{"id":30832,"date":"2021-06-18T13:00:58","date_gmt":"2021-06-18T13:00:58","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30832"},"modified":"2025-01-02T03:18:37","modified_gmt":"2025-01-02T03:18:37","slug":"%e7%8a%b6%e6%80%81%e6%96%b9%e7%a8%8b%e4%b8%8e%e7%8a%b6%e6%80%81%e5%87%bd%e6%95%b0","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e7%8a%b6%e6%80%81%e6%96%b9%e7%a8%8b%e4%b8%8e%e7%8a%b6%e6%80%81%e5%87%bd%e6%95%b0\/","title":{"rendered":"\u72b6\u6001\u65b9\u7a0b\u4e0e\u72b6\u6001\u51fd\u6570"},"content":{"rendered":"<style>\n    p, ul, ol {\n        text-align: justify;\n    }\n    h1, h2 {\n        text-align: center;\n    }\n<\/style>\n<h1>\u72b6\u6001\u65b9\u7a0b\u4e0e\u72b6\u6001\u51fd\u6570<\/h1>\n<p style=\"text-align:center;\"><em>\u70ed\u529b\u5b66\u63ed\u793a\u4e86\u5982\u4f55\u901a\u8fc7\u72b6\u6001\u51fd\u6570\u548c\u72b6\u6001\u65b9\u7a0b\u7b49\u6982\u5ff5\u6765\u63cf\u8ff0\u548c\u8fde\u63a5\u7cfb\u7edf\u7684\u72b6\u6001\u3002\u538b\u529b\u3001\u6e29\u5ea6\u548c\u7406\u60f3\u6c14\u4f53\u65b9\u7a0b\u662f\u5982\u4f55\u76f8\u5173\u7684\uff1f\u672c\u5185\u5bb9\u5c06\u5f15\u5bfc\u60a8\u7406\u89e3\u652f\u914d\u5b87\u5b99\u5e73\u8861\u7684\u6570\u5b66\u548c\u7269\u7406\u89c4\u5219\uff0c\u6311\u6218\u60a8\u7684\u76f4\u89c9\uff0c\u62d3\u5bbd\u60a8\u7684\u89c6\u91ce\u3002<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5728\u672c\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f<\/p>\n<ol>\n<li><strong>\u63cf\u8ff0<\/strong>\u72b6\u6001\u51fd\u6570\u7684\u6982\u5ff5\u53ca\u5176\u4e0e\u70ed\u5e73\u8861\u5728\u70ed\u529b\u5b66\u7cfb\u7edf\u4e2d\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u533a\u5206<\/strong>\u72b6\u6001\u51fd\u6570\u548c\u975e\u72b6\u6001\u51fd\u6570\u7684\u91cf\uff0c\u5e76\u8bc6\u522b\u8fd9\u4e24\u7c7b\u7684\u5177\u4f53\u4f8b\u5b50\u3002<\/li>\n<li><strong>\u5206\u6790<\/strong>\u5982\u7406\u60f3\u6c14\u4f53\u65b9\u7a0b\u7b49\u72b6\u6001\u65b9\u7a0b\u5982\u4f55\u5728\u5e73\u8861\u7cfb\u7edf\u4e2d\u8fde\u63a5\u72b6\u6001\u51fd\u6570\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u5185\u5bb9\u76ee\u5f55<\/u>\uff1a<\/strong><br \/>\n<a href=\"#1\">\u72b6\u6001\u51fd\u6570\u3001\u7cfb\u7edf\u4e0e\u70ed\u5e73\u8861<\/a><br \/>\n<a href=\"#2\">\u72b6\u6001\u65b9\u7a0b\u548c\u72b6\u6001\u53d8\u91cf<\/a><br \/>\n<a href=\"#3\">\u72b6\u6001\u51fd\u6570\u7684\u6570\u5b66\u6982\u5ff5<\/a><br \/>\n<a href=\"#4\">\u7406\u60f3\u6c14\u4f53\u65b9\u7a0b\u662f\u72b6\u6001\u65b9\u7a0b<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ZXX3KAS5WKs\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>\u7ecf\u5178\u70ed\u529b\u5b66\u7684\u4e00\u4e2a\u6838\u5fc3\u6982\u5ff5\u662f\u72b6\u6001\u65b9\u7a0b\u4e0e\u72b6\u6001\u51fd\u6570\u3002\u901a\u8fc7\u8fd9\u4e9b\u6982\u5ff5\uff0c\u6211\u4eec\u80fd\u591f\u63cf\u8ff0\u5904\u4e8e\u70ed\u529b\u5b66\u5e73\u8861\u72b6\u6001\u7684\u7cfb\u7edf\u3002<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u72b6\u6001\u51fd\u6570\u3001\u7cfb\u7edf\u4