{"id":30071,"date":"2021-03-10T13:00:10","date_gmt":"2021-03-10T13:00:10","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30071"},"modified":"2025-10-20T07:31:27","modified_gmt":"2025-10-20T07:31:27","slug":"%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/","title":{"rendered":"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923"},"content":{"rendered":"<style>\np, ul, ol{\n  text-align: justify;\n}\nh1{\n  text-align:center;\n  text-transform: uppercase;\n}\nh2{\n  text-align:center;\n  text-transform: uppercase;\n  font-size:24pt;\n}\nh3 { \n  text-align: center;\n  text-transform: uppercase;\n  font-size: 24px !important;\n}\n.example{\n  background:#f6f8fa; \n  border-left:4px solid #d00000; \n  padding:12px 14px; \n  margin:14px 0;\n}\n.small{\n  font-size: 0.95em;\n  color:#333;\n}\n<\/style>\n<h1>\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0915\u093e \u0905\u0928\u0941\u092d\u0935\u091c\u0928\u094d\u092f \u0938\u0942\u0924\u094d\u0930\u0940\u0915\u0930\u0923<\/h1>\n<p style=\"text-align:center;\" dir=\"ltr\">\u0915\u094d\u092f\u093e \u0906\u092a\u0928\u0947 \u0915\u092d\u0940 \u0938\u094b\u091a\u093e \u0939\u0948 \u0915\u093f \u091c\u092c \u090f\u0915 \u0917\u0941\u092c\u094d\u092c\u093e\u0930\u0947 \u0915\u094b \u0917\u0930\u094d\u092e \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u0935\u0939 \u0915\u094d\u092f\u094b\u0902 \u092b\u0948\u0932\u0924\u093e \u0939\u0948 \u092f\u093e \u091c\u092c \u090a\u0901\u091a\u093e\u0908 \u092c\u0926\u0932\u0924\u0940 \u0939\u0948 \u0924\u094b \u091f\u093e\u092f\u0930 \u0915\u093e \u0926\u092c\u093e\u0935 \u0915\u094d\u092f\u094b\u0902 \u092c\u0926\u0932\u0924\u093e \u0939\u0948? \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u0909\u0928 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947 \u091c\u094b \u0907\u0928 \u0935\u094d\u092f\u0935\u0939\u093e\u0930\u094b\u0902 \u0915\u094b \u0928\u093f\u092f\u0902\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092f\u0939 \u0915\u0948\u0938\u0947 \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923, \u0909\u0938\u0915\u0947 \u0935\u093f\u091a\u093e\u0930\u094b\u0902 \u0914\u0930 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0940 \u0913\u0930 \u0932\u0947 \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><b>\u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/b><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\u0917\u093e:<\/p>\n<ol>\n<li><b>\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0930\u0928\u093e<\/b> \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938\u094b\u0902 \u0915\u0947 \u0905\u0928\u0941\u092d\u0935\u091c\u0928\u094d\u092f \u0928\u093f\u092f\u092e\u094b\u0902 (Boyle\u2013Mariotte, Charles, Gay-Lussac) \u0914\u0930 \u0909\u0928\u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 \u0938\u0902\u092f\u094b\u091c\u0928 (<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV = nRT<\/span><\/span>, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV = N k_B T<\/span><\/span>) \u0915\u094b\u0964<\/li>\n<li><b>\u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u093e<\/b> \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0938\u0902\u092c\u0902\u0927 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV\/T = cte<\/span><\/span> \u0915\u093e, \u0924\u093e\u0915\u093f \u0938\u092e\u0930\u0942\u092a \u0907\u0915\u093e\u0907\u092f\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0905\u0935\u0938\u094d\u0925\u093e \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928\u094b\u0902 \u0915\u094b \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964<\/li>\n<li><b>\u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u093e<\/b> \u0938\u092e\u0924\u093e\u092a\u0940\u092f, \u0938\u092e\u0926\u092c \u0914\u0930 \u0938\u092e\u0906\u092f\u0924\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u094b \u0924\u0925\u093e \u0909\u0928\u0915\u0947 \u092e\u093e\u0930\u094d\u0917\u094b\u0902 \u0915\u094b <i>P\u2013V<\/i>, <i>V\u2013T<\/i> \u0914\u0930 <i>P\u2013T<\/i> \u0906\u0930\u0947\u0916\u094b\u0902 \u092e\u0947\u0902\u0964<\/li>\n<li><b>\u092a\u0939\u091a\u093e\u0928\u0928\u093e<\/b> \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0915\u0947 \u0935\u0948\u0927\u0924\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0915\u094b \u0914\u0930 \u091c\u092c \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0939\u094b \u0924\u094b \u0935\u0948\u0915\u0932\u094d\u092a\u093f\u0915 \u092e\u0949\u0921\u0932\u094b\u0902 (van der Waals, \u0915\u094d\u0935\u093e\u0902\u091f\u092e, \u0938\u093e\u092a\u0947\u0915\u094d\u0937\u0935\u093e\u0926\u0940) \u0915\u093e \u091a\u092f\u0928 \u0915\u0930\u0928\u093e\u0964<\/li>\n<\/ol>\n<p style=\"text-align:center;\" dir=\"ltr\">\n<b>\u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0938\u0942\u091a\u0915\u093e\u0902\u0915<\/b><br \/>\n<a href=\"#1\">\u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0928\u0941\u092d\u0935\u091c\u0928\u094d\u092f \u0928\u093f\u092f\u092e<\/a><br \/>\n<a href=\"#2\">\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0938\u0902\u092f\u094b\u091c\u0928<\/a><br \/>\n<a href=\"#3\">\u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/a><br \/>\n<a href=\"#4\">\u091f\u093f\u092a\u094d\u092a\u0923\u093f\u092f\u093e\u0901 \u0914\u0930 \u0938\u0942\u0915\u094d\u0937\u094d\u092e \u092a\u0943\u0937\u094d\u0920\u092d\u0942\u092e\u093f<\/a><br \/>\n<a href=\"#5\">\u0935\u0948\u0927\u0924\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0914\u0930 \u0938\u0940\u092e\u093e\u090f\u0901<\/a><br \/>\n<a href=\"#6\">\u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u091f\u093f\u092a\u094d\u092a\u0923\u093f\u092f\u093e\u0901<\/a>\n<\/p>\n<p><center><br \/>\n <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/7WkrH_FS290?si=xWJQ-VAtbWgzm9bQ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n<\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0928\u0941\u092d\u0935\u091c\u0928\u094d\u092f \u0928\u093f\u092f\u092e<\/h2>\n<p>\u0917\u0948\u0938\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0915\u093f\u090f \u0917\u090f \u092a\u094d\u0930\u092f\u094b\u0917 \u0926\u092c\u093e\u0935 <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span>, \u0906\u092f\u0924\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> \u0914\u0930 \u0924\u093e\u092a\u092e\u093e\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u0915\u0947 \u092c\u0940\u091a \u0928\u093f\u0930\u094d\u092d\u0930\u0924\u093e \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0928\u093f\u092f\u0902\u0924\u094d\u0930\u093f\u0924 \u092a\u0930\u093f\u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0924\u0940\u0928 \u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0928\u0941\u092d\u0935\u091c\u0928\u094d\u092f \u0928\u093f\u092f\u092e \u0926\u0947\u0916\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ol>\n<li><strong>Boyle\u2013Mariotte \u0915\u093e \u0928\u093f\u092f\u092e (\u0938\u092e\u0924\u093e\u092a\u0940\u092f):<\/strong> \u0938\u094d\u0925\u093f\u0930 \u0924\u093e\u092a\u092e\u093e\u0928 \u092a\u0930 \u0915\u093f\u0938\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u092e\u0947\u0902, \u0917\u0948\u0938 \u0915\u093e \u0906\u092f\u0924\u0928 \u0914\u0930 \u0926\u092c\u093e\u0935 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u0915\u094d\u0930\u092e\u093e\u0928\u0941\u092a\u093e\u0924\u0940 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902; \u0905\u0930\u094d\u0925\u093e\u0924\u094d:\n<div style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P \\propto \\dfrac{1}{V}\\quad\\Leftrightarrow\\quad PV=\\text{cte.}<\/span><\/div>\n<div class=\"example\">\n  <strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong> \u090f\u0915 \u0917\u0948\u0938 \u091c\u094b \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0926\u092c\u093e\u0935 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P_1 = 15\\ \\mathrm{MPa}<\/span><\/span> \u092a\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948, \u092f\u0926\u093f \u0935\u0939 \u0938\u092e\u0924\u093e\u092a\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \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 = 1{,}00\\ \\mathrm{L}<\/span><\/span> \u0938\u0947 \u0905\u0902\u0924\u093f\u092e \u0906\u092f\u0924\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_2 = 2{,}00\\ \\mathrm{L}<\/span><\/span> \u0924\u0915 \u092b\u0948\u0932\u0924\u0940 \u0939\u0948, \u0924\u094b \u0909\u0938\u0915\u093e \u0926\u092c\u093e\u0935 \u0906\u0927\u093e \u0939\u094b \u091c\u093e\u090f\u0917\u093e\u0964 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0917\u0941\u0923\u0928\u092b\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV=\\text{cte.}<\/span><\/span> \u0939\u0948, \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P_1 V_1 = P_2 V_2<\/span><\/span> \u092a\u0942\u0930\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n  P_2 = \\dfrac{P_1 V_1}{V_2}\n\n      = 15\\ \\mathrm{MPa}\\left(\\dfrac{1{,}00\\ \\mathrm{L}}{2{,}00\\ \\mathrm{L}}\\right)\n\n      = 7{,}50\\ \\mathrm{MPa}\n\n  <\/span>\n<p>  <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/pv-isotermico.jpg\" alt=\"\u0938\u092e\u0924\u093e\u092a\u0940\u092f \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0932\u093f\u090f PV \u0906\u0930\u0947\u0916\" width=\"480\" height=\"293\" class=\"aligncenter size-full wp-image-34975 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/pv-isotermico.jpg\" alt=\"\u0938\u092e\u0924\u093e\u092a\u0940\u092f \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0932\u093f\u090f PV \u0906\u0930\u0947\u0916\" width=\"480\" height=\"293\" class=\"aligncenter size-full wp-image-34975 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/pv-isotermico.jpg 480w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/pv-isotermico-300x183.jpg 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/noscript><\/center>\n<\/div>\n<\/li>\n<li><strong>Charles \u0915\u093e \u0928\u093f\u092f\u092e (\u0938\u092e\u0926\u092c):<\/strong> \u0938\u094d\u0925\u093f\u0930 \u0926\u092c\u093e\u0935 \u092a\u0930 \u0915\u093f\u0938\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u092e\u0947\u0902, \u0917\u0948\u0938 \u0915\u093e \u0906\u092f\u0924\u0928 \u0914\u0930 \u0924\u093e\u092a\u092e\u093e\u0928 \u0938\u0940\u0927\u0947 \u0905\u0928\u0941\u092a\u093e\u0924\u0940 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902; \u0905\u0930\u094d\u0925\u093e\u0924\u094d:\n<div style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V \\propto T \\quad\\Leftrightarrow\\quad \\dfrac{V}{T}=\\text{cte.}<\/span><\/div>\n<div class=\"example\">\n  <strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong> \u090f\u0915 \u0917\u0948\u0938 \u091c\u094b \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0924\u093e\u092a\u092e\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_1 = 300\\ \\mathrm{K}<\/span><\/span> \u092a\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948, \u092f\u0926\u093f \u0909\u0938\u0947 \u0938\u092e\u0926\u092c \u0930\u0942\u092a \u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_2 = 450\\ \\mathrm{K}<\/span><\/span> \u0924\u0915 \u0917\u0930\u094d\u092e \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u093e \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 = 2{,}00\\ \\mathrm{L}<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u0909\u0938\u0915\u093e \u0906\u092f\u0924\u0928 50&nbsp;% \u092c\u0922\u093c \u091c\u093e\u090f\u0917\u093e (\u090f\u0915 \u0915\u093e\u0930\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tfrac{3}{2}<\/span><\/span>)\u0964 \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tfrac{V}{T}=\\text{cte.