{"id":2520,"date":"2026-10-14T07:02:35","date_gmt":"2026-10-14T06:02:35","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-przemiany-adiabatycznej\/"},"modified":"2026-10-14T07:02:35","modified_gmt":"2026-10-14T06:02:35","slug":"kalkulator-przemiany-adiabatycznej","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-przemiany-adiabatycznej\/","title":{"rendered":"Kalkulator przemiany adiabatycznej"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Oblicz stan ko\u0144cowy gazu doskona\u0142ego po adiabatycznym spr\u0119\u017ceniu lub rozpr\u0119\u017caniu<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2520\" data-favorite-title=\"Przemiana adiabatyczna\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-przemiany-adiabatycznej\/\" data-favorite-excerpt=\"Oblicz ko\u0144cowe ci\u015bnienie, obj\u0119to\u015b\u0107 i temperatur\u0119 gazu doskona\u0142ego po odwracalnym spr\u0119\u017caniu lub rozpr\u0119\u017caniu adiabatycznym (izentropowym). Wpisz stan pocz\u0105tkowy, jedn\u0105 wielko\u015b\u0107 ko\u0144cow\u0105 oraz wyk\u0142adnik adiabaty \u03b3.\" aria-label=\"Dodaj do ulubionych\" data-favorite-icon=\"icon icon-physic\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-przemiany-adiabatycznej\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2520\" data-post=\"2520\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Znam<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"znam\"><option value=\"v2\" selected>Obj\u0119to\u015b\u0107 ko\u0144cow\u0105 (oblicz ci\u015bnienie ko\u0144cowe)<\/option><option value=\"p2\">Ci\u015bnienie ko\u0144cowe (oblicz obj\u0119to\u015b\u0107 ko\u0144cow\u0105)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"is-single field\" id=\"input-2\"><span class=\"font-semibold\">Stan pocz\u0105tkowy<\/span><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Ci\u015bnienie pocz\u0105tkowe (P\u2081)<\/label><div class=\"term\">P\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"cinienie_pocztkowe_p\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 100\" min=\"0\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"kpa\" selected>kPa<\/option><option value=\"bar\">bar<\/option><option value=\"atm\">atm<\/option><option value=\"psi\">psi<\/option><option value=\"mmhg\">mmHg<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-3\">Ci\u015bnienie na pocz\u0105tku procesu. Jedna atmosfera \u2248 101,3 kPa.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-5\">Obj\u0119to\u015b\u0107 pocz\u0105tkowa (V\u2081)<\/label><div class=\"term\">V\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"objto_pocztkowa_v\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"m3\" selected>m\u00b3<\/option><option value=\"l\">L<\/option><option value=\"cm3\">cm\u00b3<\/option><option value=\"ft3\">ft\u00b3<\/option><option value=\"in3\">in\u00b3<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-5\">Obj\u0119to\u015b\u0107 gazu na pocz\u0105tku procesu.<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-7\">Temperatura pocz\u0105tkowa (T\u2081)<\/label><div class=\"term\">T\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"temperatura_pocztkowa_t\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 300\" min=\"0\" value=\"300\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"k\" selected>K<\/option><option value=\"c\">\u00b0C<\/option><option value=\"f\">\u00b0F<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-7\">Temperatura na pocz\u0105tku procesu. Temperatura pokojowa \u2248 293 K (20 \u00b0C).