{"id":30863,"date":"2021-07-03T13:00:20","date_gmt":"2021-07-03T13:00:20","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30863"},"modified":"2025-01-02T04:49:34","modified_gmt":"2025-01-02T04:49:34","slug":"%d8%a7%d9%84%d9%82%d8%a7%d9%86%d9%88%d9%86-%d8%a7%d9%84%d8%a3%d9%88%d9%84-%d9%84%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1%d9%8a%d8%a9","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d9%82%d8%a7%d9%86%d9%88%d9%86-%d8%a7%d9%84%d8%a3%d9%88%d9%84-%d9%84%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1%d9%8a%d8%a9\/","title":{"rendered":"\u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\t\ttext-align: center;\n\t}\n<\/style>\n<h1>\u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/h1>\n<p style=\"text-align:center;\">\n\t<em><br \/>\n\t\t\u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0647\u0648 \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0630\u064a \u064a\u0631\u0628\u0637 \u0628\u064a\u0646 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0645\u062b\u0644 \u0627\u0644\u062d\u0631\u0627\u0631\u0629\u060c \u0627\u0644\u0634\u063a\u0644 \u0648\u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629\u060c \u062d\u064a\u062b \u064a\u0646\u0635 \u0639\u0644\u0649 \u0623\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u0644\u0627 \u062a\u064f\u062e\u0644\u0642 \u0648\u0644\u0627 \u062a\u064f\u0641\u0646\u0649 \u0628\u0644 \u062a\u062a\u062d\u0648\u0644 \u0645\u0646 \u0634\u0643\u0644 \u0625\u0644\u0649 \u0622\u062e\u0631. \u064a\u0633\u062a\u0643\u0634\u0641 \u0647\u0630\u0627 \u0627\u0644\u0646\u0635 \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0627 \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0639\u0644\u0649 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u063a\u0644\u0642\u0629\u060c \u0645\u0639 \u0627\u0644\u062a\u0639\u0645\u0642 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0634\u063a\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u060c \u0627\u0644\u0633\u0639\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0648\u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0644\u0644\u063a\u0627\u0632\u0627\u062a. \u0645\u0646 \u062e\u0644\u0627\u0644 \u0645\u0632\u064a\u062c \u0645\u0646 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0648\u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u060c \u0633\u062a\u0643\u062a\u0634\u0641 \u0623\u062f\u0648\u0627\u062a \u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0641\u0647\u0645 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0637\u0627\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u0639\u0642\u062f\u0629.<br \/>\n\t<\/em>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><\/p>\n<p>\u0628\u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u0627\u064b \u0639\u0644\u0649:<\/p>\n<ol>\n<li><strong>\u062a\u0628\u0631\u064a\u0631<\/strong> \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u063a\u0644\u0642\u0629\u060c \u0648\u0634\u0631\u062d \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0628\u064a\u0646 \u0627\u0644\u062d\u0631\u0627\u0631\u0629\u060c \u0627\u0644\u0634\u063a\u0644 \u0648\u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629.<\/li>\n<li><strong>\u062a\u062d\u0644\u064a\u0644<\/strong> \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0634\u063a\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a \u0627\u0644\u062d\u0631\u0627\u0631\u064a \u0641\u064a \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0627\u0646\u0636\u063a\u0627\u0637 \u0648\u0627\u0644\u062a\u0645\u062f\u062f \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629.<\/li>\n<li><strong>\u062d\u0633\u0627\u0628<\/strong> \u0627\u0644\u0633\u0639\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0638\u0644 \u0638\u0631\u0648\u0641 \u062d\u062c\u0645 \u0648\u0636\u063a\u0637 \u062b\u0627\u0628\u062a\u064a\u0646\u060c \u0645\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0642\u064a\u0648\u062f \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629.<\/li>\n<li><strong>\u0634\u0631\u062d<\/strong> \u062a\u0648\u0632\u064a\u0639 \u0645\u0627\u0643\u0633\u0648\u064a\u0644-\u0628\u0648\u0644\u062a\u0632\u0645\u0627\u0646 \u0648\u0645\u0628\u062f\u0623 \u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0637\u0627\u0642\u0629 \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062c\u0632\u064a\u0626\u064a\u0629.