}<\/span><\/span> \u0939\u0948, \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{V_1}{T_1}=\\dfrac{V_2}{T_2}<\/span><\/span> \u092a\u0942\u0930\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n  V_2 = V_1 \\cdot \\dfrac{T_2}{T_1}\n\n      = 2{,}00\\ \\mathrm{L}\\left(\\dfrac{450\\ \\mathrm{K}}{300\\ \\mathrm{K}}\\right)\n\n      = 3{,}00\\ \\mathrm{L}\n\n  <\/span>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/isobara-proc.jpg\" alt=\"\" width=\"480\" height=\"298\" class=\"aligncenter size-full wp-image-34984 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/isobara-proc.jpg\" alt=\"\" width=\"480\" height=\"298\" class=\"aligncenter size-full wp-image-34984 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/isobara-proc.jpg 480w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/isobara-proc-300x186.jpg 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/noscript><\/center><\/p>\n<\/div>\n<\/li>\n<li><strong>Gay-Lussac \u0915\u093e \u0928\u093f\u092f\u092e (\u0938\u092e\u0906\u092f\u0924\u0928):<\/strong> \u0938\u094d\u0925\u093f\u0930 \u0906\u092f\u0924\u0928 \u092a\u0930 \u0915\u093f\u0938\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u092e\u0947\u0902, \u0917\u0948\u0938 \u0915\u093e \u0926\u092c\u093e\u0935 \u0914\u0930 \u0924\u093e\u092a\u092e\u093e\u0928 \u0938\u0940\u0927\u0947 \u0905\u0928\u0941\u092a\u093e\u0924\u0940 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902; \u0905\u0930\u094d\u0925\u093e\u0924\u094d:\n<div style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P \\propto T \\quad\\Leftrightarrow\\quad \\dfrac{P}{T}=\\text{cte.}<\/span><\/div>\n<div class=\"example\">\n  <strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong> \u090f\u0915 \u0917\u0948\u0938 \u091c\u094b \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0924\u093e\u092a\u092e\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_1 = 300\\ \\mathrm{K}<\/span><\/span> \u092a\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948, \u092f\u0926\u093f \u0909\u0938\u0947 \u0938\u092e\u0906\u092f\u0924\u0928 \u0930\u0942\u092a \u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_2 = 450\\ \\mathrm{K}<\/span><\/span> \u0924\u0915 \u0917\u0930\u094d\u092e \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u093e \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0926\u092c\u093e\u0935 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P_1 = 1{,}00\\ \\mathrm{MPa}<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u0909\u0938\u0915\u093e \u0926\u092c\u093e\u0935 \u0909\u0938\u0940 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u092c\u0922\u093c\u0947\u0917\u093e\u0964 \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tfrac{P}{T}=\\text{cte.}<\/span><\/span> \u0939\u0948, \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{P_1}{T_1}=\\dfrac{P_2}{T_2}<\/span><\/span> \u092a\u0942\u0930\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n  P_2 = P_1 \\cdot \\dfrac{T_2}{T_1}\n\n      = 1{,}00\\ \\mathrm{MPa}\\left(\\dfrac{450\\ \\mathrm{K}}{300\\ \\mathrm{K}}\\right)\n\n      = 1{,}50\\ \\mathrm{MPa}\n\n  <\/span>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/icororico-proc.jpg\" alt=\"\" width=\"480\" height=\"291\" class=\"aligncenter size-full wp-image-34987 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/icororico-proc.jpg\" alt=\"\" width=\"480\" height=\"291\" class=\"aligncenter size-full wp-image-34987 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/icororico-proc.jpg 480w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/icororico-proc-300x182.jpg 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/noscript><\/center>\n<\/div>\n<\/li>\n<\/ol>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0938\u0902\u092f\u094b\u091c\u0928<\/h2>\n<p>\u0907\u0928 \u0924\u0940\u0928\u094b\u0902 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u094b \u090f\u0915 \u0939\u0940 \u0938\u092e\u093e\u0928\u0941\u092a\u093e\u0924\u0940 \u0938\u0902\u092c\u0902\u0927 \u092e\u0947\u0902 \u0938\u0902\u0915\u094d\u0937\u0947\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV \\propto T<\/span>\n<p>\u091c\u0939\u093e\u0901, \u092a\u094d\u0930\u093e\u092f\u094b\u0917\u093f\u0915 \u0914\u0930 \u0938\u0942\u0915\u094d\u0937\u094d\u092e \u0935\u093f\u091a\u093e\u0930\u094b\u0902 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930, \u0938\u092e\u093e\u0928\u0941\u092a\u093e\u0924\u0940 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0915\u094b \u0915\u0923\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u0914\u0930 Boltzmann \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k_B = 1{,}380\\,649\\times10^{-23}\\ \\mathrm{J\\,K^{-1}}<\/span><\/span> \u0915\u0947 \u0917\u0941\u0923\u0928\u092b\u0932 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e\u092f\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0938\u0942\u0915\u094d\u0937\u094d\u092e \u0938\u0902\u092c\u0902\u0927 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{PV = N\\,k_B\\,T}<\/span>\n<p>\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, \u092e\u094b\u0932\u0930 \u0930\u0942\u092a \u092e\u0947\u0902, \u0938\u092e\u093e\u0928\u0941\u092a\u093e\u0924\u0940 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0915\u094b \u092e\u094b\u0932\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0914\u0930 \u0917\u0948\u0938\u094b\u0902 \u0915\u0947 \u0938\u093e\u0930\u094d\u0935\u092d\u094c\u092e\u093f\u0915 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">R=8{,}314\\,462\\,6\\ \\mathrm{J\\,mol^{-1}\\,K^{-1}}=0{,}082\\,057\\ \\mathrm{L\\,atm\\,mol^{-1}\\,K^{-1}}<\/span><\/span> \u0915\u0947 \u0917\u0941\u0923\u0928\u092b\u0932 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u092e\u094b\u0932\u0930 \u0938\u0902\u092c\u0902\u0927 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{PV = n\\,R\\,T}<\/span>\n<p>\u091a\u093e\u0939\u0947 \u0915\u094b\u0908 \u092d\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0939\u094b, \u092f\u0939 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0939\u0948 \u0915\u093f \u0917\u0941\u0923\u0928\u092b\u0932 <span class=\"katex-eq\" data-katex-display=\"false\">PV<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> \u0915\u0947 \u092c\u0940\u091a \u090f\u0915 \u092a\u094d\u0930\u0924\u094d\u092f\u0915\u094d\u0937 \u0938\u092e\u093e\u0928\u0941\u092a\u093e\u0924\u0940 \u0938\u0902\u092c\u0902\u0927 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u092f\u0939 \u0939\u0948 \u0915\u093f \u092f\u0926\u093f \u090f\u0915 \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0926\u094b \u0905\u0935\u0938\u094d\u0925\u093e\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948 \u2014 \u090f\u0915 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\alpha, V_\\alpha, T_\\alpha)<\/span><\/span> \u0914\u0930 \u0926\u0942\u0938\u0930\u0940 \u0905\u0902\u0924\u093f\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\omega, V_\\omega, T_\\omega)<\/span><\/span> \u2014 \u0924\u094b \u0935\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u092c\u0902\u0927 \u0915\u094b \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{P_\\alpha V_\\alpha}{T_\\alpha} =  \\dfrac{P_\\omega V_\\omega}{T_\\omega}<\/span>\n<p>\u0914\u0930 \u0907\u0938\u0932\u093f\u090f, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV\/T = cte.<\/span><\/span><\/p>\n<p>\u092f\u0939 \u0938\u0902\u092c\u0902\u0927, \u091c\u093f\u0938\u0947 \u092a\u094d\u0930\u092f\u094b\u0917\u093e\u0924\u094d\u092e\u0915 \u0906\u0927\u093e\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0924\u093e\u0915\u093f \u0938\u0942\u0915\u094d\u0937\u094d\u092e \u0914\u0930 \u092e\u094b\u0932\u0930 \u0926\u094b\u0928\u094b\u0902 \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0915\u093e \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947, \u0938\u0940\u0927\u0947 Boyle\u2013Mariotte, Charles \u0914\u0930 Gay-Lussac \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917\u093e\u0924\u094d\u092e\u0915 \u0928\u093f\u092f\u092e\u094b\u0902 \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0924\u0930\u094d\u0915 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/p>\n<p>\u0939\u092e \u0907\u0938\u0947 \u0924\u0940\u0928 \u092e\u093e\u0930\u094d\u0917\u094b\u0902 \u0938\u0947 \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ol>\n<li>\u090f\u0915 <b>\u0906\u092f\u0924\u0928<\/b> \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0938\u092e\u0924\u093e\u092a\u0940\u092f \u0914\u0930 \u0938\u092e\u0926\u092c \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u093e\u0926<\/li>\n<li>\u090f\u0915 <b>\u0926\u092c\u093e\u0935<\/b> \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0938\u092e\u0924\u093e\u092a\u0940\u092f \u0914\u0930 \u0938\u092e\u0906\u092f\u0924\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u093e\u0926<\/li>\n<li>\u090f\u0915 <b>\u0924\u093e\u092a\u092e\u093e\u0928<\/b> \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0938\u092e\u0926\u092c \u0914\u0930 \u0938\u092e\u0906\u092f\u0924\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u093e\u0926<\/li>\n<\/ol>\n<p>\u0907\u0928 \u0924\u0940\u0928\u094b\u0902 \u092e\u093e\u092e\u0932\u094b\u0902 \u0915\u0947 \u0935\u093f\u0915\u093e\u0938 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e\u0947\u0902 \u090f\u0915 \u092e\u0927\u094d\u092f\u0935\u0930\u094d\u0924\u0940 \u0905\u0935\u0938\u094d\u0925\u093e \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0917\u0940 \u091c\u093f\u0938\u0915\u0947 \u092e\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_i,V_i,T_i)<\/span><\/span> \u0939\u094b\u0902\u0964<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h2>\n<h3>\u0906\u092f\u0924\u0928 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h3>\n<p>\u092f\u0926\u093f \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0905\u0935\u0938\u094d\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\alpha,V_\\alpha,T_\\alpha)<\/span><\/span> \u092e\u0927\u094d\u092f\u0935\u0930\u094d\u0924\u0940 \u0905\u0935\u0938\u094d\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_i,V_i,T_i)<\/span><\/span> \u0938\u0947 \u090f\u0915 \u0938\u092e\u0924\u093e\u092a\u0940\u092f \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u091c\u0941\u0921\u093c\u0940 \u0939\u094b, \u0914\u0930 \u092b\u093f\u0930 \u092e\u0927\u094d\u092f\u0935\u0930\u094d\u0924\u0940 \u0905\u0935\u0938\u094d\u0925\u093e \u0905\u0902\u0924\u093f\u092e \u0905\u0935\u0938\u094d\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\omega,V_\\omega,T_\\omega)<\/span><\/span> \u0938\u0947 \u090f\u0915 \u0938\u092e\u0926\u092c \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u091c\u0941\u0921\u093c\u0940 \u0939\u094b, \u0924\u094b \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rclcl}\n\n &amp; P_\\alpha V_\\alpha= P_i V_i &amp; &amp; V_i\/T_i = V_\\omega\/T_\\omega   &amp; \\\\\n\n &amp;\\text{\u0938\u092e\u0924\u093e\u092a\u0940\u092f}&amp; &amp;\\text{\u0938\u092e\u0926\u092c} &amp; \\\\\n\nP_\\alpha &amp; \\longrightarrow &amp; P_i = \\dfrac{P_\\alpha V_\\alpha}{V_i}  &amp; \\longrightarrow &amp; P_\\omega = P_i \\\\ \\\\\n\nV_\\alpha &amp; \\longrightarrow &amp; V_i = \\dfrac{P_\\alpha V_\\alpha}{P_i} &amp; \\longrightarrow &amp; V_\\omega = \\dfrac{V_i T_\\omega}{T_i} \\\\ \\\\\n\nT_\\alpha &amp; \\longrightarrow &amp; T_i = T_\\alpha &amp; \\longrightarrow &amp; T_\\omega = \\dfrac{V_\\omega T_i}{V_i}\n\n\\end{array}\n\n<\/span>\n<p>\u0907\u0938\u0938\u0947 \u092f\u0939 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n&amp; V_\\omega = \\left(\\dfrac{T_\\omega}{T_i}\\right) V_i = \\left(\\dfrac{T_\\omega}{T_i}\\right) \\left(\\dfrac{P_\\alpha}{P_i} \\right) V_\\alpha = \\dfrac{T_\\omega P_\\alpha V_\\alpha}{T_\\alpha P_\\omega} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{P_\\alpha V_\\alpha}{T_\\alpha} = \\dfrac{P_\\omega V_\\omega}{T_\\omega}\n\n\\end{array}<\/span>\n<h3>\u0926\u092c\u093e\u0935 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h3>\n<p>\u092f\u0926\u093f \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0905\u0935\u0938\u094d\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\alpha,V_\\alpha,T_\\alpha)<\/span><\/span> \u092e\u0927\u094d\u092f\u0935\u0930\u094d\u0924\u0940 \u0905\u0935\u0938\u094d\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_i,V_i,T_i)<\/span><\/span> \u0938\u0947 \u090f\u0915 \u0938\u092e\u0924\u093e\u092a\u0940\u092f \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u091c\u0941\u0921\u093c\u0940 \u0939\u094b, \u0914\u0930 \u092b\u093f\u0930 \u092e\u0927\u094d\u092f\u0935\u0930\u094d\u0924\u0940 \u0905\u0935\u0938\u094d\u0925\u093e \u0905\u0902\u0924\u093f\u092e \u0905\u0935\u0938\u094d\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\omega,V_\\omega,T_\\omega)<\/span><\/span> \u0938\u0947 \u090f\u0915 \u0938\u092e\u0906\u092f\u0924\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u091c\u0941\u0921\u093c\u0940 \u0939\u094b, \u0924\u094b \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rclcl}\n\n &amp; P_\\alpha V_\\alpha= P_i V_i &amp; &amp; P_i\/T_i = P_\\omega\/T_\\omega   &amp; \\\\\n\n &amp;\\text{\u0938\u092e\u0924\u093e\u092a\u0940\u092f}&amp; &amp;\\text{\u0938\u092e\u0906\u092f\u0924\u0928} &amp; \\\\\n\nP_\\alpha &amp; \\longrightarrow &amp; P_i = \\dfrac{P_\\alpha V_\\alpha}{V_i}  &amp; \\longrightarrow &amp; P_\\omega = \\dfrac{P_i T_\\omega}{T_i} \\\\ \\\\\n\nV_\\alpha &amp; \\longrightarrow &amp; V_i = \\dfrac{P_\\alpha V_\\alpha}{P_i} &amp; \\longrightarrow &amp; V_\\omega = V_i \\\\ \\\\\n\nT_\\alpha &amp; \\longrightarrow &amp; T_i = T_\\alpha &amp; \\longrightarrow &amp; T_\\omega = \\dfrac{V_\\omega T_i}{V_i}\n\n\\end{array}\n\n<\/span>\n<p>\u0907\u0938\u0938\u0947 \u092f\u0939 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n &amp; P_\\omega = \\left(\\dfrac{T_\\omega}{T_i}\\right) P_i = \\left(\\dfrac{T_\\omega}{T_i}\\right) \\left(\\dfrac{V_\\alpha}{V_i}\\right)P_\\alpha = \\dfrac{T_\\omega V_\\alpha P_\\alpha}{T_\\alpha V_\\omega} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{P_\\alpha V_\\alpha}{T_\\alpha} = \\dfrac{P_\\omega V_\\omega}{T_\\omega}\n\n\\end{array}<\/span>\n<h3>\u0924\u093e\u092a\u092e\u093e\u0928 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h3>\n<p>\u092f\u0926\u093f \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0905\u0935\u0938\u094d\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\alpha,V_\\alpha,T_\\alpha)<\/span><\/span> \u092e\u0927\u094d\u092f\u0935\u0930\u094d\u0924\u0940 \u0905\u0935\u0938\u094d\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_i,V_i,T_i)<\/span><\/span> \u0938\u0947 \u090f\u0915 \u0938\u092e\u0926\u092c \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u091c\u0941\u0921\u093c\u0940 \u0939\u094b, \u0914\u0930 \u092b\u093f\u0930 \u092e\u0927\u094d\u092f\u0935\u0930\u094d\u0924\u0940 \u0905\u0935\u0938\u094d\u0925\u093e \u0905\u0902\u0924\u093f\u092e \u0905\u0935\u0938\u094d\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(P_\\omega,V_\\omega,T_\\omega)<\/span><\/span> \u0938\u0947 \u090f\u0915 \u0938\u092e\u0906\u092f\u0924\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u091c\u0941\u0921\u093c\u0940 \u0939\u094b, \u0924\u094b \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rclcl}\n\n &amp; V_\\alpha\/ T_\\alpha= V_i \/ T_i &amp; &amp; P_i\/T_i = P_\\omega\/T_\\omega   &amp; \\\\\n\n &amp;\\text{\u0938\u092e\u0926\u092c}&amp; &amp;\\text{\u0938\u092e\u0906\u092f\u0924\u0928} &amp; \\\\\n\nP_\\alpha &amp; \\longrightarrow &amp; P_i = P_\\alpha  &amp; \\longrightarrow &amp; P_\\omega = \\dfrac{P_i T_\\omega}{T_i} \\\\ \\\\\n\nV_\\alpha &amp; \\longrightarrow &amp; V_i = \\dfrac{V_\\alpha T_i}{T_\\alpha} &amp; \\longrightarrow &amp; V_\\omega = V_i \\\\ \\\\\n\nT_\\alpha &amp; \\longrightarrow &amp; T_i = \\dfrac{V_i T_\\alpha}{V_\\alpha} &amp; \\longrightarrow &amp; T_\\omega = \\dfrac{P_\\omega T_i}{P_i}\n\n\\end{array}\n\n<\/span>\n<p>\u0907\u0938\u0938\u0947 \u092f\u0939 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n &amp; T_\\omega = \\left(\\dfrac{P_\\omega}{P_i}\\right) T_i = \\left(\\dfrac{P_\\omega}{P_i}\\right) \\left(\\dfrac{V_i}{V_\\alpha}\\right)T_\\alpha = \\dfrac{P_\\omega V_\\omega T_\\alpha}{P_\\alpha V_\\alpha}  \\\\ \\\\\n\n\\equiv &amp; \\dfrac{P_\\alpha V_\\alpha}{T_\\alpha} = \\dfrac{P_\\omega V_\\omega}{T_\\omega}\n\n\\end{array}<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u091f\u093f\u092a\u094d\u092a\u0923\u093f\u092f\u093e\u0901 \u0914\u0930 \u0938\u0942\u0915\u094d\u0937\u094d\u092e \u092a\u0943\u0937\u094d\u0920\u092d\u0942\u092e\u093f<\/h2>\n<p>\u092f\u0926\u094d\u092f\u092a\u093f \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u0938\u0942\u0924\u094d\u0930\u0940\u0915\u0930\u0923 \u0905\u0928\u0941\u092d\u0935\u091c\u0928\u094d\u092f \u0939\u0948, \u0907\u0938\u0947 \u0917\u0948\u0938\u094b\u0902 \u0915\u0947 \u0917\u0924\u093f\u091c \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092a\u094d\u0930\u0925\u092e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924\u094b\u0902 \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u092e\u0949\u0921\u0932 \u092e\u0947\u0902, \u0917\u0948\u0938 \u0915\u0923\u094b\u0902 \u0915\u093e \u090f\u0915 \u0938\u092e\u0942\u0939 \u0939\u0948 \u091c\u094b \u0917\u0924\u093f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0924\u0925\u093e \u092a\u093e\u0924\u094d\u0930 \u0915\u0940 \u0926\u0940\u0935\u093e\u0930\u094b\u0902 \u0938\u0947 \u091f\u0915\u0930\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u093e\u0928\u094d\u092f\u0924\u093e\u0913\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0906\u0926\u0930\u094d\u0936\u0940\u0915\u0943\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<ol>\n<li>\u0915\u0923\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0906\u0915\u0930\u094d\u0937\u0923 \u092f\u093e \u0935\u093f\u0915\u0930\u094d\u0937\u0923 \u092c\u0932 \u0915\u0940 \u0905\u0928\u0941\u092a\u0938\u094d\u0925\u093f\u0924\u093f\u0964<\/li>\n<li>\u0917\u094b\u0932\u093e\u0915\u093e\u0930 \u0906\u0915\u093e\u0930 \u0915\u0947 \u092c\u093f\u0902\u0926\u0941-\u091c\u0948\u0938\u0947 \u092f\u093e \u0928\u0917\u0923\u094d\u092f \u0906\u0915\u093e\u0930 \u0915\u0947 \u0915\u0923\u0964<\/li>\n<li>\u0915\u0923\u094b\u0902 \u0914\u0930 \u0926\u0940\u0935\u093e\u0930\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u092a\u0942\u0930\u094d\u0923\u0924\u0903 \u092a\u094d\u0930\u0924\u094d\u092f\u093e\u0938\u094d\u0925 \u091f\u0915\u094d\u0915\u0930\u0947\u0902\u0964<\/li>\n<\/ol>\n<p>\u092f\u0947 \u0906\u0926\u0930\u094d\u0936\u0940\u0915\u0930\u0923 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u094b \u0938\u0930\u0932 \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u092f\u0926\u094d\u092f\u092a\u093f \u0915\u094b\u0908 \u092d\u0940 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0917\u0948\u0938 \u0907\u0928\u094d\u0939\u0947\u0902 \u092a\u0942\u0930\u094d\u0923\u0924\u0903 \u0928\u0939\u0940\u0902 \u092e\u093e\u0928\u0924\u0940, \u092b\u093f\u0930 \u092d\u0940 \u092f\u0947 \u0915\u0908 \u0917\u0948\u0938\u094b\u0902 \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0926\u093e\u092f\u0930\u0947 \u092e\u0947\u0902 \u0905\u091a\u094d\u091b\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 \u0914\u0930 <strong>\u0936\u093e\u0938\u094d\u0924\u094d\u0930\u0940\u092f \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940<\/strong> \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0906\u0927\u093e\u0930 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902, \u091c\u093f\u0938\u0915\u0947 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0924\u093e\u092a \u0907\u0902\u091c\u0928 \u0938\u0947 \u0932\u0947\u0915\u0930 \u0935\u093e\u092f\u0941\u092e\u0902\u0921\u0932\u0940\u092f \u092d\u094c\u0924\u093f\u0915\u0940 \u0914\u0930 \u0916\u0917\u094b\u0932 \u092d\u094c\u0924\u093f\u0915\u0940 \u0924\u0915 \u092b\u0948\u0932\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0935\u0948\u0927\u0924\u093e \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0914\u0930 \u0938\u0940\u092e\u093e\u090f\u0901<\/h2>\n<p>\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0915\u093e \u0928\u093f\u092f\u092e \u0938\u093e\u0930\u094d\u0935\u092d\u094c\u092e\u093f\u0915 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u092f\u0939 \u0924\u092c \u0935\u093f\u091a\u0932\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e\u090f\u0901 \u092f\u0925\u093e\u0930\u094d\u0925 \u0928\u0939\u0940\u0902 \u0930\u0939\u0924\u0940\u0902 \u092f\u093e \u091c\u092c \u0936\u093e\u0938\u094d\u0924\u094d\u0930\u0940\u092f \u092d\u094c\u0924\u093f\u0915\u0940 \u0938\u0947 \u092a\u0930\u0947 \u092a\u094d\u0930\u092d\u093e\u0935 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<ul>\n<li><strong>\u0909\u091a\u094d\u091a \u0926\u092c\u093e\u0935 \u0914\u0930 \u0928\u093f\u092e\u094d\u0928 \u0924\u093e\u092a\u092e\u093e\u0928:<\/strong> \u0905\u0923\u0941\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u0905\u0902\u0924\u0903\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901 \u0905\u092c \u0928\u0917\u0923\u094d\u092f \u0928\u0939\u0940\u0902 \u0930\u0939\u0924\u0940\u0902 \u0914\u0930 \u0915\u0923\u094b\u0902 \u0915\u093e \u0938\u0940\u092e\u093f\u0924 \u0906\u0915\u093e\u0930 \u092e\u0939\u0924\u094d\u0935 \u0930\u0916\u0924\u093e \u0939\u0948\u0964 \u090f\u0915 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0941\u0927\u093e\u0930 van der Waals \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u0948:\n<div style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(P + a\\left(\\dfrac{n}{V}\\right)^2\\right)\\,(V - nb)=nRT<\/span><\/div>\n<p>    \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0917\u0948\u0938 \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0939\u0948\u0902\u0964\n  <\/li>\n<li><strong>\u0915\u094d\u0935\u093e\u0902\u091f\u092e \u0915\u094d\u0937\u0947\u0924\u094d\u0930:<\/strong> \u092c\u0939\u0941\u0924 \u0928\u093f\u092e\u094d\u0928 \u0924\u093e\u092a\u092e\u093e\u0928 \u092f\u093e \u0909\u091a\u094d\u091a \u0918\u0928\u0924\u094d\u0935\u094b\u0902 \u092a\u0930 Bose\u2013Einstein \u092f\u093e Fermi\u2013Dirac \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u092a\u094d\u0930\u0915\u091f \u0939\u094b\u0924\u0940 \u0939\u0948\u0902, \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f <em>\u0915\u094d\u0935\u093e\u0902\u091f\u092e \u0917\u0948\u0938\u094b\u0902<\/em> \u0915\u0947 \u092e\u0949\u0921\u0932 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n<li><strong>\u0938\u093e\u092a\u0947\u0915\u094d\u0937\u0935\u093e\u0926\u0940 \u0915\u094d\u0937\u0947\u0924\u094d\u0930:<\/strong> \u092f\u0926\u093f \u0915\u0923\u094b\u0902 \u0915\u0940 \u0917\u0924\u093f \u092a\u094d\u0930\u0915\u093e\u0936 \u0915\u0940 \u0917\u0924\u093f \u0915\u0947 \u0928\u093f\u0915\u091f \u0939\u094b, \u0924\u094b \u0938\u093e\u092a\u0947\u0915\u094d\u0937\u0935\u093e\u0926\u0940 \u0938\u0941\u0927\u093e\u0930 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n<\/ul>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u091f\u093f\u092a\u094d\u092a\u0923\u093f\u092f\u093e\u0901<\/h2>\n<ul>\n<li>\u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u092e\u0947\u0902 \u0939\u092e\u0947\u0936\u093e \u0924\u093e\u092a\u092e\u093e\u0928 \u0915\u094b <strong>\u0915\u0947\u0932\u094d\u0935\u093f\u0928<\/strong> \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T(\\mathrm{K}) = T(^{\\circ}\\mathrm{C}) + 273{,}15<\/span><\/span>\u0964<\/li>\n<li>\u0907\u0915\u093e\u0907\u092f\u094b\u0902 \u0915\u0940 \u0938\u0902\u0917\u0924\u093f \u0915\u093e \u0927\u094d\u092f\u093e\u0928 \u0930\u0916\u0947\u0902: \u092f\u0926\u093f \u0906\u092a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{atm}<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{L}<\/span><\/span> \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u0930\u094d\u092f \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">R=0{,}082\\,057\\ \\mathrm{L\\,atm\\,mol^{-1}\\,K^{-1}}<\/span><\/span> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902; \u092f\u0926\u093f \u0906\u092a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{Pa}<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m^3}<\/span><\/span> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">R=8{,}314\\,462\\,6\\ \\mathrm{J\\,mol^{-1}\\,K^{-1}}<\/span><\/span> \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0964<\/li>\n<li>\u092f\u093e\u0926 \u0930\u0916\u0947\u0902 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0928\u0941\u092d\u0935\u091c\u0928\u094d\u092f \u0928\u093f\u092f\u092e \u090f\u0915 \u091a\u0930 \u0915\u094b \u0938\u094d\u0925\u093f\u0930 \u0930\u0916\u0924\u0947 \u0939\u0941\u090f \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0925\u093e\u0964 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u094b \u0938\u0902\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u094b\u0928\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091a\u0930\u0923 \u092e\u0947\u0902 \u0915\u094c\u0928 \u0938\u0940 \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0940 \u091c\u093e \u0930\u0939\u0940 \u0939\u0948\u0964<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0915\u093e \u0905\u0928\u0941\u092d\u0935\u091c\u0928\u094d\u092f \u0938\u0942\u0924\u094d\u0930\u0940\u0915\u0930\u0923 \u0915\u094d\u092f\u093e \u0906\u092a\u0928\u0947 \u0915\u092d\u0940 \u0938\u094b\u091a\u093e \u0939\u0948 \u0915\u093f \u091c\u092c \u090f\u0915 \u0917\u0941\u092c\u094d\u092c\u093e\u0930\u0947 \u0915\u094b \u0917\u0930\u094d\u092e \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u0935\u0939 \u0915\u094d\u092f\u094b\u0902 \u092b\u0948\u0932\u0924\u093e \u0939\u0948 \u092f\u093e \u091c\u092c \u090a\u0901\u091a\u093e\u0908 \u092c\u0926\u0932\u0924\u0940 \u0939\u0948 \u0924\u094b \u091f\u093e\u092f\u0930 \u0915\u093e \u0926\u092c\u093e\u0935 \u0915\u094d\u092f\u094b\u0902 \u092c\u0926\u0932\u0924\u093e \u0939\u0948? \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u0909\u0928 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947 \u091c\u094b \u0907\u0928 \u0935\u094d\u092f\u0935\u0939\u093e\u0930\u094b\u0902 \u0915\u094b \u0928\u093f\u092f\u0902\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092f\u0939 \u0915\u0948\u0938\u0947 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":35104,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":4,"footnotes":""},"categories":[927,643],"tags":[],"class_list":["post-30071","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 v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\ud83c\udf21\ufe0f \u0916\u094b\u091c\u093f\u090f \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0930\u094b\u091a\u0915 \u0926\u0941\u0928\u093f\u092f\u093e: \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0914\u0930 \u0907\u0938\u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0902 \ud83d\ude80\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/hi\/\u0906\u0926\u0930\u094d\u0936-\u0917\u0948\u0938-\u0938\u092e\u0940\u0915\u0930\u0923\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923\" \/>\n<meta property=\"og:description\" content=\"\ud83c\udf21\ufe0f \u0916\u094b\u091c\u093f\u090f \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0930\u094b\u091a\u0915 \u0926\u0941\u0928\u093f\u092f\u093e: \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0914\u0930 \u0907\u0938\u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0902 \ud83d\ude80\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/hi\/\u0906\u0926\u0930\u094d\u0936-\u0917\u0948\u0938-\u0938\u092e\u0940\u0915\u0930\u0923\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-03-10T13:00:10+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-10-20T07:31:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/min3-5.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1536\" \/>\n\t<meta property=\"og:image:height\" content=\"1024\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923\" \/>\n<meta name=\"twitter:description\" content=\"\ud83c\udf21\ufe0f \u0916\u094b\u091c\u093f\u090f \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0930\u094b\u091a\u0915 \u0926\u0941\u0928\u093f\u092f\u093e: \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0914\u0930 \u0907\u0938\u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0902 \ud83d\ude80\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/min3-5.