<\/small><\/div><div class=\"is-single field\" id=\"input-6\"><span class=\"font-semibold\">Stan ko\u0144cowy<\/span><\/div><div class=\"field has-term\" id=\"input-7\" hidden><label for=\"field-10\">Obj\u0119to\u015b\u0107 ko\u0144cowa (V\u2082)<\/label><div class=\"term\">V\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"objto_kocowa_v\" id=\"field-10\" aria-describedby=\"calc-info-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.5\" min=\"0\" value=\"0.5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-11\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"m3\" selected>m\u00b3<\/option><option value=\"l\">L<\/option><option value=\"cm3\">cm\u00b3<\/option><option value=\"ft3\">ft\u00b3<\/option><option value=\"in3\">in\u00b3<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-10\">Obj\u0119to\u015b\u0107 na ko\u0144cu procesu. Warto\u015b\u0107 mniejsza od V\u2081 oznacza spr\u0119\u017canie; wi\u0119ksza \u2014 rozpr\u0119\u017canie.<\/small><\/div><div class=\"field has-term\" id=\"input-8\" hidden><label for=\"field-12\">Ci\u015bnienie ko\u0144cowe (P\u2082)<\/label><div class=\"term\">P\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"cinienie_kocowe_p\" id=\"field-12\" aria-describedby=\"calc-info-12\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 200\" min=\"0\" value=\"200\"\/><div class=\"grid grid-cols-1\"><select id=\"field-13\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"kpa\" selected>kPa<\/option><option value=\"bar\">bar<\/option><option value=\"atm\">atm<\/option><option value=\"psi\">psi<\/option><option value=\"mmhg\">mmHg<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-12\">Ci\u015bnienie na ko\u0144cu procesu. Warto\u015b\u0107 wi\u0119ksza od P\u2081 oznacza spr\u0119\u017canie; mniejsza \u2014 rozpr\u0119\u017canie.<\/small><\/div><div class=\"field has-term\" id=\"input-9\"><label for=\"field-14\">Wyk\u0142adnik adiabaty (\u03b3)<\/label><div class=\"term\">\u03b3<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"wykadnik_adiabaty_\" id=\"field-14\" aria-describedby=\"calc-info-14\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1.4\" min=\"1\" value=\"1.4\"\/><small id=\"calc-info-14\">\u03b3 = c\u1d58\/c\u1d5b. Gaz jednoatomowy \u2248 1,67; gaz dwuatomowy (powietrze, N\u2082, O\u2082) \u2248 1,40; wieloatomowy (CO\u2082) \u2248 1,29.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2520\">Oblicz<\/button><button type=\"reset\">Wyczy\u015b\u0107<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Obliczaj automatycznie<\/label><small>Po w\u0142\u0105czeniu wynik aktualizuje si\u0119 automatycznie po zmianie dowolnej warto\u015bci.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Wyniki przemiany adiabatycznej<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Ci\u015bnienie ko\u0144cowe (P\u2082)<\/span><span class=\"result-term\">P\u2082<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Obj\u0119to\u015b\u0107 ko\u0144cowa (V\u2082)<\/span><span class=\"result-term\">V\u2082<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Temperatura ko\u0144cowa (T\u2082)<\/span><span class=\"result-term\">T\u2082<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Wykonana praca i szczeg\u00f3\u0142y<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Kopiuj link do tego obliczenia<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Zostaw komentarz<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"2520\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Jak oceniasz ten wynik?