<\/li>\n<li><strong>\u0625\u062b\u0628\u0627\u062a<\/strong> \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0628\u064a\u0646 \u0627\u0644\u0633\u0639\u0627\u062a \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\u060c \u0627\u0644\u0645\u0624\u0634\u0631 \u0627\u0644\u0623\u062f\u064a\u0628\u0627\u062a\u064a \u0648\u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0623\u062e\u0631\u0649 \u0644\u0644\u063a\u0627\u0632\u0627\u062a \u0627\u0644\u0645\u062b\u0627\u0644\u064a\u0629.<\/li>\n<\/ol>\n<p style=\"text-align:center\"><strong><u>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/u>:<\/strong><br \/>\n\t<a href=\"#1\">\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/a><br \/>\n\t<a href=\"#2\">\u0627\u0644\u0634\u063a\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a \u0627\u0644\u062d\u0631\u0627\u0631\u064a<\/a><br \/>\n\t<a href=\"#3\">\u0627\u0644\u0633\u0639\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/a><br \/>\n\t<a href=\"#4\">\u062a\u0648\u0632\u064a\u0639 \u0645\u0627\u0643\u0633\u0648\u064a\u0644-\u0628\u0648\u0644\u062a\u0632\u0645\u0627\u0646 \u0648\u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0637\u0627\u0642\u0629<\/a><br \/>\n\t<a href=\"#5\">\u062a\u0645\u0627\u0631\u064a\u0646<\/a>\n<\/p>\n<p><center><br \/>\n\t<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/T6K1Nizc5NE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/h2>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=140s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>\u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/strong><br \/>\n\t<\/a> \u064a\u0646\u0635 \u0639\u0644\u0649:\n<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #c0ffc0;\">\n\t<span style=\"color: #000080;\"><br \/>\n\t\t<strong>\u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/strong><br \/>\n\t\t\u0627\u0644\u0637\u0627\u0642\u0629 \u0644\u0627 \u062a\u064f\u062e\u0644\u0642 \u0648\u0644\u0627 \u062a\u064f\u0641\u0646\u0649\u061b \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0648\u0627\u0644\u0634\u063a\u0644 \u0647\u0645\u0627 \u0623\u0634\u0643\u0627\u0644 \u0645\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 (\u064a\u062a\u0645 \u0625\u0635\u062f\u0627\u0631\u0647\u0627\u060c \u0627\u0645\u062a\u0635\u0627\u0635\u0647\u0627 \u0623\u0648 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0628\u0648\u0627\u0633\u0637\u0629 \u0639\u0645\u0644\u064a\u0629 \u0645\u0639\u064a\u0646\u0629).<br \/>\n\t<\/span>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">U<\/span> \u0647\u064a \u062f\u0627\u0644\u0629 \u062d\u0627\u0644\u0629 \u0644\u0623\u0646 \u0644\u0647\u0627 \u0642\u064a\u0645\u0629 \u0645\u062d\u062f\u062f\u0629 \u0644\u0643\u0644 \u062d\u0627\u0644\u0629 \u062a\u0648\u0627\u0632\u0646 \u0644\u0644\u0646\u0638\u0627\u0645. \u064a\u0645\u0643\u0646 \u062a\u063a\u064a\u064a\u0631 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0644\u0644\u0646\u0638\u0627\u0645 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span> \u0623\u0648 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0634\u063a\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">W<\/span>\u061b \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0634\u063a\u0644 \u0648\u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0644\u064a\u0633\u0627 \u062f\u0627\u0644\u062a\u064a\u0646 \u0644\u0644\u062d\u0627\u0644\u0629. \u064a\u0639\u0648\u062f \u0630\u0644\u0643 \u0625\u0644\u0649 \u0623\u0646 \u0643\u0644\u0627\u0647\u0645\u0627 \u064a\u0639\u062a\u0645\u062f\u0627\u0646 \u0639\u0644\u0649 \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0645\u0646 \u062e\u0644\u0627\u0644\u0647\u0627 \u0625\u0636\u0627\u0641\u0629 \u0623\u0648 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0627\u0644\u0637\u0627\u0642\u0629\u060c \u0648\u0628\u0645\u062c\u0631\u062f \u0627\u0646\u062a\u0647\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0629\u060c \u0644\u0627 \u064a\u0645\u0643\u0646 \u0645\u0639\u0631\u0641\u0629 \u0643\u0645\u064a\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0623\u0648 \u0627\u0644\u0634\u063a\u0644 \u0627\u0644\u0630\u064a \u062a\u0645 \u0644\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629.