{"id":30870,"date":"2021-07-03T13:00:44","date_gmt":"2021-07-03T13:00:44","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30870"},"modified":"2025-01-02T04:55:27","modified_gmt":"2025-01-02T04:55:27","slug":"%e0%a4%8a%e0%a4%b7%e0%a5%8d%e0%a4%ae%e0%a4%be%e0%a4%97%e0%a4%a4%e0%a4%bf%e0%a4%95%e0%a5%80-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b9%e0%a4%b2%e0%a4%be-%e0%a4%a8%e0%a4%bf%e0%a4%af%e0%a4%ae","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%8a%e0%a4%b7%e0%a5%8d%e0%a4%ae%e0%a4%be%e0%a4%97%e0%a4%a4%e0%a4%bf%e0%a4%95%e0%a5%80-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b9%e0%a4%b2%e0%a4%be-%e0%a4%a8%e0%a4%bf%e0%a4%af%e0%a4%ae\/","title":{"rendered":"\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\ttext-align:center;\n\t}\n<\/style>\n<h1>\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e<\/h1>\n<p style=\"text-align:center;\"><em>\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e \u0917\u0930\u094d\u092e\u0940, \u0915\u093e\u092e \u0914\u0930 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u091c\u0948\u0938\u0947 \u092e\u094c\u0932\u093f\u0915 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u093e \u0906\u0927\u093e\u0930 \u0939\u0948, \u092f\u0939 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u090a\u0930\u094d\u091c\u093e \u0928 \u0924\u094b \u092c\u0928\u093e\u0908 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0928 \u0939\u0940 \u0928\u0937\u094d\u091f \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948, \u0915\u0947\u0935\u0932 \u0930\u0942\u092a\u093e\u0902\u0924\u0930\u093f\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u092f\u0939 \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u092f\u0939 \u0926\u093f\u0916\u093e\u0924\u0940 \u0939\u0948 \u0915\u093f \u092f\u0939 \u0928\u093f\u092f\u092e \u092c\u0902\u0926 \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 \u092a\u0930 \u0915\u0948\u0938\u0947 \u0932\u093e\u0917\u0942 \u0939\u094b\u0924\u093e \u0939\u0948, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940\u092f \u0915\u093e\u0930\u094d\u092f, \u090a\u0937\u094d\u092e\u093e \u0915\u094d\u0937\u092e\u0924\u093e \u0914\u0930 \u0917\u0948\u0938\u094b\u0902 \u0915\u0947 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u0917\u0941\u0923\u094b\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f\u0964 \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u0942\u0924\u094d\u0930\u0940\u0915\u0930\u0923 \u0914\u0930 \u092d\u094c\u0924\u093f\u0915 \u0924\u0930\u094d\u0915\u094b\u0902 \u0915\u0947 \u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947, \u0906\u092a \u091c\u091f\u093f\u0932 \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u090a\u0930\u094d\u091c\u093e \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0909\u092a\u0915\u0930\u0923 \u0916\u094b\u091c\u0947\u0902\u0917\u0947\u0964<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0936\u093f\u0915\u094d\u0937\u0923 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f:<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902 \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947\n<\/p>\n<ol>\n<li><strong>\u0928\u094d\u092f\u093e\u092f\u0938\u0902\u0917\u0924<\/strong> \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u0947 \u092a\u0939\u0932\u0947 \u0928\u093f\u092f\u092e \u0915\u094b \u092c\u0902\u0926 \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f, \u0917\u0930\u094d\u092e\u0940, \u0915\u093e\u092e \u0914\u0930 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0915\u094b \u0938\u092e\u091d\u093e\u0924\u0947 \u0939\u0941\u090f\u0964<\/li>\n<li><strong>\u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923<\/strong> \u0938\u0902\u092a\u0940\u0921\u093c\u0928 \u0914\u0930 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940\u092f \u0915\u093e\u0930\u094d\u092f \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e, \u0905\u0902\u0924\u0930 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f\u0964<\/li>\n<li><strong>\u0917\u0923\u0928\u093e<\/strong> \u0938\u094d\u0925\u093f\u0930 \u0906\u092f\u0924\u0928 \u0914\u0930 \u0926\u092c\u093e\u0935 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u090a\u0937\u094d\u092e\u093e \u0915\u094d\u0937\u092e\u0924\u093e, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940\u092f \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927 \u0932\u093e\u0917\u0942 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u093e\u0928\u093e<\/strong> \u092e\u0948\u0915\u094d\u0938\u0935\u0947\u0932-\u092c\u094b\u0932\u094d\u091f\u094d\u091c\u093c\u092e\u0948\u0928 \u0935\u093f\u0924\u0930\u0923 \u0914\u0930 \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u094b \u0906\u0923\u0935\u093f\u0915 \u092a\u094d\u0930\u0923\u093e\u0932\u093f\u092f\u094b\u0902 \u092e\u0947\u0902\u0964<\/li>\n<li><strong>\u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928<\/strong> \u090a\u0937\u094d\u092e\u093e \u0915\u094d\u0937\u092e\u0924\u093e\u0913\u0902, \u090f\u0921\u093f\u092f\u093e\u092c\u0947\u091f\u093f\u0915 \u0938\u0942\u091a\u0915\u093e\u0902\u0915 \u0914\u0930 \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0905\u0928\u094d\u092f \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940\u092f \u0917\u0941\u0923\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u0938\u0902\u092c\u0902\u0927\u0964<\/li>\n<\/ol>\n<p style=\"text-align:center\"><strong><u>\u0935\u093f\u0937\u092f \u0938\u0942\u091a\u0940<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u0947 \u092a\u0939\u0932\u0947 \u0928\u093f\u092f\u092e \u0915\u093e \u0938\u0942\u0924\u094d\u0930\u0940\u0915\u0930\u0923<\/a><br \/>\n<a href=\"#2\">\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940\u092f \u0915\u093e\u0930\u094d\u092f<\/a><br \/>\n<a href=\"#3\">\u090a\u0937\u094d\u092e\u093e \u0915\u094d\u0937\u092e\u0924\u093e<\/a><br \/>\n<a href=\"#4\">\u092e\u0948\u0915\u094d\u0938\u0935\u0947\u0932-\u092c\u094b\u0932\u094d\u091f\u094d\u091c\u093c\u092e\u0948\u0928 \u0935\u093f\u0924\u0930\u0923 \u0914\u0930 \u090a\u0930\u094d\u091c\u093e \u0915\u0940 \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e<\/a><br \/>\n<a href=\"#5\">\u0905\u092d\u094d\u092f\u093e\u0938<\/a>\n<\/p>\n<p><center><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><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u0947 \u092a\u0939\u0932\u0947 \u0928\u093f\u092f\u092e \u0915\u093e \u0938\u0942\u0924\u094d\u0930\u0940\u0915\u0930\u0923<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=140s\" target=\"_blank\" rel=\"noopener\"><strong>\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e<\/strong><\/a> \u092f\u0939 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948:<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #c0ffc0;\"><span style=\"color: #000080;\">\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e<br \/>\n<strong>\u090a\u0930\u094d\u091c\u093e \u0928 \u0924\u094b \u092c\u0928\u093e\u0908 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0928 \u0939\u0940 \u0928\u0937\u094d\u091f \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948; \u0914\u0930 \u0917\u0930\u094d\u092e\u0940 \u0914\u0930 \u0915\u093e\u092e \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u0930\u0942\u092a \u0939\u0948\u0902 (\u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u0924\u094d\u0938\u0930\u094d\u091c\u093f\u0924, \u0905\u0935\u0936\u094b\u0937\u093f\u0924 \u092f\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u090f \u0917\u090f)\u0964 <\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e <span class=\"katex-eq\" data-katex-display=\"false\">U<\/span> \u090f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u091a\u0930 \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u0902\u0924\u0941\u0932\u0928 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u094d\u092a\u0937\u094d\u091f \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u092e\u093e\u0928 \u0930\u0916\u0924\u0940 \u0939\u0948\u0964 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u0915\u094b \u0917\u0930\u094d\u092e\u0940 <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span> \u092f\u093e \u0915\u093e\u092e <span