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923\",\"datePublished\":\"2021-03-10T13:00:10+00:00\",\"dateModified\":\"2025-10-20T07:31:27+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/\"},\"wordCount\":904,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/min3-5.jpg\",\"articleSection\":[\"\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940\",\"\u092d\u094c\u0924\u093f\u0915\u0940\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/\",\"name\":\"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/min3-5.jpg\",\"datePublished\":\"2021-03-10T13:00:10+00:00\",\"dateModified\":\"2025-10-20T07:31:27+00:00\",\"description\":\"\ud83c\udf21\ufe0f \u0916\u094b\u091c\u093f\u090f \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0930\u094b\u091a\u0915 \u0926\u0941\u0928\u093f\u092f\u093e: \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0914\u0930 \u0907\u0938\u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0902 \ud83d\ude80\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/#primaryimage\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/min3-5.jpg\",\"contentUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/min3-5.jpg\",\"width\":1536,\"height\":1024},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/hi\\\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\\\/material\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/groups\\\/toposuranos\",\"https:\\\/\\\/x.com\\\/topuranos\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\\\/\\\/www.linkedin.com\\\/company\\\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\\\/\\\/toposuranos.com\\\/material\"],\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 - toposuranos.com\/material","description":"\ud83c\udf21\ufe0f \u0916\u094b\u091c\u093f\u090f \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0930\u094b\u091a\u0915 \u0926\u0941\u0928\u093f\u092f\u093e: \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0914\u0930 \u0907\u0938\u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0902 \ud83d\ude80","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/toposuranos.com\/material\/hi\/\u0906\u0926\u0930\u094d\u0936-\u0917\u0948\u0938-\u0938\u092e\u0940\u0915\u0930\u0923\/","og_locale":"es_ES","og_type":"article","og_title":"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923","og_description":"\ud83c\udf21\ufe0f \u0916\u094b\u091c\u093f\u090f \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0930\u094b\u091a\u0915 \u0926\u0941\u0928\u093f\u092f\u093e: \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0914\u0930 \u0907\u0938\u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0902 \ud83d\ude80","og_url":"https:\/\/toposuranos.com\/material\/hi\/\u0906\u0926\u0930\u094d\u0936-\u0917\u0948\u0938-\u0938\u092e\u0940\u0915\u0930\u0923\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-03-10T13:00:10+00:00","article_modified_time":"2025-10-20T07:31:27+00:00","og_image":[{"width":1536,"height":1024,"url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/min3-5.jpg","type":"image\/jpeg"}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923","twitter_description":"\ud83c\udf21\ufe0f \u0916\u094b\u091c\u093f\u090f \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0930\u094b\u091a\u0915 \u0926\u0941\u0928\u093f\u092f\u093e: \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0914\u0930 \u0907\u0938\u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0902 \ud83d\ude80","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/min3-5.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"4 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923","datePublished":"2021-03-10T13:00:10+00:00","dateModified":"2025-10-20T07:31:27+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/"},"wordCount":904,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/min3-5.jpg","articleSection":["\u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940","\u092d\u094c\u0924\u093f\u0915\u0940"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/","url":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/","name":"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/min3-5.jpg","datePublished":"2021-03-10T13:00:10+00:00","dateModified":"2025-10-20T07:31:27+00:00","description":"\ud83c\udf21\ufe0f \u0916\u094b\u091c\u093f\u090f \u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0930\u094b\u091a\u0915 \u0926\u0941\u0928\u093f\u092f\u093e: \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924, \u090a\u0937\u094d\u092e\u093e\u0917\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0914\u0930 \u0907\u0938\u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0902 \ud83d\ude80","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/min3-5.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/min3-5.jpg","width":1536,"height":1024},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%86%e0%a4%a6%e0%a4%b0%e0%a5%8d%e0%a4%b6-%e0%a4%97%e0%a5%88%e0%a4%b8-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0906\u0926\u0930\u094d\u0936 \u0917\u0948\u0938 \u0938\u092e\u0940\u0915\u0930\u0923"}]},{"@type":"WebSite","@id":"https:\/\/toposuranos.com\/material\/#website","url":"https:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"https:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"https:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"https:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/30071","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=30071"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/30071\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/35104"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=30071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=30071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=30071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}