<\/p>\n<p>\u064a\u0645\u0643\u0646 \u0643\u062a\u0627\u0628\u0629 \u062a\u063a\u064a\u0631 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0644\u0644\u0646\u0638\u0627\u0645 \u0643\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta U = \\Delta Q + \\Delta W<\/span><\/span>,<\/p>\n<p>\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta Q<\/span><\/span> \u0647\u064a \u0643\u0645\u064a\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0627\u0644\u0645\u0636\u0627\u0641\u0629 \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta W<\/span><\/span> \u0647\u064a \u0643\u0645\u064a\u0629 \u0627\u0644\u0634\u063a\u0644 \u0627\u0644\u0645\u0628\u0630\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0646\u0638\u0627\u0645. \u0648\u0641\u0642\u0627\u064b \u0644\u0644\u0627\u062a\u0641\u0627\u0642\u064a\u0629\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta Q<\/span><\/span> \u062a\u0643\u0648\u0646 \u0645\u0648\u062c\u0628\u0629 \u0639\u0646\u062f \u0625\u0636\u0627\u0641\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0644\u0644\u0646\u0638\u0627\u0645\u061b \u0648\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta Q<\/span><\/span> \u0633\u0627\u0644\u0628\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u062a\u064f\u0632\u0627\u0644 \u0645\u0646 \u0627\u0644\u0646\u0638\u0627\u0645\u061b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta W<\/span><\/span> \u062a\u0643\u0648\u0646 \u0645\u0648\u062c\u0628\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u064f\u0628\u0630\u0644 \u0634\u063a\u0644 \u0639\u0644\u0649 \u0627\u0644\u0646\u0638\u0627\u0645\u061b \u0648\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta W<\/span><\/span> \u0633\u0627\u0644\u0628\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u064a\u0628\u0630\u0644 \u0634\u063a\u0644\u0627\u064b \u0639\u0644\u0649 \u0627\u0644\u0628\u064a\u0626\u0629.<\/p>\n<p>\u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u0627\u064b \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0634\u063a\u0644\u060c \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0648\u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0628\u0634\u0643\u0644 \u062a\u0641\u0627\u0636\u0644\u064a \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0639\u0644\u0627\u0642\u0629:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dU = \\delta Q + \\delta W<\/span><\/span>.<\/p>\n<p>\u0647\u0646\u0627\u060c \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062d\u0631\u0641 <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u0627\u062a \u063a\u064a\u0631 \u0627\u0644\u0643\u0627\u0645\u0644\u0629.<\/p>\n<p>\u064a\u064f\u0639\u0631\u0641 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u0639\u0632\u0648\u0644 \u062d\u0631\u0627\u0631\u064a\u0627\u064b \u0628\u0623\u0646\u0647 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0630\u064a \u0644\u0627 \u064a\u0645\u0643\u0646\u0647 \u062a\u0628\u0627\u062f\u0644 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0645\u0639 \u0628\u064a\u0626\u062a\u0647. \u0639\u0646\u062f\u0645\u0627 \u064a\u062d\u062f\u062b \u0630\u0644\u0643\u060c \u0641\u0625\u0646\u0647 \u064a\u0643\u0648\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d U = \\delta W<\/span><\/span>. \u0647\u0630\u0627 \u0647\u0648 <strong>\u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/strong> \u0627\u0644\u0645\u0642\u062a\u0635\u0631 \u0639\u0644\u0649 \u0646\u0638\u0627\u0645 \u0623\u062f\u064a\u0628\u0627\u062a\u064a.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u0627\u0644\u0633\u0639\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/h2>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=677s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>\u0644\u0646\u0641\u062a\u0631\u0636 \u0627\u0644\u0622\u0646<\/strong><br \/>\n\t<\/a> \u0623\u0646\u0646\u0627 \u0646\u0631\u064a\u062f \u0641\u0647\u0645 \u0627\u0644\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u0641\u0627\u0635\u064a\u0644 \u062d\u0648\u0644 \u0643\u064a\u0641\u064a\u0629 \u062a\u063a\u064a\u0631 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0644\u0644\u0646\u0638\u0627\u0645 \u0639\u0646\u062f \u0625\u0636\u0627\u0641\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629. \u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0647\u064a \u062f\u0627\u0644\u0629 \u0644\u0644\u062d\u0631\u0627\u0631\u0629 \u0648\u0627\u0644\u062d\u062c\u0645\u060c \u0644\u0630\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0643\u062a\u0627\u0628\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U=U(T,V)<\/span><\/span>. \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0648\u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u062f\u0627\u0644\u0629 \u0643\u0627\u0645\u0644\u0629\u060c \u0641\u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u062a\u063a\u064a\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">U<\/span> \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0640 <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0639\u0644\u0627\u0642\u0629:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle dU = \\left(\\frac{\\partial U}{\\partial T}\\right)_V dT + \\left(\\frac{\\partial U}{\\partial V}\\right)_T dV<\/span><\/span>.