class=\"katex-eq\" data-katex-display=\"false\">W<\/span> \u0932\u093e\u0917\u0942 \u0915\u0930\u0915\u0947 \u092c\u0926\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948; \u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u0915\u093e\u092e \u0914\u0930 \u0917\u0930\u094d\u092e\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u091a\u0930 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0907\u0938\u0932\u093f\u090f \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u0907\u0938 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u091c\u093f\u0938\u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u090a\u0930\u094d\u091c\u093e \u091c\u094b\u0921\u093c\u0940 \u092f\u093e \u0928\u093f\u0915\u093e\u0932\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u0914\u0930 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0938\u092e\u093e\u092a\u094d\u0924 \u0939\u094b\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926 \u092f\u0939 \u092a\u0924\u093e \u0932\u0917\u093e\u0928\u093e \u0905\u0938\u0902\u092d\u0935 \u0939\u0948 \u0915\u093f \u0938\u0902\u0924\u0941\u0932\u0928 \u0915\u0940 \u0907\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 \u092a\u0939\u0941\u0902\u091a\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0924\u0928\u0940 \u0917\u0930\u094d\u092e\u0940 \u092f\u093e \u0915\u093e\u092e \u0915\u093f\u092f\u093e \u0917\u092f\u093e\u0964<\/p>\n<p>\u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/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>\u091c\u0939\u093e\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta Q<\/span><\/span> \u0906\u092a\u0942\u0930\u094d\u0924\u093f \u0915\u0940 \u0917\u0908 \u0917\u0930\u094d\u092e\u0940 \u0915\u0940 \u092e\u093e\u0924\u094d\u0930\u093e \u0939\u0948 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta W<\/span><\/span> \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u092a\u0930 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0915\u093e\u092e \u0939\u0948\u0964 \u092a\u0930\u0902\u092a\u0930\u093e\u0917\u0924 \u0930\u0942\u092a \u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta Q<\/span><\/span> \u0924\u092c \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u094b \u0917\u0930\u094d\u092e\u0940 \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948; \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta Q<\/span><\/span> \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u0948, \u0924\u094b \u0917\u0930\u094d\u092e\u0940 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u0940 \u091c\u093e \u0930\u0939\u0940 \u0939\u0948; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta W<\/span><\/span> \u0924\u092c \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u092a\u0930 \u0915\u093e\u092e \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948; \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta W<\/span><\/span> \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u0948, \u0924\u094b \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u092a\u0930\u094d\u092f\u093e\u0935\u0930\u0923 \u092a\u0930 \u0915\u093e\u092e \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p>\u0915\u093e\u092e, \u0917\u0930\u094d\u092e\u0940 \u0914\u0930 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0915\u094b \u092d\u0940 \u092d\u093f\u0928\u094d\u0928 \u0930\u0942\u092a \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/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>\u092f\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u0905\u0915\u094d\u0937\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0938\u091f\u0940\u0915 \u0935\u093f\u092d\u0947\u0926\u0915\u094b\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u090f\u0915 \u090a\u0937\u094d\u092e\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u092a\u0943\u0925\u0915 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u094b \u0909\u0938 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u091c\u094b \u0905\u092a\u0928\u0947 \u092a\u0930\u093f\u0935\u0947\u0936 \u0915\u0947 \u0938\u093e\u0925 \u0917\u0930\u094d\u092e\u0940 \u0915\u093e \u0906\u0926\u093e\u0928-\u092a\u094d\u0930\u0926\u093e\u0928 \u0928\u0939\u0940\u0902 \u0915\u0930 \u0938\u0915\u0924\u0940\u0964 \u091c\u092c \u0910\u0938\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d U = \\delta W<\/span><\/span> \u0939\u094b\u0917\u093e\u0964 \u092f\u0939 <strong>\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e<\/strong> \u090f\u0915 \u0910\u0921\u093f\u092f\u093e\u092c\u0947\u091f\u093f\u0915 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0924\u0915 \u0938\u0940\u092e\u093f\u0924 \u0939\u0948\u0964<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u090a\u0937\u094d\u092e\u093e \u0915\u094d\u0937\u092e\u0924\u093e<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=677s\" target=\"_blank\" rel=\"noopener\"><strong>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0905\u092c<\/strong><\/a> \u0939\u092e \u092f\u0939 \u0938\u092e\u091d\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u091c\u092c \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u092e\u0947\u0902 \u0917\u0930\u094d\u092e\u0940 \u091c\u094b\u0921\u093c\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u0924\u094b \u0907\u0938\u0915\u0940 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u0915\u0948\u0938\u0947 \u092c\u0926\u0932\u0924\u0940 \u0939\u0948\u0964 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u0938\u0947, \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u0924\u093e\u092a\u092e\u093e\u0928 \u0914\u0930 \u0906\u092f\u0924\u0928 \u0915\u093e \u090f\u0915 \u092b\u0932\u0928 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u0939\u092e \u0907\u0938\u0947 \u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U=U(T,V)<\/span><\/span>\u0964 \u092b\u093f\u0930, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u090a\u0930\u094d\u091c\u093e \u090f\u0915 \u0938\u091f\u0940\u0915 \u0935\u093f\u092d\u0947\u0926\u0928 \u0939\u0948, <span class=\"katex-eq\" data-katex-display=\"false\">U<\/span> \u0915\u093e <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><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>.<\/p>\n<p>\u0905\u092c, \u0938\u0902\u092c\u0902\u0927\u094b\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dU=\\delta Q + \\delta W<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta W=-PdV<\/span><\/span> \u0938\u0947, \u0939\u092e <strong>\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e<\/strong> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u094d\u0915\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092b\u093f\u0930 \u0938\u0947 \u0924\u0948\u092f\u093e\u0930 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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>\u092f\u0939 \u0905\u0902\u0924\u093f\u092e \u0930\u0942\u092a \u0915\u093f\u0938\u0940 \u092d\u0940 \u0924\u093e\u092a\u092e\u093e\u0928 \u0914\u0930 \u0906\u092f\u0924\u0928 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u0932\u093f\u090f \u092e\u093e\u0928\u094d\u092f \u0939\u0948\u0964<\/p>\n<p>\u0939\u092e\u0928\u0947 \u091c\u094b \u0939\u093e\u0938\u093f\u0932 \u0915\u093f\u092f\u093e \u0939\u0948 \u0909\u0938\u0938\u0947 \u0939\u092e \u092f\u0939 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0924\u093e\u092a\u092e\u093e\u0928 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u094b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0924\u0928\u0940 \u0917\u0930\u094d\u092e\u0940 \u091c\u094b\u0921\u093c\u0928\u0940 \u0939\u094b\u0917\u0940, \u0915\u0941\u091b \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927\u094b\u0902 \u0915\u0947 \u0924\u0939\u0924\u0964<\/p>\n<h3>\u0938\u094d\u0925\u093f\u0930 \u0906\u092f\u0924\u0928 \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927<\/h3>\n<p>\u092f\u0939 \u0926\u0947\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u0938\u094d\u0925\u093f\u0930 \u0906\u092f\u0924\u0928 \u092a\u0930 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u092f\u093e\u0926 \u0930\u0916\u0947\u0902 \u0915\u093f \u0938\u094d\u0925\u093f\u0930 \u0906\u092f\u0924\u0928 \u092a\u0930 \u090a\u0937\u094d\u092e\u093e \u0915\u094d\u0937\u092e\u0924\u093e \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V=(\\partial Q\/ \\partial T)_V<\/span><\/span> \u0939\u0948\u0964 \u092b\u093f\u0930, \u092f\u0926\u093f \u0939\u092e \u092a\u093f\u091b\u0932\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u092e\u0947\u0902 \u0906\u092f\u0924\u0928 \u0915\u094b \u0938\u094d\u0925\u093f\u0930 \u0930\u0916\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dV\/dT<\/span><\/span> \u0936\u092c\u094d\u0926 \u0915\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta Q\/dT<\/span><\/span> \u0915\u0940 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u092e\u0947\u0902 \u0939\u091f\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0939\u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u0928\u0947 \u0915\u093e \u0914\u091a\u093f\u0924\u094d\u092f \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  C_V = \\left(\\frac{\\partial U}{\\partial T} \\right)_V<\/span><\/span><\/p>\n<h3>\u0938\u094d\u0925\u093f\u0930 \u0926\u092c\u093e\u0935 \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927<\/h3>\n<p>\u092f\u0926\u093f \u0939\u092e \u0926\u092c\u093e\u0935 \u0915\u094b \u0938\u094d\u0925\u093f\u0930 \u0930\u0916\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092f\u0939 \u0939\u094b\u0917\u093e:<\/p>\n<p style=\"text-align: center;\"><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>.<\/p>\n<h3>\u090f\u0915 \u090f\u0915\u093e\u0924\u094d\u092e\u0915 \u0917\u0948\u0938 \u0915\u0940 \u090a\u0937\u094d\u092e\u093e \u0915\u094d\u0937\u092e\u0924\u093e<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=974s\" target=\"_blank\" rel=\"noopener\"><strong>\u091c\u092c \u0939\u092e<\/strong><\/a> \u090f\u0915 \u090f\u0915\u093e\u0924\u094d\u092e\u0915 \u0917\u0948\u0938 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u0923\u094b\u0902 \u0915\u0940 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u0915\u093e\u0930\u0923 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u0915\u093e \u0930\u0942\u092a <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n U=\\frac{3}{2}Nk_BT<\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u0939\u0940 \u0920\u0939\u0930\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0947 \u0915\u0923\u094b\u0902 \u0915\u0940 \u0917\u0924\u093f \u0915\u0947 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0938\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u092e\u0948\u0915\u094d\u0938\u0935\u0947\u0932-\u092c\u094b\u0932\u094d\u091f\u094d\u091c\u093c\u092e\u0948\u0928 \u0935\u093f\u0924\u0930\u0923 \u0914\u0930 \u090a\u0930\u094d\u091c\u093e \u0915\u093e \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=1027s\" target=\"_blank\" rel=\"noopener\"><strong>\u091a\u0942\u0902\u0915\u093f \u0915\u093f\u0938\u0940 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u090a\u0930\u094d\u091c\u093e<\/strong><\/a> \u0907\u0938\u0915\u0947 <strong>\u092c\u094b\u0932\u094d\u091f\u094d\u091c\u093c\u092e\u0948\u0928 \u0915\u093e\u0930\u0915<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">e^{-E\/(k_BT)}<\/span><\/span> \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0914\u0930 \u092f\u0939 \u092e\u093e\u0928\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u0915\u0923\u094b\u0902 \u0915\u0940 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u093e \u0930\u0942\u092a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  E_{cin}=\\frac{1}{2}mv^2<\/span><\/span> \u0939\u0948, \u0939\u092e \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0947 \u0915\u0923\u094b\u0902 \u0915\u0947 \u0917\u0924\u093f \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u090a\u0930\u094d\u091c\u093e, \u091c\u093f\u0938\u0947 \u0915\u093f\u0938\u0940 \u090f\u0915 \u0938\u092e\u0928\u094d\u0935\u092f \u0905\u0915\u094d\u0937 (\u092e\u093e\u0928 \u0932\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/span>) \u092a\u0930 \u092a\u094d\u0930\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u0915\u0940 \u0935\u0947\u0917 \u0935\u093f\u0924\u0930\u0923 