{"id":101497,"date":"2025-06-16T14:43:53","date_gmt":"2025-06-16T12:43:53","guid":{"rendered":"https:\/\/www.linseis.com\/bez-kategorii\/rozszerzalnosc-cieplna\/"},"modified":"2026-01-15T09:51:54","modified_gmt":"2026-01-15T08:51:54","slug":"rozszerzalnosc-cieplna","status":"publish","type":"post","link":"https:\/\/www.linseis.com\/pl\/wiedza\/rozszerzalnosc-cieplna\/","title":{"rendered":"Rozszerzalno\u015b\u0107 cieplna"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"101497\" class=\"elementor elementor-101497 elementor-87275\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-20e7cce e-con-full e-flex e-con e-parent\" data-id=\"20e7cce\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-330d9bc e-con-full e-flex e-con e-child\" data-id=\"330d9bc\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element 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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<div class=\"elementor-element elementor-element-8a71db9 elementor-widget elementor-widget-spacer\" data-id=\"8a71db9\" 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<div class=\"elementor-element elementor-element-5ef1fd4 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"5ef1fd4\" 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\">Rozszerzalno\u015b\u0107 cieplna<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2a88229 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"2a88229\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Wprowadzenie do rozszerzalno\u015bci cieplnej<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-77833f4 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"77833f4\" 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>Rozszerzalno\u015b\u0107 cieplna &#8211; znana r\u00f3wnie\u017c jako rozszerzalno\u015b\u0107 cieplna &#8211; jest zjawiskiem fizycznym, kt\u00f3re jest r\u00f3wnie istotne w \u017cyciu codziennym, jak i w technologii. Opisuje ono zmian\u0119 wymiar\u00f3w geometrycznych cia\u0142a przy zmianie jego temperatury. Zrozumienie i precyzyjny pomiar tej w\u0142a\u015bciwo\u015bci jest szczeg\u00f3lnie wa\u017cny w budownictwie, in\u017cynierii mechanicznej i badaniach materia\u0142owych.    <\/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-50e1380 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"50e1380\" 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\">Podstawy rozszerzalno\u015bci cieplnej<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cffc1d6 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"cffc1d6\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Co to jest rozszerzalno\u015b\u0107 cieplna?<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d182312 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"d182312\" 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>Wzrost temperatury zwi\u0119ksza ruch molekularny na poziomie cz\u0105steczek materia\u0142u, a co za tym idzie, zwi\u0119ksza si\u0119 r\u00f3wnie\u017c jego zapotrzebowanie na przestrze\u0144. Efektem tego jest rozszerzanie si\u0119 materia\u0142u. Po och\u0142odzeniu zapotrzebowanie na przestrze\u0144 ponownie spada i nast\u0119puje skurcz termiczny.    <\/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-0f43171 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"0f43171\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Przyczyny i zasady fizyczne<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a261340 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"a261340\" 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<ul><li>Powodem tego jest wzrost energii kinetycznej cz\u0105stek podczas ogrzewania.<\/li><li>Zwi\u0119ksza to odleg\u0142o\u015b\u0107 mi\u0119dzy cz\u0105steczkami.<\/li><li>Ka\u017cdy materia\u0142 ma charakterystyczny wsp\u00f3\u0142czynnik rozszerzalno\u015bci, kt\u00f3ry wskazuje, jak bardzo rozszerza si\u0119, gdy zmienia si\u0119 temperatura, w zale\u017cno\u015bci od zawartych w nim cz\u0105stek i ich stopni swobody.