\n<\/p>\n<p>\u0627\u0644\u0622\u0646\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dU=\\delta Q + \\delta W<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta W=-PdV<\/span><\/span>\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u0639\u0627\u062f\u0629 \u0635\u064a\u0627\u063a\u0629 <strong>\u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/strong> \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\delta Q &amp;= dU + PdV\\\\ \\\\\n\n&amp; \\displaystyle  =\\left(\\frac{\\partial U}{\\partial T}\\right)_V dT + \\left(\\frac{\\partial U}{\\partial V}\\right)_T dV + PdV\\\\ \\\\\n\n&amp; \\displaystyle =\\left(\\frac{\\partial U}{\\partial T}\\right)_V dT + \\left[\\left(\\frac{\\partial U}{\\partial V}\\right)_T + P\\right]dV \\\\ \\\\\n\n\\displaystyle  \\frac{\\delta Q}{dT} &amp; \\displaystyle  =\\left(\\frac{\\partial U}{\\partial T}\\right)_V + \\left[\\left(\\frac{\\partial U}{\\partial V}\\right)_T + P\\right]\\frac{dV}{dT}.\n\n\\end{array}\n\n<\/span>\n<p>\u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0635\u0627\u0644\u062d\u0629 \u0644\u0623\u064a \u062a\u063a\u064a\u064a\u0631 \u0641\u064a \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0648\u0627\u0644\u062d\u062c\u0645.<\/p>\n<p>\u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u062d\u062f\u064a\u062f \u0643\u0645\u064a\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0627\u0644\u062a\u064a \u064a\u062c\u0628 \u0625\u0636\u0627\u0641\u062a\u0647\u0627 \u0644\u0625\u062d\u062f\u0627\u062b \u062a\u063a\u064a\u0631 \u0641\u064a \u062f\u0631\u062c\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u062a\u062d\u062a \u0642\u064a\u0648\u062f \u0645\u0639\u064a\u0646\u0629.<\/p>\n<h3>\u0627\u0644\u0642\u064a\u0648\u062f \u0639\u0646\u062f \u062d\u062c\u0645 \u062b\u0627\u0628\u062a<\/h3>\n<p>\u0644\u0645\u0639\u0631\u0641\u0629 \u0645\u0627 \u064a\u062d\u062f\u062b \u0639\u0646\u062f \u062b\u0628\u0627\u062a \u0627\u0644\u062d\u062c\u0645\u060c \u0646\u062a\u0630\u0643\u0631 \u0623\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0633\u0639\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0639\u0646\u062f \u062d\u062c\u0645 \u062b\u0627\u0628\u062a \u0647\u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V=(\\partial Q\/ \\partial T)_V<\/span><\/span>. \u0625\u0630\u0627 \u0642\u064a\u062f\u0646\u0627 \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0633\u0627\u0628\u0642 \u0628\u0627\u0644\u062d\u062c\u0645 \u0627\u0644\u062b\u0627\u0628\u062a\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0635\u0637\u0644\u062d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dV\/dT<\/span><\/span> \u0641\u064a \u0627\u0644\u062a\u0639\u0628\u064a\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta Q\/dT<\/span><\/span> \u064a\u062a\u0645 \u0625\u0644\u063a\u0627\u0624\u0647. \u0647\u0630\u0627 \u064a\u0633\u0645\u062d \u0644\u0646\u0627 \u0628\u0627\u0644\u0643\u062a\u0627\u0628\u0629:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  C_V = \\left(\\frac{\\partial U}{\\partial T} \\right)_V<\/span><\/span>.\n<\/p>\n<h3>\u0627\u0644\u0642\u064a\u0648\u062f \u0639\u0646\u062f \u0636\u063a\u0637 \u062b\u0627\u0628\u062a<\/h3>\n<p>\u0625\u0630\u0627 \u0623\u0628\u0642\u064a\u0646\u0627 \u0627\u0644\u0636\u063a\u0637 \u062b\u0627\u0628\u062a\u0627\u064b\u060c \u0641\u064a\u0645\u0643\u0646\u0646\u0627 \u0643\u062a\u0627\u0628\u0629:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle C_p =\\left(\\frac{\\partial Q}{\\partial T}\\right)_P=\\left(\\frac{\\partial U}{\\partial T}\\right)_V + \\left[\\left(\\frac{\\partial U}{\\partial V}\\right)_T + P\\right]\\left(\\frac{\\partial V}{\\partial T}\\right)_p<\/span><\/span>.