{"id":3115,"date":"2022-03-24T09:30:26","date_gmt":"2022-03-24T03:30:26","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3115"},"modified":"2022-03-24T22:27:35","modified_gmt":"2022-03-24T16:27:35","slug":"molecular-dynamics-of-gas","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/molecular-dynamics-of-gas\/","title":{"rendered":"\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09a3\u09ac\u09bf\u0995 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac, \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8, \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u0993 \u0985\u09cd\u09af\u09be\u09ae\u09be\u0997\u09be\u09b0 \u09aa\u09b0\u09c0\u0995\u09cd\u09b7\u09be"},"content":{"rendered":"

\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09a3\u09ac\u09bf\u0995 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac, \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8, \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8 (Molecular Dynamics of Gas, Standard Gas, Real Gas)<\/strong><\/h2>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09ac\u09b2\u09a4\u09c7 \u0995\u09bf \u09ac\u09c1\u099d? \u098f \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af\u09b8\u09ae\u09c2\u09b9 \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u0995\u09b0\u0964<\/strong><\/h4>\n

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\u09e7\u0964 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a0\u09a8 : \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09be\u09a4\u09cd\u09b0\u0987 \u0985\u0997\u09a3\u09bf\u09a4 \u09b8\u09c1\u0995\u09cd\u09b7\u09be\u09a4\u09bf-\u09b8\u09c1\u0995\u09cd\u09b7\u09cd\u09ae \u0995\u09a3\u09be\u09b0 \u09b8\u09ae\u09a8\u09cd\u09ac\u09af\u09bc\u09c7 \u0997\u09a0\u09bf\u09a4\u0964 \u098f\u09a6\u09c7\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u09c0\u09af\u09bc \u0985\u09a3\u09c1 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u098f\u0995\u0987 <\/span>
\n<\/span>\u00a0 \u00a0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09ac\u0985\u09a3\u09c1\u0997\u09c1\u09b2\u09cb\u09b0 \u09ad\u09b0 \u098f\u09ac\u0982 \u0986\u0995\u09be\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/span><\/p>\n

\u09e8\u0964 \u0986\u09af\u09bc\u09a4\u09a8 : \u0997\u09cd\u09af\u09be\u09b8\u0997\u09c1\u09b2\u09cb \u099c\u09cd\u09af\u09be\u09ae\u09bf\u09a4\u09bf\u0995 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09ae\u09a4 \u098f\u09a4\u0987 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0\u09be\u0995\u09c3\u09a4\u09bf\u09b0 \u09af\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09a8\u09bf\u099c\u09b8\u09cd\u09ac \u09ae\u09cb\u099f\u00a0 \u0986\u09af\u09bc\u09a4\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09be\u09a7\u09be\u09b0\u09c7\u09b0 <\/span>\u0986\u09af\u09bc\u09a4\u09a8\u09c7\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09af\u09bc \u0985\u09a4\u09bf\u09b6\u09df \u09a8\u0997\u09a8\u09cd\u09af\u0964<\/span><\/p>\n

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\u09ea\u0964 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09bf\u0995\u09b0\u09cd\u09b7\u09a3 : \u0985\u09a8\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09a8\u09bf\u099c\u09c7\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09ac\u09be \u0985\u09a8\u09c1 \u0993 \u0997\u09cd\u09af\u09be\u09b8\u09be\u09a7\u09be\u09b0\u09c7\u09b0 \u09a6\u09c7\u09af\u09bc\u09be\u09b2\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0995\u09cb\u09a8 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09be \u09ac\u09bf\u0995\u09b7\u09b0\u09cd\u09a3 <\/span>\u09a8\u09c7\u0987\u0964<\/span><\/p>\n

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\u09ec\u0964 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09aa : \u0997\u09cd\u09af\u09be\u09b8\u09be\u09a7\u09be\u09b0\u09c7\u09b0 \u09a6\u09c7\u09af\u09bc\u09be\u09b2\u09c7\u09b0 \u0989\u09aa\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a8\u09c1\u0997\u09c1\u09b2\u09cb\u09b0 \u0985\u09ac\u09bf\u09b0\u09be\u09ae \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u09ab\u09b2\u09c7\u0987 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09aa\u09c7\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf <\/span>
\n<\/span>\u00a0 \u00a0 \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