e0e\u70ed\u5e73\u8861<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=ZXX3KAS5WKs&amp;t=115s\" target=\"_blank\" rel=\"noopener\"><strong>\u5728\u70ed\u529b\u5b66\u4e2d\uff0c\u7cfb\u7edf\u88ab\u5b9a\u4e49\u4e3a<\/strong><\/a>\u88ab\u9009\u62e9\u7528\u6765\u7814\u7a76\u7684\u5b87\u5b99\u7684\u4e00\u90e8\u5206\uff0c\u5176\u5468\u56f4\u662f\u73af\u5883\u3002\u6211\u4eec\u77e5\u9053\uff0c\u5982\u679c\u7cfb\u7edf\u7684\u5b8f\u89c2\u53ef\u89c2\u6d4b\u91cf\uff08\u4f8b\u5982\uff1a\u538b\u529b\u3001\u6e29\u5ea6\uff09\u5728\u65f6\u95f4\u4e0a\u4fdd\u6301\u4e0d\u53d8\uff0c\u90a3\u4e48\u7cfb\u7edf\u4e0e\u73af\u5883\u5904\u4e8e\u70ed\u5e73\u8861\u72b6\u6001\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u5c06\u6c14\u4f53\u7f6e\u4e8e\u5bb9\u5668\u5185\uff0c\u5176\u6e29\u5ea6\u5728\u65f6\u95f4\u4e0a\u4fdd\u6301\u7a33\u5b9a\uff0c\u5219\u6211\u4eec\u8bf4\u6c14\u4f53\u5904\u4e8e\u70ed\u529b\u5b66\u5e73\u8861\u72b6\u6001\uff0c\u800c\u8fd9\u4e9b\u5b8f\u89c2\u53ef\u89c2\u6d4b\u91cf<strong>\u51b3\u5b9a\u4e86\u5176\u72b6\u6001\u3002<\/strong>\u76f8\u53cd\uff0c\u5982\u679c\u5bb9\u5668\u7684\u67d0\u4e00\u4fa7\u7a81\u7136\u65bd\u52a0\u5927\u91cf\u70ed\u91cf\uff0c\u90a3\u4e48\u81f3\u5c11\u5728\u4e00\u6bb5\u65f6\u95f4\u5185\uff0c\u6c14\u4f53\u5c06\u5904\u4e8e\u4e0d\u540c\u4e8e\u70ed\u5e73\u8861\u7684\u72b6\u6001\uff0c\u5176\u72b6\u6001\u5c06\u968f\u65f6\u95f4\u53d8\u5316\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u72b6\u6001\u65b9\u7a0b\u548c\u72b6\u6001\u53d8\u91cf<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=ZXX3KAS5WKs&amp;t=115s\" target=\"_blank\" rel=\"noopener\"><strong>\u5f53\u4e00\u4e2a\u7cfb\u7edf\u5904\u4e8e\u70ed\u5e73\u8861\u72b6\u6001\u65f6<\/strong><\/a>\uff0c\u6211\u4eec\u53ef\u4ee5\u8bc6\u522b\u51fa\u4e24\u79cd\u7c7b\u578b\u7684\u91cf\uff1a\u4e00\u79cd\u53d6\u51b3\u4e8e\u7cfb\u7edf\u8fbe\u5230\u5e73\u8861\u7684\u65b9\u5f0f\uff0c\u53e6\u4e00\u79cd\u4e0e\u8be5\u8fc7\u7a0b\u65e0\u5173\u3002\u540e\u4e00\u7c7b\u91cf\u88ab\u79f0\u4e3a<strong>\u72b6\u6001\u51fd\u6570<\/strong>\uff08\u6709\u65f6\u4e5f\u79f0\u4e3a<strong>\u72b6\u6001\u53d8\u91cf<\/strong>\uff09\u3002\u72b6\u6001\u51fd\u6570\u662f\u5bf9\u6bcf\u4e2a\u5e73\u8861\u72b6\u6001\u90fd\u5177\u6709\u786e\u5b9a\u503c\u7684\u7269\u7406\u91cf\u3002\u56e0\u6b64\uff0c\u5728\u70ed\u5e73\u8861\u4e2d\uff0c\u8fd9\u4e9b\u53d8\u91cf\u4e0d\u968f\u65f6\u95f4\u53d8\u5316\u3002\u4e00\u4e9b\u793a\u4f8b\u5305\u62ec\uff1a<\/p>\n<ul>\n<li>\u538b\u529b<\/li>\n<li>\u6e29\u5ea6<\/li>\n<li>\u4f53\u79ef<\/li>\n<li>\u5185\u80fd<\/li>\n<\/ul>\n<p>\u4e00\u4e9b\u4e0d\u662f\u72b6\u6001\u51fd\u6570\u7684\u91cf\u7684\u793a\u4f8b\u5305\u62ec\u7cfb\u7edf\u4e2d\u67d0\u7279\u5b9a\u7c92\u5b50\u7684\u4f4d\u7f6e\u3001\u65bd\u52a0\u5728\u7cfb\u7edf\u4e0a\u7684\u603b\u529f\u548c\u603b\u70ed\u91cf\u3002\u76f4\u89c2\u5730\u770b\uff0c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u89c2\u5bdf\u5230\u60a8\u7684\u53cc\u624b\u53ef\u4ee5\u901a\u8fc7\u4e24\u79cd\u4e0d\u540c\u7684\u8fc7\u7a0b\u8fbe\u5