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Lubi\u0119 to <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Pomocne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Niejasne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Rozczarowanie <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Niedok\u0142adne <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Przemiana adiabatyczna<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Wz\u00f3r<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ P_1 V_1^{\\gamma} = P_2 V_2^{\\gamma} \\qquad T_1 V_1^{\\gamma-1} = T_2 V_2^{\\gamma-1} \\qquad W = \\frac{P_1 V_1 - P_2 V_2}{\\gamma - 1} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Gdzie:<\/strong><\/p>\n<ul>\n<li>\\(P_1, V_1, T_1\\) \u2014 ci\u015bnienie, obj\u0119to\u015b\u0107 i temperatura bezwzgl\u0119dna gazu w stanie pocz\u0105tkowym<\/li>\n<li>\\(P_2, V_2, T_2\\) \u2014 ci\u015bnienie, obj\u0119to\u015b\u0107 i temperatura bezwzgl\u0119dna w stanie ko\u0144cowym<\/li>\n<li>\\(\\gamma = c_p \/ c_v\\) \u2014 wyk\u0142adnik adiabaty gazu (1,67 dla gaz\u00f3w jednoatomowych, 1,40 dla gaz\u00f3w dwuatomowych, takich jak powietrze)<\/li>\n<li>\\(W\\) \u2014 praca wykonana <em>przez<\/em> gaz podczas przemiany (J)<\/li>\n<\/ul>\n<p>Zale\u017cno\u015bci te opisuj\u0105 odwracaln\u0105 przemian\u0119 adiabatyczn\u0105 (izentropow\u0105) gazu doskona\u0142ego: poniewa\u017c gaz nie wymienia ciep\u0142a z otoczeniem, ci\u015bnienie, obj\u0119to\u015b\u0107 i temperatura s\u0105 zwi\u0105zane sta\u0142\u0105 \\(P V^{\\gamma}\\), a cz\u0142on pracowy wynika z pierwszej zasady termodynamiki przy \\(Q = 0\\), czyli \\(\\Delta U = -W\\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Przemiana adiabatyczna \u2013 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> 1 m\u00b3 powietrza o ci\u015bnieniu 100 kPa i temperaturze 300 K spr\u0119\u017camy adiabatycznie do po\u0142owy pierwotnej obj\u0119to\u015bci. Dla powietrza \u03b3 = 1,4.<\/p>\n<p>\\[ P_2 = P_1 \\left( \\frac{V_1}{V_2} \\right)^{\\gamma} = 100\\,\\text{kPa} \\times 2^{1.4} \\approx 263.9\\,\\text{kPa} \\]<\/p>\n<p>\\[ T_2 = T_1 \\left( \\frac{V_1}{V_2} \\right)^{\\gamma-1} = 300\\,\\text{K} \\times 2^{0.4} \\approx 395.85\\,\\text{K} \\; (\\approx 122.7\\,\\text{\u00b0C}) \\]<\/p>\n<p>\\[ W = \\frac{P_1 V_1 - P_2 V_2}{\\gamma - 1} = \\frac{100\\,000 \\times 1 - 263\\,902 \\times 0.5}{0.4} \\approx -79\\,877\\,\\text{J} \\]<\/p>\n<p><strong>Wynik:<\/strong> ci\u015bnienie ko\u0144cowe wynosi \u2248 263,9 kPa (\u2248 2,60 atm), temperatura ko\u0144cowa \u2248 395,85 K (\u2248 122,7 \u00b0C), a na gazie wykonano prac\u0119 oko\u0142o 79,9 kJ \u2014 w\u0142a\u015bnie dlatego si\u0119 nagrzewa.<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora<\/h2>\n<ol>\n<li>Z rozwijanej listy <strong>\u201eZnam warto\u015b\u0107 ko\u0144cow\u0105\u201d<\/strong> wybierz, czy znana jest ci obj\u0119to\u015b\u0107 ko\u0144cowa (a szukasz ci\u015bnienia ko\u0144cowego), czy ci\u015bnienie ko\u0144cowe (a szukasz obj\u0119to\u015bci ko\u0144cowej).