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(v_x)<\/span><\/span> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0939\u094b\u0917\u0940:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(v_x)= A e^{-mv_x^2\/(2k_BT)}<\/span><\/span>,<\/p>\n<p>\u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u090f\u0915 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u093e \u0939\u0948\u0964 \u0905\u092c, \u091a\u0942\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(v_x)<\/span><\/span> \u090f\u0915 \u0935\u093f\u0924\u0930\u0923 \u092b\u0932\u0928 \u0939\u0948, \u0907\u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f \u0915\u093f:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\int_{-\\infty}^{+\\infty} g(v_x)dv_x= 1<\/span><\/span><\/p>\n<p>\u0907\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0909\u092a\u092f\u094b\u0917\u0940 \u092a\u0930\u093f\u0923\u093e\u092e \u0917\u0949\u0938\u093f\u092f\u0928 \u0938\u092e\u093e\u0915\u0932\u0928 \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\int_{-\\infty}^{+\\infty} e^{-x^2}dx= \\sqrt{\\pi}<\/span><\/span><\/p>\n<p>\u0907\u0938\u0938\u0947 \u092f\u0939 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0915\u093f:<\/p>\n<p style=\"text-align: center;\"><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><\/p>\n<p>\u0914\u0930 \u0907\u0938\u0932\u093f\u090f:<\/p>\n<p style=\"text-align: center;\"><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><\/p>\n<p>\u0907\u0938 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u0947 \u0938\u093e\u0925 \u0905\u092c \u0939\u092e \u0905\u0915\u094d\u0937 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/span> \u092a\u0930 \u092a\u094d\u0930\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0914\u0938\u0924 \u0935\u0947\u0917 \u0935\u0930\u094d\u0917 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left&lt; v_x^2\\right&gt;<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><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><\/p>\n<p>\u091a\u0942\u0902\u0915\u093f \u0914\u0938\u0924 \u0935\u0947\u0917 \u0935\u0930\u094d\u0917 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><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>,<\/p>\n<p>\u0914\u0930 \u0907\u0928\u092e\u0947\u0902 \u0938\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0918\u091f\u0915 \u0915\u093e \u0935\u093f\u0915\u093e\u0938 \u0914\u0930 \u092a\u0930\u093f\u0923\u093e\u092e \u0938\u092e\u093e\u0928 \u0939\u0948, \u0939\u092e \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0947 \u0915\u0923\u094b\u0902 \u0915\u0940 \u0914\u0938\u0924 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center;\"><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>.<\/p>\n<p>\u0907\u0938\u0947 \u00ab\u090a\u0930\u094d\u091c\u093e \u0915\u093e \u0938\u092e\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924\u00bb \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0906\u0927\u093e\u0930 \u092a\u0930, \u092f\u0926\u093f \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u0915\u0923 \u0939\u0948\u0902, \u091c\u093f\u0928\u0915\u0940 \u0914\u0938\u0924 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left\\lt E_{cin}\\right\\gt<\/span><\/span> \u0939\u0948 \u0914\u0930 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u0915\u0941\u0932 \u090a\u0930\u094d\u091c\u093e \u0915\u0947\u0935\u0932 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0939\u0948, \u0924\u094b \u0939\u092e \u092f\u0939 \u0928\u0939\u0940\u0902 \u0915\u0947\u0935\u0932 \u0915\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n U=3Nk_BT\/2<\/span> \u0939\u0948 (\u091c\u0948\u0938\u093e \u092a\u0939\u0932\u0947 \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u092f\u093e \u0917\u092f\u093e \u0925\u093e), \u092c\u0932\u094d\u0915\u093f \u092f\u0939 \u092d\u0940 \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 \u0926\u093f\u0916\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u0915\u0947\u0935\u0932 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0947 \u0924\u093e\u092a\u092e\u093e\u0928 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u0940 \u0939\u0948, \u091c\u093f\u0938\u0938\u0947:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left(\\frac{\\partial U}{\\partial V}\\right)_T = 0<\/span><\/span><\/p>\n<h3>\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=1027s\" target=\"_blank\" rel=\"noopener\"><strong>\u0905\u092c, \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b \u0927\u094d\u092f\u093e\u0928 \u092e\u0947\u0902 \u0930\u0916\u0924\u0947 \u0939\u0941\u090f<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV=Nk_BT =nRT<\/span><\/span>\u0964 \u092f\u0926\u093f \u0939\u092e \u0906\u092f\u0924\u0928 \u0915\u093e \u0928\u093f\u0930\u093e\u0915\u0930\u0923 \u0915\u0930\u0947\u0902 \u0924\u094b \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  V= \\frac{nRT}{P}<\/span><\/span><\/p>\n<p>\u0914\u0930 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930:<\/p>\n<p style=\"text-align: center;\"><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><\/p>\n<p>\u0914\u0930 \u091c\u092c \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_P<\/span><\/span> \u0915\u0940 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u094b \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u092a\u0924\u093e \u091a\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\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}<\/span>\n<p>\u0905\u092c, \u091a\u0942\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  C_V=(\\partial U \/ \\partial T)_V<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U=3Nk_BT\/2=3nRT\/2<\/span><\/span>, \u0924\u094b:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle  C_V = \\frac{3}{2}nR\n\n<\/span>\n<p>\u0914\u0930 \u0907\u0938\u0932\u093f\u090f:<\/p>\n<p style=\"text-align: center;\"><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>\u090f\u0921\u093f\u092f\u093e\u092c\u0947\u091f\u093f\u0915 \u0917\u0941\u0923\u093e\u0902\u0915<\/h3>\n<p>\u090f\u0915 \u0905\u0915\u094d\u0938\u0930 \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u092e\u093e\u092a\u093e\u0902\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_P<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V<\/span><\/span> \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u093e \u0939\u0948, \u091c\u093f\u0938\u0947 <strong>\u090f\u0921\u093f\u092f\u093e\u092c\u0947\u091f\u093f\u0915 \u0917\u0941\u0923\u093e\u0902\u0915<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\gamma = \\displaystyle  \\frac{C_P}{C_V}\n\n<\/span>\n<p>\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f, \u090f\u0921\u093f\u092f\u093e\u092c\u0947\u091f\u093f\u0915 \u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u093e \u092e\u093e\u0928 \u0938\u091f\u0940\u0915 \u0939\u0948:<\/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>\u0905\u092d\u094d\u092f\u093e\u0938<\/h2>\n<ol>\n<li>\u0915\u094d\u092f\u093e \u092f\u0939 \u0939\u092e\u0947\u0936\u093e \u0938\u0924\u094d\u092f \u0939\u094b\u0917\u093e \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dU=C_VdT<\/span><\/span>? \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u092e\u093e\u092e\u0932\u0947 \u0915\u0940 \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938\u094b\u0902 \u0938\u0947 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0947\u0902 \u0914\u0930 \u0905\u092a\u0928\u0947 \u0909\u0924\u094d\u0924\u0930 \u0915\u094b \u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924 \u092c\u0928\u093e\u090f\u0902\u0964<\/li>\n<li>\u092e\u093e\u0928\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u090f\u0915 \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0915\u0947 \u0932\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U=C_VT<\/span><\/span> \u0938\u0924\u094d\u092f \u0939\u0948, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902: (i) \u0926\u094d\u0930\u0935\u094d\u092f\u092e\u093e\u0928 \u092a\u094d\u0930\u0924\u093f \u0907\u0915\u093e\u0908 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u0914\u0930 (ii) \u0906\u092f\u0924\u0928 \u092a\u094d\u0930\u0924\u093f \u0907\u0915\u093e\u0908 