\n<\/p>\n<h3>\u0627\u0644\u0633\u0639\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0644\u063a\u0627\u0632 \u0623\u062d\u0627\u062f\u064a \u0627\u0644\u0630\u0631\u0629<\/h3>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=974s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>\u0639\u0646\u062f \u062f\u0631\u0627\u0633\u0629<\/strong><br \/>\n\t<\/a> \u063a\u0627\u0632 \u0623\u062d\u0627\u062f\u064a \u0627\u0644\u0630\u0631\u0629\u060c \u062a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0627\u0644\u0646\u0627\u062a\u062c\u0629 \u0639\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062d\u0631\u0643\u064a\u0629 \u0644\u062c\u0632\u064a\u0626\u0627\u062a\u0647 \u0639\u0644\u0649 \u0627\u0644\u0634\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\tU=\\frac{3}{2}Nk_BT<\/span><\/span>. \u064a\u062a\u0645 \u062a\u0628\u0631\u064a\u0631 \u0647\u0630\u0627 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0645\u0646 \u062e\u0644\u0627\u0644 \u0645\u0628\u062f\u0623 \u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u0630\u064a \u064a\u0645\u0643\u0646 \u062f\u0631\u0627\u0633\u062a\u0647 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0645\u0646\u0647\u062c \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a \u0644\u062d\u0631\u0643\u0629 \u0627\u0644\u062c\u0633\u064a\u0645\u0627\u062a.\n<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u062a\u0648\u0632\u064a\u0639 \u0645\u0627\u0643\u0633\u0648\u064a\u0644-\u0628\u0648\u0644\u062a\u0632\u0645\u0627\u0646 \u0648\u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0637\u0627\u0642\u0629<\/h2>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=1027s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>\u0646\u0638\u0631\u0627\u064b \u0644\u0623\u0646 \u0637\u0627\u0642\u0629 \u0627\u0644\u0646\u0638\u0627\u0645<\/strong><br \/>\n\t<\/a> \u062a\u062a\u0646\u0627\u0633\u0628 \u0645\u0639 <strong>\u0639\u0627\u0645\u0644 \u0628\u0648\u0644\u062a\u0632\u0645\u0627\u0646<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">e^{-E\/(k_BT)}<\/span><\/span>\u060c \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u0648\u0628\u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0623\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062d\u0631\u0643\u064a\u0629 \u0644\u0644\u062c\u0633\u064a\u0645\u0627\u062a \u062a\u0623\u062e\u0630 \u0627\u0644\u0634\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  E_{cin}=\\frac{1}{2}mv^2<\/span><\/span>\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0623\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u062d\u0631\u0643\u0629 \u0627\u0644\u062c\u0633\u064a\u0645\u0627\u062a \u0641\u064a \u0623\u062d\u062f \u0627\u0644\u0645\u062d\u0627\u0648\u0631 (\u0644\u0646\u0631\u0643\u0632 \u0645\u0624\u0642\u062a\u0627\u064b \u0639\u0644\u0649 \u0627\u0644\u0645\u062d\u0648\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/span>) \u0633\u062a\u0643\u0648\u0646 \u0645\u062a\u0646\u0627\u0633\u0628\u0629 \u0645\u0639 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0633\u0631\u0639\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(v_x)<\/span><\/span> \u0628\u0627\u0644\u0634\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">e^{-mv_x^2\/(2k_BT)}<\/span><\/span>. \u0623\u064a:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(v_x)= A e^{-mv_x^2\/(2k_BT)}<\/span><\/span>,\n<\/p>\n<p>\u062d\u064a\u062b \u0623\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0647\u0648 \u062b\u0627\u0628\u062a \u064a\u062c\u0628 \u062a\u062d\u062f\u064a\u062f\u0647. \u0648\u0628\u0645\u0627 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(v_x)<\/span><\/span> \u062f\u0627\u0644\u0629 \u062a\u0648\u0632\u064a\u0639\u060c \u0641\u0625\u0646\u0647 \u064a\u062c\u0628 \u062a\u0637\u0628\u064a\u0639\u0647\u0627 \u0628\u062d\u064a\u062b:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\int_{-\\infty}^{+\\infty} g(v_x)dv_x= 1<\/span><\/span>.\n<\/p>\n<p>\u0648\u0627\u062d\u062f\u0629 \u0645\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0645\u0641\u064a\u062f\u0629 \u0644\u062a\u062d\u0644\u064a\u0644 \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0647\u064a \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u063a\u0627\u0648\u0633\u064a:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\int_{-\\infty}^{+\\infty} e^{-x^2}dx= \\sqrt{\\pi}<\/span><\/span>.