<\/li><\/ul>\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-affb892 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"affb892\" 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\">Formy rozszerzalno\u015bci cieplnej<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-397871d elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"397871d\" 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>Rozszerzalno\u015b\u0107 cieplna mo\u017ce objawia\u0107 si\u0119 w r\u00f3\u017cnych wymiarach w zale\u017cno\u015bci od kszta\u0142tu cia\u0142a i sk\u0142adu materia\u0142u: w d\u0142ugo\u015bci, powierzchni lub obj\u0119to\u015bci.<\/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-81c6ff9 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"81c6ff9\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Rozszerzenie liniowe<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-521c097 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"521c097\" 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>W przypadku rozszerzalno\u015bci liniowej d\u0142ugo\u015b\u0107 cia\u0142a zmienia si\u0119 wzd\u0142u\u017c osi, na przyk\u0142ad w przypadku metalowego pr\u0119ta, kt\u00f3ry wyra\u017anie wyd\u0142u\u017ca si\u0119 po podgrzaniu. Ta forma rozszerzalno\u015bci cieplnej jest \u0142atwa do zmierzenia i jest najcz\u0119stszym zastosowaniem.   <\/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-499af99 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"499af99\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Rozszerzenie powierzchni<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7083afa elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"7083afa\" 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>Zwi\u0119ksza to powierzchni\u0119 cia\u0142a &#8211; zazwyczaj w przypadku arkuszy lub folii, kt\u00f3re rozszerzaj\u0105 si\u0119 r\u00f3wnomiernie w dw\u00f3ch kierunkach przestrzennych.<\/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-8709bba elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"8709bba\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Rozszerzenie obj\u0119to\u015bci<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1303a2e elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"1303a2e\" 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>Rozszerzalno\u015b\u0107 obj\u0119to\u015bciowa odnosi si\u0119 do rozszerzalno\u015bci przestrzennej we wszystkich trzech kierunkach. Wyst\u0119puje g\u0142\u00f3wnie w cieczach i gazach, ale mo\u017cna j\u0105 r\u00f3wnie\u017c zaobserwowa\u0107 w cia\u0142ach sta\u0142ych i mo\u017cna j\u0105 cz\u0119\u015bciowo obliczy\u0107 na podstawie rozszerzalno\u015bci liniowej osi.   <\/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-5fe1e3d elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-image\" data-id=\"5fe1e3d\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"800\" height=\"800\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2025\/06\/Thermal-Expansion-1.png\" class=\"attachment-large size-large wp-image-85843\" alt=\"\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2025\/06\/Thermal-Expansion-1.png 1024w, https:\/\/www.linseis.com\/wp-content\/uploads\/2025\/06\/Thermal-Expansion-1-300x300.png 300w, https:\/\/www.linseis.com\/wp-content\/uploads\/2025\/06\/Thermal-Expansion-1-150x150.png 150w, https:\/\/www.linseis.com\/wp-content\/uploads\/2025\/06\/Thermal-Expansion-1-768x768.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\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-3120c46 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"3120c46\" 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\">Opis matematyczny<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aae0b1f elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"aae0b1f\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Rozszerzenie liniowe<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e48ceb0 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"e48ceb0\" 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>\\(<br>\\Delta