w 1931 roku St\u00e5lhane i Pyk zmierzyli przewodno\u015b\u0107 ciepln\u0105 proszk\u00f3w przy u\u017cyciu aparatu, kt\u00f3ry by\u0142 bardzo podobny do dzisiejszej metody; znale\u017ali nast\u0119puj\u0105c\u0105 korelacj\u0119 empiryczn\u0105:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-eac9a92 elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-image\" data-id=\"eac9a92\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"800\" height=\"316\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel.png\" class=\"attachment-large size-large wp-image-33635\" alt=\"\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel.png 987w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-300x119.png 300w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-768x303.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-33229bc elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"33229bc\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Bior\u0105c pod uwag\u0119 r\u00f3wnanie przewodzenia ciep\u0142a, temperatur\u0119 <em>T<\/em> dla przewodu grzejnego jako liniowego \u017ar\u00f3d\u0142a ciep\u0142a w odleg\u0142o\u015bci<em> r<\/em> od przewodu w okre\u015blonym czasie <em>t<\/em> mo\u017cna obliczy\u0107 w nast\u0119puj\u0105cy spos\u00f3b:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1c3873f elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-image\" data-id=\"1c3873f\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"116\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit.png\" class=\"attachment-large size-large wp-image-33639\" alt=\"\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit.png 1012w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit-300x44.png 300w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit-768x112.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-71e5f71 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"71e5f71\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"text-decoration: underline;\">R\u00f3wnanie 2<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-71398e8 elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"71398e8\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Umo\u017cliwia to obliczenie przewodno\u015bci cieplnej <em>\u03bb<\/em> na podstawie zmiany temperatury w dw\u00f3ch r\u00f3\u017cnych momentach <em>\n  <sub>t1<\/sub>\n<\/em> i <em>\n  <sub>t2<\/sub>\n<\/em>:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c93723c elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-image\" data-id=\"c93723c\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"300\" height=\"95\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit-2-300x95-1.png\" class=\"attachment-large size-large wp-image-33643\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-256e8e9 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"256e8e9\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"text-decoration: underline;\">R\u00f3wnanie 3<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1f62fdd elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"1f62fdd\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Poniewa\u017c przewodno\u015b\u0107 cieplna <em><strong>\u03bb<\/strong>,<\/em> dyfuzyjno\u015b\u0107 cieplna, pojemno\u015b\u0107 cieplna w\u0142a\u015bciwa <em>\n  <sub>cp<\/sub>\n<\/em> i g\u0119sto\u015b\u0107 <em>\n  <strong>\u03c1<\/strong>\n<\/em> s\u0105 powi\u0105zane w nast\u0119puj\u0105cy spos\u00f3b,<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b2cb2c6 elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-image\" data-id=\"b2cb2c6\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"483\" height=\"87\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit-Dichte-3.png\" class=\"attachment-large size-large wp-image-33647\" alt=\"\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit-Dichte-3.png 483w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit-Dichte-3-300x54.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3f23e24 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"3f23e24\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>pojemno\u015b\u0107 ciepln\u0105 w\u0142a\u015bciw\u0105 <em>cp<\/em>mo\u017cna okre\u015bli\u0107 <em>\n  <sub>za pomoc\u0105 <\/sub>\n<\/em>r\u00f3wnania 3:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fca354a elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-image\" data-id=\"fca354a\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"324\" height=\"80\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit-Dichte-4.png\" class=\"attachment-large size-large wp-image-33651\" alt=\"\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit-Dichte-4.png 324w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Cp-THB-Formel-Temperaturleitfaehigkeit-Dichte-4-300x74.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2cbc2e6 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"2cbc2e6\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Metoda przej\u015bciowego gor\u0105cego mostka (THB)\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-681528f elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"681528f\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Dalszym rozwini\u0119ciem metody transient hot-wire jest metoda transient-hot-bridge opracowana przez Physikalisch-Technische Bundesanstalt w Braunschweig, kt\u00f3ra zosta\u0142a wprowadzona na rynek europejski w 2005 roku (zob. <a href=\"https:\/\/www.linseis.com\/messgeraete\/waermeleitfaehigkeit\/thb-l56\/\">\n  <strong>THB<\/strong>\n<\/a>).<\/p><p>Opatentowany czujnik jest tutaj kluczowym elementem. Podczas gdy w metodzie drutu grzejnego wykorzystywana jest tylko jedna ta\u015bma grzejna, THB wykorzystuje cztery meandruj\u0105ce ta\u015bmy grzejne. Asymetryczny podzia\u0142 poprzeczny ka\u017cdej ta\u015bmy i r\u00f3\u017cne odleg\u0142o\u015bci mi\u0119dzy ta\u015bmami w po\u0142\u0105czeniu z obwodem mostka Wheatstone&#8217;a umo\u017cliwiaj\u0105 skuteczn\u0105 kompensacj\u0119 znacznych systematycznych odchyle\u0144 pomiarowych.  <\/p><p>Zale\u017cna od czasu metoda gor\u0105cego mostka umo\u017cliwia jednoczesny pomiar termofizycznych w\u0142a\u015bciwo\u015bci materia\u0142owych \u03bb, a i cp wielu materia\u0142\u00f3w i geometrii. Metoda dostarcza wyniki dla cia\u0142 sta\u0142ych i cieczy, a tak\u017ce proszk\u00f3w i past z wysok\u0105 dok\u0142adno\u015bci\u0105 pomiaru i niskim nak\u0142adem czasu. <\/p><p>Metoda pomiarowa jest wykorzystywana w szerokim zakresie zastosowa\u0144, w tym do oceny materia\u0142\u00f3w magazynuj\u0105cych ciep\u0142o i materia\u0142\u00f3w izolacyjnych, a tak\u017ce do analizy komponent\u00f3w elektronicznych i materia\u0142\u00f3w wykorzystywanych w nanotechnologii.  <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7703270 elementor-widget elementor-widget-spacer\" data-id=\"7703270\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Pojemno\u015b\u0107 cieplna w\u0142a\u015bciwa jest podstawow\u0105 w\u0142a\u015bciwo\u015bci\u0105 termofizyczn\u0105 materia\u0142\u00f3w i jest przydatna do oceny materia\u0142\u00f3w i obszar\u00f3w ich zastosowania. Mo\u017cna j\u0105 okre\u015bli\u0107 za pomoc\u0105 dynamicznej r\u00f3\u017cnicowej kalorymetrii skaningowej (DSC). <\/p>\n","protected":false},"author":3,"featured_media":33623,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[596],"tags":[],"class_list":["post-101640","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-wiedza"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/posts\/101640","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/comments?post=101640"}],"version-history":[{"count":0,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/posts\/101640\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/media\/33623"}],"wp:attachment":[{"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/media?parent=101640"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/categories?post=101640"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/tags?post=101640"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}