<\/li>\n<li>Wpisz <strong>Ci\u015bnienie pocz\u0105tkowe (P\u2081)<\/strong>, <strong>Obj\u0119to\u015b\u0107 pocz\u0105tkow\u0105 (V\u2081)<\/strong> i <strong>Temperatur\u0119 pocz\u0105tkow\u0105 (T\u2081)<\/strong>, wybieraj\u0105c dla ka\u017cdego pola jednostk\u0119 (kPa, bar, atm, psi, mmHg; m\u00b3, L, cm\u00b3, ft\u00b3, in\u00b3; K, \u00b0C, \u00b0F). Wszystkie dane s\u0105 automatycznie przeliczane na jednostki uk\u0142adu SI.<\/li>\n<li>Wpisz znan\u0105 wielko\u015b\u0107 ko\u0144cow\u0105: <strong>Obj\u0119to\u015b\u0107 ko\u0144cow\u0105 (V\u2082)<\/strong> lub <strong>Ci\u015bnienie ko\u0144cowe (P\u2082)<\/strong> \u2014 zgodnie z wyborem z kroku 1.<\/li>\n<li>Podaj <strong>Wyk\u0142adnik adiabaty (\u03b3)<\/strong> gazu \u2014 1,4 dla powietrza i innych gaz\u00f3w dwuatomowych, 1,67 dla gaz\u00f3w jednoatomowych, takich jak hel czy argon, oko\u0142o 1,29 dla CO\u2082.<\/li>\n<li>Odczytaj wyniki: ci\u015bnienie ko\u0144cowe w kilku jednostkach, obj\u0119to\u015b\u0107 ko\u0144cow\u0105 w kilku jednostkach, temperatur\u0119 ko\u0144cow\u0105 w K, \u00b0C i \u00b0F oraz bilans energetyczny (wykonan\u0105 prac\u0119, zmian\u0119 energii wewn\u0119trznej i sta\u0142\u0105 \\(P V^{\\gamma}\\) w obu stanach).<\/li>\n<\/ol>\n<h2>Czym jest przemiana adiabatyczna?<\/h2>\n<p>Przemiana adiabatyczna to przemiana termodynamiczna, w kt\u00f3rej gaz nie wymienia ciep\u0142a z otoczeniem (\\(Q = 0\\)). Energia nadal mo\u017ce dop\u0142ywa\u0107 do gazu lub z niego odp\u0142ywa\u0107 \u2014 ale wy\u0142\u0105cznie w postaci pracy mechanicznej. Przy spr\u0119\u017caniu praca wykonana na gazie zwi\u0119ksza jego energi\u0119 wewn\u0119trzn\u0105 i temperatura ro\u015bnie; przy rozpr\u0119\u017caniu gaz zu\u017cywa w\u0142asn\u0105 energi\u0119 wewn\u0119trzn\u0105 na odpychanie otoczenia i si\u0119 och\u0142adza. Dlatego pompka rowerowa nagrzewa si\u0119 przy szybkim pompowaniu, a spr\u0119\u017cone powietrze uciekaj\u0105ce z puszki aerozolowej wydaje si\u0119 zimne, gdy si\u0119 rozpr\u0119\u017ca.<\/p>\n<p>Kalkulator modeluje <em>odwracaln\u0105<\/em> (kwazistatyczn\u0105, izentropow\u0105) przemian\u0119 adiabatyczn\u0105 gazu <em>doskona\u0142ego<\/em>. W tym przypadku zmienne stanu spe\u0142niaj\u0105 \\(P V^{\\gamma} = \\text{sta\u0142a}\\) oraz \\(T V^{\\gamma-1} = \\text{sta\u0142a}\\). W por\u00f3wnaniu z przemian\u0105 izotermiczn\u0105 ci\u015bnienie zmienia si\u0119 wraz z obj\u0119to\u015bci\u0105 szybciej, poniewa\u017c jednocze\u015bnie zmienia si\u0119 temperatura: podwojenie g\u0119sto\u015bci powietrza (\\(\\gamma = 1,4\\)) zwi\u0119ksza ci\u015bnienie \\(2^{1.4} \\approx 2.64\\) raza, a nie dwa razy.<\/p>\n<p>Znak pracy wskazuje kierunek przemiany: ujemne \\(W\\) oznacza, \u017ce praca zosta\u0142a wykonana <em>na<\/em> gazie (spr\u0119\u017canie, nagrzewanie), dodatnie \\(W\\) \u2014 \u017ce gaz wykona\u0142 prac\u0119 <em>na<\/em> otoczeniu (rozpr\u0119\u017canie, ch\u0142odzenie). Poniewa\u017c \\(Q = 0\\), pierwsza zasada termodynamiki sprowadza si\u0119 do \\(\\Delta U = -W\\): zmiana temperatury, kt\u00f3r\u0105 widzisz w wynikach, jest bezpo\u015brednim nast\u0119pstwem wymienionej pracy.