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e\u0964<\/li>\n<li>\u090f\u0915 \u0906\u0926\u0930\u094d\u0936 \u090f\u0915 \u092a\u0930\u092e\u093e\u0923\u0941 \u0917\u0948\u0938 \u0915\u0947 \u090f\u0915 \u092e\u094b\u0932 \u0915\u094b \u090f\u0915 \u0938\u093f\u0932\u0947\u0902\u0921\u0930 \u092e\u0947\u0902 \u090f\u0915 \u092a\u093f\u0938\u094d\u091f\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u0940\u092e\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0914\u0930 \u0907\u0938\u0947 \u090f\u0915 \u0925\u0930\u094d\u092e\u0932 \u0930\u093f\u091c\u0930\u094d\u0935 \u0915\u0947 \u0938\u0902\u092a\u0930\u094d\u0915 \u092e\u0947\u0902 \u0930\u0916\u0915\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0924\u093e\u092a\u092e\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_0<\/span><\/span> \u092a\u0930 \u092c\u0928\u093e\u090f \u0930\u0916\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0917\u0948\u0938 \u0915\u094b \u0927\u0940\u0930\u0947-\u0927\u0940\u0930\u0947 \u090f\u0915 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0906\u092f\u0924\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_1<\/span><\/span> \u0938\u0947 \u090f\u0915 \u0905\u0902\u0924\u093f\u092e \u0906\u092f\u0924\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_2<\/span><\/span> \u0924\u0915 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u092c\u0915\u093f \u0924\u093e\u092a\u092e\u093e\u0928 \u0938\u094d\u0925\u093f\u0930 \u0930\u0939\u0924\u093e \u0939\u0948\u0964 (i) \u0915\u094d\u092f\u093e \u0917\u0948\u0938 \u0915\u0940 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u092c\u0926\u0932\u0924\u0940 \u0939\u0948? (ii) \u0917\u0948\u0938 \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u0917\u0948\u0938 \u092e\u0947\u0902 \u092a\u094d\u0930\u0935\u093e\u0939\u093f\u0924 \u0917\u0930\u094d\u092e\u0940 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902\u0964<\/li>\n<li>\u092f\u0939 \u0926\u093f\u0916\u093e\u090f\u0902 \u0915\u093f \u090f\u0915 \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u092c\u0902\u0927 \u0938\u0924\u094d\u092f \u0939\u0948\u0902:\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{R}{c_V} = \\gamma-1<\/span><\/span><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{R}{c_P} = \\frac{\\gamma -1}{\\gamma}<\/span><\/span><\/p>\n<p>\u091c\u0939\u093e\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c_V<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c_P<\/span><\/span> \u092e\u094b\u0932\u0930 \u090a\u0937\u094d\u092e\u093e \u0927\u093e\u0930\u093f\u0924\u093e \u0939\u0948\u0902\u0964<\/p>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e \u0917\u0930\u094d\u092e\u0940, \u0915\u093e\u092e \u0914\u0930 \u0906\u0902\u0924\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u091c\u0948\u0938\u0947 \u092e\u094c\u0932\u093f\u0915 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u093e \u0906\u0927\u093e\u0930 \u0939\u0948, \u092f\u0939 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u090a\u0930\u094d\u091c\u093e \u0928 \u0924\u094b \u092c\u0928\u093e\u0908 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0928 \u0939\u0940 \u0928\u0937\u094d\u091f \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948, \u0915\u0947\u0935\u0932 \u0930\u0942\u092a\u093e\u0902\u0924\u0930\u093f\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u092f\u0939 \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u092f\u0939 \u0926\u093f\u0916\u093e\u0924\u0940 \u0939\u0948 \u0915\u093f \u092f\u0939 \u0928\u093f\u092f\u092e [&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":3,"footnotes":""},"categories":[927,643],"tags":[],"class_list":["post-30870","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-927","category-643"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u092a\u0924\u093e \u0932\u0917\u093e\u090f\u0902 \u0915\u093f \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u0915\u093e \u092a\u0939\u0932\u093e \u0928\u093f\u092f\u092e \u0915\u0948\u0938\u0947 \u0917\u0930\u094d\u092e\u0940, \u0915\u093e\u092e \u0914\u0930 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