\n<\/p>\n<p>\u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u0646\u0633\u062a\u0646\u062a\u062c:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle 1= \\int_{-\\infty}^{+\\infty} Ae^{\\frac{-mv_x^2}{2k_BT}}dv_x= A\\sqrt{\\frac{\\pi}{m\/(2k_BT)}} = A\\sqrt{\\frac{2\\pi k_BT}{m}}<\/span><\/span>.\n<\/p>\n<p>\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  g(v_x) = \\sqrt{\\frac{m}{2\\pi k_BT}}e^{-mv_x^2\/(2k_BT)}<\/span><\/span>.\n<\/p>\n<p>\u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0627 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062d\u0633\u0627\u0628 \u0645\u062a\u0648\u0633\u0637 \u0645\u0631\u0628\u0639 \u0627\u0644\u0633\u0631\u0639\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u062d\u0648\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/span>\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left\\lt v_x^2\\right\\gt<\/span><\/span>. \u0627\u0644\u0646\u0627\u062a\u062c \u0647\u0648:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left\\lt v_x^2\\right\\gt = \\int_{-\\infty}^{+\\infty} v_x^2 g(v_x) dv_x = \\sqrt{\\frac{m}{2\\pi k_BT}} \\int_{-\\infty}^{+\\infty} v_x^2 e^{-mv_x^2\/(2k_BT)} = \\frac{k_BT}{m} <\/span><\/span>.\n<\/p>\n<p>\u0648\u0646\u0638\u0631\u0627\u064b \u0644\u0623\u0646 \u0645\u062a\u0648\u0633\u0637 \u0645\u0631\u0628\u0639 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u0643\u0644\u064a\u0629 \u064a\u0645\u0643\u0646 \u062a\u0642\u0633\u064a\u0645\u0647 \u0639\u0644\u0649 \u0627\u0644\u0634\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  \\left\\lt v^2\\right\\gt = \\left\\lt v_x^2\\right\\gt + \\left\\lt v_y^2\\right\\gt + \\left\\lt v_z^2\\right\\gt<\/span><\/span>\u060c \u0648\u0643\u0644 \u0645\u0643\u0648\u0646 \u0644\u0647 \u0646\u0641\u0633 \u0627\u0644\u0646\u062a\u064a\u062c\u0629\u060c \u064a\u0645\u0643\u0646 \u0643\u062a\u0627\u0628\u0629 \u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062d\u0631\u0643\u064a\u0629 \u0644\u0644\u0646\u0638\u0627\u0645 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  \\left\\lt E_{cin}\\right\\gt =\\frac{1}{2}m\\left\\lt v^2\\right\\gt  = \\frac{1}{2}m \\cdot 3\\frac{k_BT}{m}= \\frac{3}{2}k_BT<\/span><\/span>.\n<\/p>\n<p>\u0647\u0630\u0627 \u0647\u0648 \u0645\u0627 \u064a\u0633\u0645\u0649 \u0628\u0640 \u00ab\u0645\u0628\u062f\u0623 \u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0637\u0627\u0642\u0629\u00bb. \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0642\u0648\u0644 \u0625\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u064a\u062a\u0643\u0648\u0646 \u0645\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u062c\u0633\u064a\u0645\u0627\u062a \u0628\u0645\u062a\u0648\u0633\u0637 \u0637\u0627\u0642\u0629 \u062d\u0631\u0643\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left\\lt E_{cin}\\right\\gt<\/span><\/span> \u0648\u0643\u0627\u0646\u062a \u0637\u0627\u0642\u0629 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0643\u0644\u064a\u0629 \u0646\u0627\u0634\u0626\u0629 \u0641\u0642\u0637 \u0639\u0646 \u0627\u0644\u062d\u0631\u0643\u0629 \u0627\u0644\u062d\u0631\u0643\u064a\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0644\u0644\u0646\u0638\u0627\u0645 \u0633\u062a\u0643\u0648\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\tU=3Nk_BT\/2<\/span><\/span> (\u0643\u0645\u0627 \u062a\u0645 \u062a\u0648\u0642\u0639\u0647 \u0633\u0627\u0628\u0642\u0627\u064b)\u060c \u0643\u0645\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u062b\u0628\u0627\u062a \u0628\u0634\u0643\u0644 \u0648\u0627\u0636\u062d \u0623\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u062a\u0639\u062a\u0645\u062f \u0641\u0642\u0637 \u0639\u0644\u0649 \u062f\u0631\u062c\u0629 \u062d\u0631\u0627\u0631\u0629 \u0627\u0644\u0646\u0638\u0627\u0645\u060c \u0623\u064a:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left(\\frac{\\partial U}{\\partial V}\\right)_T = 0<\/span><\/span>.\n<\/p>\n<h3>\u0627\u0634\u062a\u0642\u0627\u0642 \u0644\u0644\u063a\u0627\u0632 \u0627\u0644\u0645\u062b\u0627\u0644\u064a<\/h3>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=1027s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>\u0627\u0644\u0622\u0646\u060c \u0628\u0627\u0633\u062a\u0630\u0643\u0627\u0631 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u063a\u0627\u0632 \u0627\u0644\u0645\u062b\u0627\u0644\u064a<\/strong><br \/>\n\t<\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV=Nk_BT =nRT<\/span><\/span>. \u0645\u0646 \u062e\u0644\u0627\u0644 \u062d\u0644 \u0627\u0644\u062d\u062c\u0645 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  V= \\frac{nRT}{P}<\/span><\/span>.