{"id":2929,"date":"2022-03-24T16:29:59","date_gmt":"2022-03-24T16:29:59","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=2929"},"modified":"2023-06-26T16:36:46","modified_gmt":"2023-06-26T10:36:46","slug":"kinetic-theory-of-gas-and-ideal-gas-law","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/kinetic-theory-of-gas-and-ideal-gas-law\/","title":{"rendered":"\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0993 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 (Kinetic Theory of Gas and Ideal Gas Laws)"},"content":{"rendered":"

\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0993 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 <\/b>(Kinetic Theory of Gas and Ideal Gas Laws)<\/b><\/h2>\n

\u09e7. \u09ac\u09df\u09c7\u09b2\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 <\/b>(Boyle\u2019s Law) <\/b>:<\/b><\/h3>\n

\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(10.16)<\/span> \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf <\/span>p V=\\frac{1}{3} M \\overline{c^{2}}<\/span><\/b><\/span><\/p>\n

\u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a5\u09be\u0995\u09b2\u09c7 \\overline{c^{2}}<\/span><\/span>\u00a0\u09a7\u09cd\u09b0\u09c1\u09ac \u098f\u09ac\u0982 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ad\u09b0 <\/span>M<\/span> \u09a7\u09cd\u09b0\u09c1\u09ac \u09b9\u0993\u09df\u09be\u09df \\frac{1}{3} M \\overline{c^{2}}<\/span><\/span> \u09a7\u09cd\u09b0\u09c1\u09ac\u0964<\/span><\/p>\n\\therefore p V=\\frac{1}{3} M \\overline{c^{2}}<\/span>\n\\text { \u09ac\u09be, } V \\propto \\frac{1}{p}<\/span>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09df \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ad\u09b0\u09c7\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09df\u09a4\u09a8 \u098f\u09b0 \u099a\u09be\u09aa\u09c7\u09b0 \u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u098f\u099f\u09be\u0987 \u09ac\u09df\u09c7\u09b2\u09c7\u09b0<\/strong> \u09b8\u09c2\u09a4\u09cd\u09b0\u0964<\/span><\/p>\n

\u09e8. \u099a\u09be\u09b0\u09cd\u09b2\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 <\/b>(Charles\u2019 Law) <\/b>:<\/b><\/h3>\n

\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (<\/span>10.21)<\/span> \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u0995\u09c7\u09b2\u09ad\u09bf\u09a8 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995,<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>E \\propto T<\/span><\/strong><\/p>\n

\u09ac\u09be, \\frac{1}{2} M \\overline{c^{2}} \\propto T<\/span><\/span><\/p>\n

\u09ac\u09be, \\frac{1}{2} M \\overline{c^{2}}=K T \\quad<\/span><\/span>\u00a0[\u098f\u0996\u09be\u09a8\u09c7 <\/span>K<\/span> \u098f\u0995\u099f\u09bf \u09a7\u09cd\u09b0\u09c1\u09ac\u0995]<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (<\/span>10.16)<\/span> \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n\\begin{array}{l}\n\np V=\\frac{1}{3} M \\overline{c^{2}}=\\frac{2}{3} \\times \\frac{1}{2} M \\overline{c^{2}}=\\frac{2}{3} K T \\\\\n\nV=\\frac{2 K}{3 p} \\times T\n\n\\end{array}<\/span>\n

\u099a\u09be\u09aa \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a5\u09be\u0995\u09b2\u09c7 \\frac{2 K}{3 p}<\/span><\/span>\u00a0\u09a7\u09cd\u09b0\u09c1\u09ac \u09a5\u09be\u0995\u09c7\u0964<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09cd\u09a5\u09bf\u09b0 \u099a\u09be\u09aa\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ad\u09b0\u09c7\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09df\u09a4\u09a8 \u098f\u09b0 \u0995\u09c7\u09b2\u09ad\u09bf\u09a8 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u098f\u099f\u09be\u0987 \u099a\u09be\u09b0\u09cd\u09b2\u09b8\u09c7\u09b0<\/strong> \u09b8\u09c2\u09a4\u09cd\u09b0\u0964<\/span><\/p>\n