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\u09ef\u0964 \u09b8\u0982\u0998\u09b0\u09cd\u09b7 \u09b8\u09ae\u09af\u09bc : \u0985\u09a3\u09c1\u0997\u09c1\u09b2\u09cb\u09b0 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b6\u09c1\u09a7\u09c1 \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09af\u09c7 \u09b8\u09ae\u09af\u09bc \u09ac\u09cd\u09af\u09af\u09bc \u09b9\u09af\u09bc \u09a4\u09be \u09a6\u09c1\u099f\u09bf \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 <\/span>\u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09af\u09bc \u0996\u09c1\u09ac\u0987 \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09af\u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u0995\u09bf\u09ad\u09be\u09ac\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09aa \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u09b9\u09af\u09bc, \u09a4\u09be \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u0986\u09b2\u09cb\u0995\u09c7 \u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be \u0995\u09b0\u0964<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 : <\/span>\u00a0<\/b>\u0997\u09cd\u09af\u09be\u09b8\u09c0\u09af\u09bc \u099a\u09be\u09aa\u09c7\u09b0 \u0989\u09ce\u09aa\u09a4\u09cd\u09a4\u09bf : \u09af\u09c7 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09b8\u0982\u0996\u09cd\u09af \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0985\u09a3\u09c1\u09b0 \u09b8\u09ae\u09a8\u09cd\u09ac\u09af\u09bc\u09c7 \u0997\u09a0\u09bf\u09a4\u0964 \u09aa\u09be\u09a4\u09cd\u09b0\u09c7\u09b0 \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c7 \u0985\u09a3\u09c1\u0997\u09c1\u09b2\u09cb \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09a6\u09bf\u0995\u09c7 \u0985\u09a4\u09bf \u09a6\u09cd\u09b0\u09c1\u09a4 \u0997\u09a4\u09bf\u09a4\u09c7 \u0987\u09a4\u0983\u09b8\u09cd\u09a4\u09c1\u09a4 \u09a7\u09be\u09ac\u09ae\u09be\u09a8\u0964 \u09ab\u09b2\u09c7 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u098f\u09ac\u0982 \u0997\u09cd\u09af\u09be\u09b8\u09be\u09a7\u09be\u09f1\u09c7\u09f1 \u09ad\u09bf\u09a4\u09b0\u09c7\u09b0 \u09a6\u09c7\u0993\u09af\u09bc\u09be\u09b2\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u0985\u09a8\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0985\u09ac\u09bf\u09b0\u09be\u09ae \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b8\u0982\u0998\u09b0\u09cd\u09b7 \u099a\u09b2\u09a4\u09c7 \u09a5\u09be\u0995\u09c7\u0964 \u098f \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9 \u0997\u09cd\u09af\u09be\u09b8\u09be\u09a7\u09be\u09b0\u09c7\u09b0 \u09a6\u09c7\u0993\u09af\u09bc\u09be\u09b2\u09c7\u09b0 \u0989\u09aa\u09b0 \u09ac\u09be \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u00a0 \u0995\u09b0\u09c7\u0964 \u098f\u09ad\u09be\u09ac\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09aa \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u0986\u09b0\u09cd\u09a6\u09b6 \u0993 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u09ac\u09b2\u09a4\u09c7 \u0995\u09bf \u09ac\u09c1\u099d?<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 : <\/span>\u0986\u09b0\u09cd\u09a6\u09b6 \u0997\u09cd\u09af\u09be\u09b8 :<\/strong> \u09af\u09c7 \u09b8\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u0995\u09b2 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09ae\u09c2\u09b9 \u09af\u09a5\u09be : \u09ac\u09af\u09bc\u09c7\u09b2 \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0, \u099a\u09be\u09b0\u09cd\u09b2\u09b8 \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u0993 \u0985\u09cd\u09af\u09be\u09ad\u09cb\u0997\u09be\u09a1\u09cd\u09b0\u09cb \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09c1\u09b0\u09cb\u09aa\u09c1\u09b0\u09bf \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0\u0995\u09c7 \u0986\u09b0\u09cd\u09a6\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u0985\u09a8\u09cd\u09af\u09ad\u09be\u09ac\u09c7 \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc, \u09af\u09c7 \u09b8\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u0995\u09b2 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 <\/span>PV = nRT<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09af\u09a5\u09be\u09af\u09a5\u09ad\u09be\u09ac\u09c7 \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u09ac\u09b2\u09be \u09b9\u09af\u09bc \u0964 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0985\u09b0\u09cd\u09a5\u09c7 \u0995\u09cb\u09a8\u09cb \u0997\u09cd\u09af\u09be\u09b8\u0987 \u0986\u09a6\u09b0\u09cd\u09b6 \u0986\u099a\u09b0\u09a3 \u0995\u09b0\u09c7 \u09a8\u09be\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a7\u09be\u09b0\u09a3\u09be \u0995\u09b2\u09cd\u09aa\u09a8\u09be\u09aa\u09cd\u09b0\u09b8\u09c2\u09a4 \u09ae\u09be\u09a4\u09cd\u09b0\u0964 \u0986\u09a6\u09b0\u09cd\u09b6\u00a0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09c8\u09b6\u09bf\u09b7\u09cd\u099f\u09b8\u09c2\u099a\u0995 \u09ae\u09be\u09a8\u09a6\u09a8\u09cd\u09a1 :<\/span><\/p>\n