230\u76f8\u540c\u7684\u6e29\u5ea6\uff08\u56e0\u6b64\u662f\u76f8\u540c\u7684\u72b6\u6001\uff09\u6765\u7406\u89e3\uff1a\u4e00\u79cd\u662f\u901a\u8fc7\u65bd\u52a0\u4e00\u5b9a\u91cf\u7684\u529f\uff0c\u5c06\u5b83\u4eec\u76f8\u4e92\u6469\u64e6\uff1b\u53e6\u4e00\u79cd\u662f\u901a\u8fc7\u65bd\u52a0\u70ed\u91cf\uff0c\u5c06\u624b\u653e\u5165\u6e29\u6c34\u4e2d\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u72b6\u6001\u51fd\u6570\u7684\u6570\u5b66\u6982\u5ff5<\/h2>\n<p>\u5728\u7406\u89e3\u8fd9\u4e9b\u76f4\u89c2\u60f3\u6cd5\u7684\u57fa\u7840\u4e0a\uff0c\u4e3a\u4e86\u83b7\u5f97\u66f4\u5168\u9762\u7684\u8ba4\u8bc6\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u4e00\u4e2a\u66f4\u52a0\u6570\u5b66\u5316\u7684\u53d1\u5c55\uff0c\u4ee5\u4e86\u89e3\u72b6\u6001\u51fd\u6570\u80cc\u540e\u7684\u610f\u4e49\u3002\u5047\u8bbe\u4e00\u4e2a\u7cfb\u7edf\u53ef\u4ee5\u901a\u8fc7\u53c2\u6570\u5411\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}=(x_1, x_2, x_3, \\cdots)<\/span> \u63cf\u8ff0\uff0c\u5e76\u4e14\u4ee4 <span class=\"katex-eq\" data-katex-display=\"false\">f(\\vec{x})<\/span> \u4e3a\u67d0\u4e2a\u72b6\u6001\u51fd\u6570\u3002\u5982\u679c\u7cfb\u7edf\u53c2\u6570\u4ece\u521d\u59cb\u503c <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}_i<\/span> \u53d8\u5316\u5230\u6700\u7ec8\u503c <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}_f<\/span>\uff0c\u5219\u72b6\u6001\u51fd\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u7684\u53d8\u5316\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta f = \\displaystyle \\int_{\\vec{x}_i}^{\\vec{x}_f}df = f(\\vec{x}_f) - f(\\vec{x}_i)<\/span>\n<p>\u5982\u679c\u60c5\u51b5\u786e\u5b9e\u5982\u6b64\uff0c\u5219\u72b6\u6001\u51fd\u6570\u7684\u53d8\u5316\u4ec5\u53d6\u51b3\u4e8e <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}<\/span> \u7684\u521d\u59cb\u503c\u548c\u6700\u7ec8\u503c\u3002\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\u5728\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">df<\/span> \u662f\u4e00\u4e2a<strong>\u5b8c\u5168\u5fae\u5206<\/strong>\u65f6\u3002\u6240\u6709\u72b6\u6001\u51fd\u6570\u90fd\u5177\u6709\u5b8c\u5168\u5fae\u5206\uff1b\u53cd\u4e4b\uff0c\u5176\u5fae\u5206\u4e0d\u662f\u5b8c\u5168\u5fae\u5206\u7684\u91cf\u4e0d\u80fd\u662f\u72b6\u6001\u51fd\u6570\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u7406\u60f3\u6c14\u4f53\u65b9\u7a0b\u662f\u72b6\u6001\u65b9\u7a0b<\/h2>\n<p>\u901a\u5e38\uff0c\u81f3\u5c11\u53ef\u4ee5\u8fd1\u4f3c\u627e\u5230\u4e00\u79cd\u72b6\u6001\u65b9\u7a0b\u6765\u8fde\u63a5\u72b6\u6001\u51fd\u6570\u3002\u4f8b\u5982\uff0c<a href=\"https:\/\/toposuranos.com\/la-ecuacion-de-los-gases-ideales\/\" rel=\"noopener\" target=\"_blank\">\u7406\u60f3\u6c14\u4f53\u7684\u72b6\u6001\u65b9\u7a0b<\/a> <span class=\"katex-eq\" data-katex-display=\"false\">f(P,V,T)=0<\/span> \u5177\u6709\u4ee5\u4e0b\u5f62\u5f0f\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(P,V,T) = PV - nRT = 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