<\/p>\n<h2>Za\u0142o\u017cenia, ograniczenia i wskaz\u00f3wki praktyczne<\/h2>\n<ul>\n<li><strong>Gaz doskona\u0142y:<\/strong> zale\u017cno\u015bci obowi\u0105zuj\u0105 przy ci\u015bnieniach, dla kt\u00f3rych przybli\u017cenie gazu doskona\u0142ego jest s\u0142uszne. Przy bardzo wysokich ci\u015bnieniach lub w pobli\u017cu skraplania istotne staj\u0105 si\u0119 efekty gazu rzeczywistego i wyniki odbiegaj\u0105 od rzeczywisto\u015bci.<\/li>\n<li><strong>Odwracalno\u015b\u0107 i pe\u0142na adiabatyczno\u015b\u0107:<\/strong> obliczenie zak\u0142ada, \u017ce przemiana jest na tyle powolna, by by\u0142a kwazistatyczna, i na tyle szybka (lub dobrze izolowana), by \u017cadne ciep\u0142o nie dop\u0142ywa\u0142o ani nie ucieka\u0142o. Gwa\u0142towne, turbulentne spr\u0119\u017canie lub rozpr\u0119\u017canie wprowadza nieodwracalno\u015bci i prowadzi do innych temperatur ko\u0144cowych.<\/li>\n<li><strong>Sta\u0142e \u03b3:<\/strong> wyk\u0142adnik adiabaty traktowany jest jako niezale\u017cny od temperatury. W zakresie kilkuset kelwin\u00f3w to dobre przybli\u017cenie dla powietrza; przy bardzo du\u017cych zmianach temperatury nale\u017cy korzysta\u0107 z tablicowanych warto\u015bci \\(\\gamma(T)\\).<\/li>\n<li><strong>Ostro\u017cnie z doborem \u03b3:<\/strong> u\u017cycie warto\u015bci 1,4 dla gazu jednoatomowego (albo odwrotnie) mo\u017ce przesun\u0105\u0107 temperatur\u0119 ko\u0144cow\u0105 o dziesi\u0105tki kelwin\u00f3w. Zanim zaufasz wynikowi, sprawd\u017a, jaki gaz modelujesz.<\/li>\n<li><strong>Zachowanie masy:<\/strong> kalkulator zak\u0142ada sta\u0142\u0105 ilo\u015b\u0107 gazu. Skorzystaj z <a href=\"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-gestosci\/\">Kalkulatora g\u0119sto\u015bci<\/a>, je\u015bli chcesz przeliczy\u0107 mas\u0119 na ilo\u015b\u0107 gazu, a z <a href=\"https:\/\/wpcalc.com\/pl\/fizyka\/kalkulator-cisnienia\/\">Kalkulatora ci\u015bnienia<\/a> do sprawdzenia jednostek ci\u015bnie\u0144.<\/li>\n<\/ul>\n<p>Spr\u0119\u017canie i rozpr\u0119\u017canie adiabatyczne to podstawa dzia\u0142ania silnik\u00f3w, spr\u0119\u017carek, turbin i fizyki atmosfery \u2014 na przyk\u0142ad ozi\u0119bianie wznosz\u0105cych si\u0119 mas powietrza traktuje si\u0119 w przybli\u017ceniu jako adiabatyczne. Aby umie\u015bci\u0107 te przemiany w szerszym kontek\u015bcie silnik\u00f3w cieplnych i granic ich sprawno\u015bci, zobacz <a href=\"https:\/\/wpcalc.com\/pl\/physics\/carnot-efficiency-calculator\/\">Kalkulator sprawno\u015bci Carnota<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oblicz ko\u0144cowe ci\u015bnienie, obj\u0119to\u015b\u0107 i temperatur\u0119 gazu doskona\u0142ego po odwracalnym spr\u0119\u017caniu lub rozpr\u0119\u017caniu adiabatycznym (izentropowym). Wpisz stan pocz\u0105tkowy, jedn\u0105 wielko\u015b\u0107 ko\u0144cow\u0105 oraz wyk\u0142adnik adiabaty \u03b3.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[10],"tags":[83],"class_list":["post-2520","post","type-post","status-publish","format-standard","hentry","category-fizyka","tag-energia-praca"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2520","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/comments?post=2520"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2520\/revisions"}],"predecessor-version":[{"id":2787,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2520\/revisions\/2787"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2520"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2520"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2520"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}