\u09e9. \u099a\u09be\u09aa\u09c0\u09df \u09b8\u09c2\u09a4\u09cd\u09b0 <\/b>(Pressure Law) <\/b>:<\/b><\/h3>\n

\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(10.21)<\/span> \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u0995\u09c7\u09b2\u09ad\u09bf\u09a8 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995<\/strong>\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ceE \\propto T<\/span><\/span><\/p>\n

\u09ac\u09be, \\frac{1}{2} M \\overline{c^{2}} \\propto T<\/span><\/span><\/p>\n

\u09ac\u09be, \\frac{1}{2} M \\overline{c^{2}}=K T \\quad<\/span><\/span>\u00a0 [\u098f\u0996\u09be\u09a8\u09c7 <\/span>K<\/span> \u098f\u0995\u099f\u09bf \u09a7\u09cd\u09b0\u09c1\u09ac\u0995]<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (<\/span>10.16)<\/span> \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n\\begin{array}{l}\n\np V=\\frac{1}{3} M \\overline{c^{2}}=\\frac{2}{3} \\times \\frac{1}{2} M \\overline{c^{2}}=\\frac{2}{3} K T \\\\\n\nV=\\frac{2 K}{3 p} \\times T\n\n\\end{array}<\/span>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09cd\u09a5\u09bf\u09b0 \u0986\u09df\u09a4\u09a8\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ad\u09b0\u09c7\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09aa \u098f\u09b0 \u0995\u09c7\u09b2\u09ad\u09bf\u09a8 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u098f\u099f\u09be\u0987 \u099a\u09be\u09aa\u09c0\u09df \u09b8\u09c2\u09a4\u09cd\u09b0\u0964<\/span><\/p>\n

\u09ea. \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/b>(Ideal gas equation) <\/b>:<\/b><\/h3>\n

\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (<\/span>10.21)<\/span> \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u0995\u09c7\u09b2\u09ad\u09bf\u09a8 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995,<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>E \\propto T<\/span><\/span><\/p>\n

\u09ac\u09be, \\frac{1}{2} M \\overline{c^{2}} \\propto T<\/span><\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (<\/span>10.16)<\/span> \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,\u00a0<\/span><\/p>\np V=\\frac{1}{3} M \\overline{c^{2}}<\/span>\n

 <\/p>\n

\u0985\u09a4\u098f\u09ac, <\/span>p V \\propto T<\/span><\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982, <\/span>\\quad p V=K T<\/span><\/span><\/p>\n

\u09af\u09a6\u09bf \u098f\u0995 \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09b9\u09df \u09af\u09be\u09b0 \u0986\u09df\u09a4\u09a8 <\/span>V<\/span><\/p>\n

\u09a4\u09be\u09b9\u09b2\u09c7, p V=R T<\/span><\/span>\u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 <\/span>R<\/strong> \u09b9\u099a\u09cd\u099b\u09c7 \u09b8\u09be\u09b0\u09cd\u09ac\u099c\u09a8\u09c0\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/strong>\u0964 \u0986\u09ac\u09be\u09b0 <\/span>n<\/span> \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af\u09c7, <\/span>pV=nRT<\/strong><\/b><\/span>\u0964 \u098f\u099f\u09bf\u0987 \u09b9\u099a\u09cd\u099b\u09c7 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8<\/strong> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (Ideal gas equation)<\/strong>\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0993 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 (Kinetic Theory of Gas and Ideal Gas Laws) \u09e7. \u09ac\u09df\u09c7\u09b2\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 (Boyle\u2019s Law) : \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (10.16) \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a5\u09be\u0995\u09b2\u09c7 \u00a0\u09a7\u09cd\u09b0\u09c1\u09ac \u098f\u09ac\u0982 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ad\u09b0 M \u09a7\u09cd\u09b0\u09c1\u09ac \u09b9\u0993\u09df\u09be\u09df \u09a7\u09cd\u09b0\u09c1\u09ac\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09cd\u09a5\u09bf\u09b0<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[51,4244,3028,50],"tags":[1960,2095,2094,2096],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2929"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=2929"}],"version-history":[{"count":13,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2929\/revisions"}],"predecessor-version":[{"id":7938,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2929\/revisions\/7938"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=2929"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=2929"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=2929"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}