\n<\/p>\n<p>\u0644\u0630\u0644\u0643\u060c \u064a\u0643\u0648\u0646:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  \\left(\\frac{\\partial V}{\\partial T} \\right)_P = \\frac{nR}{P}<\/span><\/span>.\n<\/p>\n<p>\u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0640 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_P<\/span><\/span>\u060c \u0646\u062c\u062f:<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nC_P - C_V &amp; \\displaystyle = \\left[\\left(\\frac{\\partial U}{\\partial V} \\right)_T + P \\right]\\left(\\frac{\\partial V}{\\partial T} \\right)_P = P\\cdot \\frac{nR}{P} = nR\n\n\\end{array}\n\n<\/span>\n<p>\u0644\u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  C_V=(\\partial U \/ \\partial T)_V<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U=3Nk_BT\/2=3nRT\/2<\/span><\/span>\u060c \u0644\u062f\u064a\u0646\u0627:<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle  C_V = \\frac{3}{2}nR\n\n<\/span>\n<p>\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nC_P = C_V + nR = \\displaystyle  \\frac{3}{2}nR + nR = \\frac{5}{2}nR\n\n<\/span>\n<h3>\u0627\u0644\u0645\u0624\u0634\u0631 \u0627\u0644\u0623\u062f\u064a\u0628\u0627\u062a\u064a<\/h3>\n<p>\u0623\u062d\u062f \u0627\u0644\u0645\u0642\u0627\u064a\u064a\u0633 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0628\u0634\u0643\u0644 \u0634\u0627\u0626\u0639 \u0647\u0648 \u0646\u0633\u0628\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_P<\/span><\/span> \u0625\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V<\/span><\/span>\u060c \u0648\u0627\u0644\u0630\u064a \u064a\u064f\u0637\u0644\u0642 \u0639\u0644\u064a\u0647 \u0627\u0633\u0645 <strong>\u0627\u0644\u0645\u0624\u0634\u0631 \u0627\u0644\u0623\u062f\u064a\u0628\u0627\u062a\u064a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span>\u060c \u0648\u064a\u064f\u0639\u0631\u064e\u0651\u0641 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\gamma = \\displaystyle  \\frac{C_P}{C_V}\n\n<\/span>\n<p>\u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u063a\u0627\u0632\u0627\u062a \u0627\u0644\u0645\u062b\u0627\u0644\u064a\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0624\u0634\u0631 \u0627\u0644\u0623\u062f\u064a\u0628\u0627\u062a\u064a \u0644\u0647 \u0627\u0644\u0642\u064a\u0645\u0629:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\gamma = \\displaystyle \\frac{5}{3}\n\n<\/span>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u062a\u0645\u0627\u0631\u064a\u0646<\/h2>\n<ol>\n<li>\n\t\t\u0647\u0644 \u0635\u062d\u064a\u062d \u062f\u0627\u0626\u0645\u0627\u064b \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dU=C_VdT<\/span><\/span>\u061f \u0642\u0627\u0631\u0646 \u0628\u064a\u0646 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0648\u062d\u0627\u0644\u0629 \u0627\u0644\u063a\u0627\u0632\u0627\u062a \u0627\u0644\u0645\u062b\u0627\u0644\u064a\u0629 \u0648\u0642\u062f\u0645 \u0627\u0644\u062a\u0628\u0631\u064a\u0631\u0627\u062a.\n\t<\/li>\n<li>\n\t\t\u0627\u0641\u062a\u0631\u0636 \u0623\u0646\u0647 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u063a\u0627\u0632 \u0627\u0644\u0645\u062b\u0627\u0644\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U=C_VT<\/span><\/span>. \u0627\u062d\u0633\u0628:<\/p>\n<ol>\n<li>\u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0644\u0643\u0644 \u0648\u062d\u062f\u0629 \u0643\u062a\u0644\u0629.<\/li>\n<li>\u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0644\u0643\u0644 \u0648\u062d\u062f\u0629 \u062d\u062c\u0645.<\/li>\n<\/ol>\n<\/li>\n<li>\n\t\t\u064a\u062a\u0645 \u0627\u062d\u062a\u062c\u0627\u0632 \u0645\u0648\u0644 \u0648\u0627\u062d\u062f \u0645\u0646 \u063a\u0627\u0632 \u0645\u062b\u0627\u0644\u064a \u0623\u062d\u0627\u062f\u064a \u0627\u0644\u0630\u0631\u0629 \u062f\u0627\u062e\u0644 \u0623\u0633\u0637\u0648\u0627\u0646\u0629 \u0628\u0648\u0627\u0633\u0637\u0629 \u0645\u0643\u0628\u0633\u060c \u0648\u064a\u064f\u062d\u0627\u0641\u0638 \u0639\u0644\u064a\u0647 \u0639\u0646\u062f \u062f\u0631\u062c\u0629 \u062d\u0631\u0627\u0631\u0629 \u062b\u0627\u0628\u062a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_0<\/span><\/span> \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0644\u0627\u0645\u0633 \u0645\u0639 \u062e\u0632\u0627\u0646 \u062d\u0631\u0627\u0631\u064a. \u064a\u062a\u0645\u062f\u062f \u0627\u0644\u063a\u0627\u0632 \u0628\u0628\u0637\u0621 \u0645\u0646 \u062d\u062c\u0645 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_1<\/span><\/span> \u0625\u0644\u0649 \u062d\u062c\u0645 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_2<\/span><\/span> \u0645\u0639 \u0627\u0644\u062d\u0641\u0627\u0638 \u0639\u0644\u0649 \u062f\u0631\u062c\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u062b\u0627\u0628\u062a\u0629 \u0637\u0648\u0627\u0644 \u0627\u0644\u0639\u0645\u0644\u064a\u0629.