L = \\alpha \\cdot L_0 \\cdot \\Delta T<br>\\quad \\text{mit} \\quad<br>\\begin{cases}<br>\\Delta L : \\text{zmiana d\u0142ugo\u015bci (m)} \\\\<br>\\alpha : \\text{wsp\u00f3\u0142czynnik rozwini\u0119cia liniowego (1\/K)} \\\\<br>L_0 : \\text{d\u0142ugo\u015b\u0107 pocz\u0105tkowa (m)} \\\\<br>\\ Delta T : \\text{zmiana temperatury (K)}<br>\\end{cases}<br>\\)<\/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-fec8579 elementor-widget elementor-widget-spacer\" data-id=\"fec8579\" 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<div class=\"elementor-element elementor-element-117eb24 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"117eb24\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Rozszerzenie obj\u0119to\u015bci<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1c7748e elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"1c7748e\" 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>\\(<br>\\Delta V = \\gamma \\cdot V_0 \\cdot \\Delta T<br>\\quad \\text{mit} \\quad<br>\\begin{cases}<br>\\Delta V : \\text{zmiana obj\u0119to\u015bci (m\u00b3)} \\\\<br>\\gamma : \\text{wsp\u00f3\u0142czynnik rozszerzalno\u015bci obj\u0119to\u015bciowej (1\/K)} \\\\<br>V_0 : \\text{obj\u0119to\u015b\u0107 pocz\u0105tkowa (m\u00b3)} \\\\<br>\\ Delta T : \\text{zmiana temperatury (K)}<br>\\end{cases}<br>\\)<\/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-10ceced elementor-widget elementor-widget-spacer\" data-id=\"10ceced\" 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<div class=\"elementor-element elementor-element-eee1ba8 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"eee1ba8\" 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\">Metody pomiarowe do okre\u015blania rozszerzalno\u015bci cieplnej<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-727b42d elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"727b42d\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Dilatometr<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f231dcf elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"f231dcf\" 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>A <a href=\"https:\/\/www.linseis.com\/messgeraete\/dilatometer\/\">\n  <strong>dylatometr<\/strong>\n<\/a> mierzy zmian\u0119 d\u0142ugo\u015bci lub obj\u0119to\u015bci pr\u00f3bki przy okre\u015blonej temperaturze i zmianie temperatury. Pr\u00f3bka jest podgrzewana lub ch\u0142odzona, a zmiana jej d\u0142ugo\u015bci jest przenoszona do przetwornika przemieszczenia za po\u015brednictwem popychacza. Nieod\u0142\u0105czna rozszerzalno\u015b\u0107 uk\u0142adu pomiarowego jest kompensowana lub korygowana za pomoc\u0105 materia\u0142u odniesienia.  <\/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-2cf348c elementor-widget elementor-widget-spacer\" data-id=\"2cf348c\" 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<div class=\"elementor-element elementor-element-0687a0f elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"0687a0f\" 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><strong>Typowe mierzone zmienne:<\/strong><\/p><ul><li><a href=\"https:\/\/www.linseis.com\/wissen\/bestimmung-der-cte-dichte\/\"><strong>Liniowy wsp\u00f3\u0142czynnik rozszerzalno\u015bci cieplnej (CTE)<\/strong><\/a><\/li><li>Temperatury i etapy spiekania<\/li><li><a href=\"https:\/\/www.linseis.com\/wissen\/glasuebergangstemperatur\/\"><strong>Temperatura zeszklenia (Tg)<\/strong><\/a><\/li><li>Przej\u015bcia fazowe<\/li><li><a href=\"https:\/\/www.linseis.com\/wissen\/bestimmung-der-cte-dichte\/\"><strong>Zmiany obj\u0119to\u015bci i g\u0119sto\u015bci<\/strong><\/a><\/li><\/ul><p><strong>Obszary zastosowa\u0144:<\/strong><\/p><ul><li>Materia\u0142y: metale, ceramika, szk\u0142o, polimery, kompozyty<\/li><li>Mo\u017cliwy zakres temperatur: od -260 \u00b0C do +2800 \u00b0C (w zale\u017cno\u015bci od konfiguracji urz\u0105dzenia)<\/li><\/ul>\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-eed1324 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"eed1324\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Analiza termomechaniczna (TMA)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4864a43 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"4864a43\" 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>Analiza <a href=\"https:\/\/www.linseis.com\/messgeraete\/thermische-analyse\/tma-thermomechanische-analyse\/\">\n  <strong>analiza termomechaniczna (TMA)<\/strong>\n<\/a> to metoda pomiaru zmian wymiar\u00f3w pod wp\u0142ywem napr\u0119\u017ce\u0144 mechanicznych w okre\u015blonej temperaturze. Sonda naciska na pr\u00f3bk\u0119 ze sta\u0142\u0105 si\u0142\u0105, podczas gdy temperatura jest powoli zmieniana. Czujnik, cz\u0119sto transformator r\u00f3\u017cnicowy lub LVDT (Linear Variable Differential Transformer), mierzy wynikaj\u0105ce z tego zmiany d\u0142ugo\u015bci w czasie rzeczywistym.  <\/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-29d7c21 elementor-widget elementor-widget-spacer\" data-id=\"29d7c21\" 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<div class=\"elementor-element elementor-element-8812c3b elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"8812c3b\" 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><strong>Zmierzone w\u0142a\u015bciwo\u015bci:<\/strong><\/p><ul><li>Rozszerzalno\u015b\u0107 liniowa i wsp\u00f3\u0142czynnik rozszerzalno\u015bci<\/li><li>Punkty zmi\u0119kczania<\/li><li>Procesy skurczu podczas spiekania<\/li><li>Przej\u015bcie szkliste, temperatura topnienia, krystalizacja<\/li><li>Pe\u0142zanie i relaksacja (zale\u017cne od czasu odkszta\u0142cenie pod obci\u0105\u017ceniem)<\/li><\/ul><p><strong>Typowe zastosowania:<\/strong><\/p><ul><li>Analiza cia\u0142 sta\u0142ych, cieczy i materia\u0142\u00f3w o konsystencji pasty<\/li><li>Nadaje si\u0119 do: Tworzywa sztuczne, elastomery, kleje, metale, ceramika, kompozyty<\/li><li>Uzupe\u0142nia inne metody, takie jak <a href=\"https:\/\/www.linseis.com\/messgeraete\/dsc-dynamische-differenz-kalorimetrie\/\">\n  <strong>DSC<\/strong>\n<\/a>, <a href=\"https:\/\/www.linseis.com\/messgeraete\/tga-thermogravimetrie\/\">\n  <strong>TGA<\/strong>\n<\/a> i DMA<\/li><\/ul>\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-d4cbe93 elementor-widget elementor-widget-spacer\" data-id=\"d4cbe93\" 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<div class=\"elementor-element elementor-element-9d000c2 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"9d000c2\" 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>Dzi\u0119ki wysokiej czu\u0142o\u015bci TMA umo\u017cliwia nie tylko okre\u015blanie rozszerzalno\u015bci, ale tak\u017ce wykrywanie s\u0142abych przej\u015b\u0107 fizycznych &#8211; takich jak zmiany w sieci krystalicznej, utwardzanie lub rozwarstwianie. Sprawia to, \u017ce jest to wszechstronne narz\u0119dzie do bada\u0144 i przemys\u0142u.   <\/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-f03bf48 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"f03bf48\" 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\">Wykorzystanie dylatometr\u00f3w do analizy rozszerzalno\u015bci cieplnej<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c3b7d41 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"c3b7d41\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Szczeg\u00f3\u0142owa funkcjonalno\u015b\u0107<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-887d0a3 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"887d0a3\" 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>Dylatometry s\u0105 wa\u017cnymi przyrz\u0105dami do okre\u015blania rozszerzalno\u015bci cieplnej materia\u0142\u00f3w. Pomiar jest przeprowadzany za pomoc\u0105 element\u00f3w mechanicznych, takich jak popychacz, lub bezkontaktowo za pomoc\u0105 czujnik\u00f3w optycznych. Pr\u00f3bka jest umieszczana w ogrzewanym piecu, w kt\u00f3rym przepuszczany jest okre\u015blony profil temperatury. Wraz ze zmian\u0105 temperatury, precyzyjny przetwornik przemieszczenia mierzy zmian\u0119 d\u0142ugo\u015bci materia\u0142u pr\u00f3bki. Pomiar ten mo\u017ce by\u0107 wykorzystany do okre\u015blenia liniowego wsp\u00f3\u0142czynnika rozszerzalno\u015bci cieplnej (CTE) &#8211; kluczowego parametru opisuj\u0105cego zachowanie termiczne materia\u0142\u00f3w.      <\/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-67d18b5 elementor-widget elementor-widget-spacer\" data-id=\"67d18b5\" 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<div class=\"elementor-element elementor-element-f439301 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"f439301\" 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><strong>Najwa\u017cniejsze kroki w procesie pomiaru:<\/strong><\/p><ul><li>Pr\u00f3bka jest podgrzewana lub ch\u0142odzona w kontrolowany spos\u00f3b.<\/li><li>Wynikaj\u0105ca z tego zmiana d\u0142ugo\u015bci jest rejestrowana z du\u017c\u0105 dok\u0142adno\u015bci\u0105.<\/li><li>Wsp\u00f3\u0142czynnik CTE jest obliczany na podstawie stosunku mi\u0119dzy zmian\u0105 d\u0142ugo\u015bci a zmian\u0105 temperatury.<\/li><\/ul><div> <\/div><p>Metoda ta zapewnia rozdzielczo\u015b\u0107 w zakresie submikrometrowym i jest odpowiednia do rutynowych kontroli jako\u015bci, a tak\u017ce do zastosowa\u0144 badawczych.<\/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-60aaa12 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"60aaa12\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Zastosowania i typowe mierzone zmienne<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-50bc3df elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"50bc3df\" 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>Dylatometry zapewniaj\u0105 szereg mierzalnych parametr\u00f3w, kt\u00f3re maj\u0105 kluczowe znaczenie dla rozwoju materia\u0142\u00f3w i proces\u00f3w przemys\u0142owych:<\/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-7580681 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"7580681\" 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><strong>Typowe zastosowania:<\/strong><\/p><ul><li>Okre\u015blanie przej\u015b\u0107 szklistych i fazowych<\/li><li>Analiza zachowania skurczowego w procesach spiekania<\/li><li>Pomiar zmian obj\u0119to\u015bci i g\u0119sto\u015bci<\/li><li>Zastosowanie w zapewnianiu jako\u015bci, opracowywaniu materia\u0142\u00f3w i badaniach<\/li><\/ul>\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-4776162 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"4776162\" 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\">R\u00f3\u017cnice mi\u0119dzy materia\u0142ami<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3cde593 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"3cde593\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Por\u00f3wnanie wsp\u00f3\u0142czynnik\u00f3w rozszerzalno\u015bci<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-eff1649 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"eff1649\" 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<ul>\n \t<li>Tworzywa sztuczne: np. PE = 2<sup>,10-4<\/sup> <sup> K-1<\/sup> K<\/li>\n \t<li>Metale: aluminium = 23<sup>,8-10-6<\/sup> <sup> K-1<\/sup>, stal = <sup> 11-1310-6<\/sup> <sup> K-1<\/sup> <\/li>\n \t<li>Ceramika\/szk\u0142o: Al\u2082O\u2083 = 7<sup>,5-10-6<\/sup> <sup> K-1<\/sup> <\/li>\n \t<li>Materia\u0142y specjalne: Invar = 0,55-1<sup>,2-10-6<\/sup> <sup> K-1<\/sup> <\/li>\n<\/ul>\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-d11584f elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"d11584f\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Znaczenie dla zastosowa\u0144 technicznych<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3334d97 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"3334d97\" 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<ul><li>Du\u017ce r\u00f3\u017cnice mog\u0105 prowadzi\u0107 do napr\u0119\u017ce\u0144 i uszkodzenia materia\u0142u.<\/li><li>Precyzyjny dob\u00f3r materia\u0142\u00f3w ma kluczowe znaczenie dla trwa\u0142o\u015bci konstrukcji.