<\/p>\n<ol>\n<li>\u0647\u0644 \u062a\u062a\u063a\u064a\u0631 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0644\u0644\u063a\u0627\u0632\u061f<\/li>\n<li>\u0627\u062d\u0633\u0628 \u0627\u0644\u0634\u063a\u0644 \u0627\u0644\u0630\u064a \u064a\u0628\u0630\u0644\u0647 \u0627\u0644\u063a\u0627\u0632 \u0648\u062a\u062f\u0641\u0642 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0625\u0644\u0649 \u0627\u0644\u063a\u0627\u0632.<\/li>\n<\/ol>\n<\/li>\n<li>\n\t\t\u0623\u062b\u0628\u062a \u0623\u0646\u0647 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u063a\u0627\u0632 \u0627\u0644\u0645\u062b\u0627\u0644\u064a \u062a\u062a\u062d\u0642\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\"text-align: center;\">\n\t\t\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{R}{C_V} = \\gamma-1<\/span><\/span>\n\t\t<\/p>\n<p style=\"text-align: center;\">\n\t\t\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{R}{C_P} = \\frac{\\gamma -1}{\\gamma}<\/span><\/span>\n\t\t<\/p>\n<p>\u062d\u064a\u062b \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_P<\/span><\/span> \u0647\u0645\u0627 \u0627\u0644\u0633\u0639\u062a\u0627\u0646 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u062a\u0627\u0646 \u0639\u0646\u062f \u062d\u062c\u0645 \u0648\u0636\u063a\u0637 \u062b\u0627\u0628\u062a\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a.<\/p>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0647\u0648 \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0630\u064a \u064a\u0631\u0628\u0637 \u0628\u064a\u0646 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0645\u062b\u0644 \u0627\u0644\u062d\u0631\u0627\u0631\u0629\u060c \u0627\u0644\u0634\u063a\u0644 \u0648\u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629\u060c \u062d\u064a\u062b \u064a\u0646\u0635 \u0639\u0644\u0649 \u0623\u0646 \u0627\u0644\u0637\u0627\u0642\u0629 \u0644\u0627 \u062a\u064f\u062e\u0644\u0642 \u0648\u0644\u0627 \u062a\u064f\u0641\u0646\u0649 \u0628\u0644 \u062a\u062a\u062d\u0648\u0644 \u0645\u0646 \u0634\u0643\u0644 \u0625\u0644\u0649 \u0622\u062e\u0631. \u064a\u0633\u062a\u0643\u0634\u0641 \u0647\u0630\u0627 \u0627\u0644\u0646\u0635 \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0627 \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0639\u0644\u0649 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u063a\u0644\u0642\u0629\u060c \u0645\u0639 \u0627\u0644\u062a\u0639\u0645\u0642 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0634\u063a\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u060c \u0627\u0644\u0633\u0639\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0648\u0627\u0644\u062e\u0635\u0627\u0626\u0635 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30854,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":23,"footnotes":""},"categories":[925,641],"tags":[],"class_list":["post-30863","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-925","category-641"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0627\u0643\u062a\u0634\u0641 \u0643\u064a\u0641 \u064a\u0631\u0628\u0637 \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 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\u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\" \/>\n<meta name=\"twitter:description\" content=\"\u0627\u0643\u062a\u0634\u0641 \u0643\u064a\u0641 \u064a\u0631\u0628\u0637 \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062d\u0631\u0627\u0631\u0629\u060c \u0627\u0644\u0634\u063a\u0644 \u0648\u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629\u060c \u0648\u062a\u0637\u0628\u064a\u0642\u0627\u062a\u0647 \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u063a\u0644\u0642\u0629 \u0648\u0627\u0644\u063a\u0627\u0632\u0627\u062a \u0627\u0644\u0645\u062b\u0627\u0644\u064a\u0629.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/primeraley.jpg\" 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