<\/li><\/ul>\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-c6db477 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"c6db477\" 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\">Praktyczne zastosowania i wyzwania<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d04f6b1 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"d04f6b1\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Znaczenie mi\u0119dzybran\u017cowe<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aff03be elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"aff03be\" 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>Rozszerzalno\u015b\u0107 cieplna jest kluczowym zagadnieniem w wielu dyscyplinach technicznych. W zale\u017cno\u015bci od obszaru zastosowania, rozszerzalno\u015b\u0107 cieplna mo\u017ce by\u0107 wykorzystywana w spos\u00f3b ukierunkowany lub musi by\u0107 aktywnie kompensowana w celu unikni\u0119cia uszkodzenia komponent\u00f3w lub utraty ich funkcjonalno\u015bci. Dobrze przemy\u015blane \u015brodki projektowe s\u0105 niezb\u0119dne, zw\u0142aszcza w przypadku sta\u0142ych waha\u0144 temperatury, kt\u00f3re wyst\u0119puj\u0105 w wielu \u015brodowiskach technicznych.    <\/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-5d66ef4 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"5d66ef4\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Typowe obszary zastosowania\n:<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bb1baa1 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"bb1baa1\" 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<ul><li>In\u017cynieria l\u0105dowa i wodna: Z\u0142\u0105cza kompensacyjne w mostach, jezdniach lub ruroci\u0105gach zapewniaj\u0105, \u017ce materia\u0142y mog\u0105 rozszerza\u0107 si\u0119 lub kurczy\u0107 wraz z wahaniami temperatury bez powodowania p\u0119kni\u0119\u0107 lub uszkodze\u0144 strukturalnych.<\/li><li>In\u017cynieria mechaniczna: W maszynach i systemach cz\u0119sto musz\u0105 wsp\u00f3\u0142pracowa\u0107 ze sob\u0105 komponenty o r\u00f3\u017cnej rozszerzalno\u015bci. Je\u015bli r\u00f3\u017cnice te nie zostan\u0105 uwzgl\u0119dnione, istnieje ryzyko napr\u0119\u017ce\u0144, wyciek\u00f3w lub przedwczesnego zu\u017cycia.   <\/li><li>Elektronika: P\u0142ytki drukowane, p\u00f3\u0142przewodniki i obudowy s\u0105 cz\u0119sto wykonane z r\u00f3\u017cnych materia\u0142\u00f3w. Nieprawid\u0142owe po\u0142\u0105czenie z r\u00f3\u017cnymi warto\u015bciami wsp\u00f3\u0142czynnika CTE mo\u017ce prowadzi\u0107 do p\u0119kni\u0119\u0107 po\u0142\u0105cze\u0144 lutowanych lub p\u0119kni\u0119\u0107 materia\u0142u.   <\/li><li>Lotnictwo i kosmonautyka: Tutaj wymagania s\u0105 szczeg\u00f3lnie wysokie. Komponenty musz\u0105 wytrzyma\u0107 zar\u00f3wno ekstremalne zimno w przestrzeni kosmicznej, jak i ekstremalne ciep\u0142o w atmosferze &#8211; bez deformacji lub utraty funkcjonalno\u015bci.   <\/li><\/ul>\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-8366138 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"8366138\" 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<h3 class=\"elementor-heading-title elementor-size-default\">Przyk\u0142ady z praktyki<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0f6c2cf elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"0f6c2cf\" 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<ul><li>Tory kolejowe s\u0105 uk\u0142adane z przerwami, aby unikn\u0105\u0107 odkszta\u0142ce\u0144 spowodowanych rozszerzalno\u015bci\u0105 ciepln\u0105.<\/li><li>Szk\u0142o borokrzemowe w naczyniach laboratoryjnych i kuchennych jest odporne na szoki termiczne dzi\u0119ki niskiemu wsp\u00f3\u0142czynnikowi rozszerzalno\u015bci.<\/li><li>Woda rozszerza si\u0119, gdy zamarza &#8211; jest to wyj\u0105tek, kt\u00f3ry sprawia, \u017ce l\u00f3d unosi si\u0119 na wodzie i izoluje j\u0105.<\/li><\/ul>\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-8836db2 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"8836db2\" 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\">Wnioski<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-492d64f elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"492d64f\" 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>Rozszerzalno\u015b\u0107 cieplna jest kluczowym zjawiskiem w fizyce i technologii. Jego dok\u0142adna znajomo\u015b\u0107 i precyzyjny pomiar za pomoc\u0105 dylatometr\u00f3w lub TMA umo\u017cliwia optymalizacj\u0119 materia\u0142\u00f3w pod k\u0105tem ich zastosowania. Umo\u017cliwia to opracowywanie produkt\u00f3w, kt\u00f3re dzia\u0142aj\u0105 niezawodnie nawet w ekstremalnych warunkach &#8211; zar\u00f3wno w przemy\u015ble, badaniach, jak i \u017cyciu codziennym.    <\/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-16379ac elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"16379ac\" 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\">Zalecane \u017ar\u00f3d\u0142a do pog\u0142\u0119bionej analizy<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2049310 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"2049310\" 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<ul><li><a href=\"https:\/\/www.leifiphysik.de\/waermelehre\/ausdehnung-bei-erwaermung\/grundwissen\/volumen-und-laengenaenderung-von-festkoerpern\" target=\"_blank\" rel=\"noopener\">LEIFIphysics: Zmiana obj\u0119to\u015bci i d\u0142ugo\u015bci cia\u0142 sta\u0142ych<\/a><br>(jasno wyja\u015bnione podstawy rozszerzalno\u015bci cieplnej)<\/li><li><a href=\"https:\/\/de.wikipedia.org\/wiki\/W%C3%A4rmeausdehnung\" target=\"_blank\" rel=\"noopener\">Wikipedia: Rozszerzalno\u015b\u0107 cieplna<\/a><br>(przegl\u0105d form, wzor\u00f3w i typowych warto\u015bci)<\/li><li><a href=\"https:\/\/studyflix.de\/ingenieurwissenschaften\/waermeausdehnungskoeffizient-1091\" target=\"_blank\" rel=\"noopener\">Studyflix: Wsp\u00f3\u0142czynnik rozszerzalno\u015bci cieplnej<\/a><br>(Kompaktowe wyja\u015bnienie z wzorami i przyk\u0142adami)<\/li><li><a href=\"https:\/\/tu-dresden.de\/mn\/physik\/ressourcen\/dateien\/studium\/lehrveranstaltungen\/praktika\/pdf\/TA.pdf?lang=de\" target=\"_blank\" rel=\"noopener\">TU Drezno Praktyczne instrukcje dotycz\u0105ce kursu: Analiza termiczna<\/a><br>(naukowe metody pomiarowe, w tym TMA i dylatometr)<\/li><li><a href=\"https:\/\/www.ptb.de\/cms\/fileadmin\/internet\/fachabteilungen\/abteilung_5\/5.3_koordinatenmesstechnik\/texte\/f_dilatometer.pdf\" target=\"_blank\" rel=\"noopener\">PTB &#8211; Physikalisch-Technische Bundesanstalt: Dilatometer<\/a><br>(Szczeg\u00f3\u0142owy opis techniczny dylatometr\u00f3w)<\/li><li><a href=\"https:\/\/wiki.polymerservice-merseburg.de\/index.php\/Thermomechanische_Analyse\" target=\"_blank\" rel=\"noopener\">Polymer Service Wiki: Analiza termomechaniczna<\/a><br>(Specyficzne zastosowanie i spos\u00f3b dzia\u0142ania TMA)<\/li><li><a href=\"https:\/\/www.uni-due.de\/materials\/dilatometrie.shtml\" target=\"_blank\" rel=\"noopener\">Uniwersytet Duisburg-Essen: Dylatometria<\/a><br>(podstawowe informacje na temat analizy termicznej cia\u0142 sta\u0142ych)<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\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>Rozszerzalno\u015b\u0107 cieplna to zmiana wymiar\u00f3w materia\u0142u spowodowana zmianami temperatury &#8211; wa\u017cny czynnik w budownictwie, in\u017cynierii i badaniach materia\u0142\u00f3w.<\/p>\n","protected":false},"author":15,"featured_media":85829,"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-101497","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\/101497","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\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/comments?post=101497"}],"version-history":[{"count":0,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/posts\/101497\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/media\/85829"}],"wp:attachment":[{"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/media?parent=101497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/categories?post=101497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/tags?post=101497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}