\u09e7\u0964 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u0995\u09b2 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 <\/span>PV\u00a0=\u00a0nRT\u00a0<\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7\u0964<\/span><\/p>\n

\u09e8\u0964 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c0\u09a3 \u09b6\u0995\u09cd\u09a4\u09bf \u098f\u09b0 \u0986\u09af\u09bc\u09a4\u09a8\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u09a8\u09be\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce,<\/span><\/p>\n\\left(\\frac{\\partial E}{\\partial V}\\right)_{T}=0<\/span>\n

\u00a0\u00a0\u00a0\u00a0\u098f\u0996\u09be\u09a8\u09c7 <\/span>E<\/span> \u2192<\/span> \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c0\u09a8 \u09b6\u0995\u09cd\u09a4\u09bf, <\/span>V<\/span> \u2192<\/span> \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09df\u09a4\u09a8 \u098f\u09ac\u0982 <\/span>T<\/span> \u2192<\/span> \u0995\u09c7\u09b2\u09ad\u09bf\u09a8 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u0964<\/span><\/p>\n

\u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8 :<\/strong> \u09af\u09c7 \u09b8\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u0995\u09b2 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0 \u0993 \u099a\u09be\u09aa\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09f0\u09b8\u09ae\u09c2\u09b9 \u09ac\u09bf\u09b6\u09c7\u09b7 \u0995\u09b0\u09c7 \u09ac\u09af\u09bc\u09c7\u09b2 \u098f \u099a\u09be\u09b0\u09cd\u09b2\u09b8 \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09a6\u09cd\u09ac\u09af\u09bc\u0995\u09c7 \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7 \u09a8\u09be, \u09a4\u09be\u09a6\u09c7\u09b0\u0995\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u09ac\u09b2\u09c7 \u0964 \u09ac\u09b8\u09cd\u09a4\u09c1\u09a4\u0983 \u09b8\u0995\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u0987 \u09b8\u0995\u09b2 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u09c2\u09a4\u09cd\u09b0\u09b8\u09ae\u09c2\u09b9 \u09b9\u09c1\u09ac\u09b9\u09c1 \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7 \u09a8\u09be\u0964 \u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u09aa\u09b0\u09bf\u099a\u09bf\u09a4 \\mathrm{O}_{2}, \\mathrm{~N}_{2}, \\mathrm{H}_{2}, \\mathrm{CO}_{2}<\/span><\/span>\u00a0\u09b8\u09ac\u0987 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u0964 \u098f\u0987 \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u09ae\u09c2\u09b9 \u09b6\u09c1\u09a7\u09c1\u09ae\u09be\u09a4\u09cd\u09b0 \u0985\u09a4\u09bf \u09a8\u09bf\u09ae\u09cd\u09a8\u099a\u09be\u09aa \u0993 \u0989\u099a\u09cd\u099a \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09b8\u09ae\u09c2\u09b9\u0995\u09c7 \u09ae\u09cb\u099f\u09be\u09ae\u09c1\u099f\u09bf \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7\u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09a7\u09b0\u09a3\u09c7\u09b0 \u0986\u09a8\u09ac\u09bf\u0995 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 – \u098f\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be \u09a6\u09be\u0993\u0964<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u09af\u09c7 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a8\u09ae\u09c1\u09a8\u09be\u09af\u09bc \u0985\u09b8\u0982\u0996\u09cd\u09af \u0985\u09a3\u09c1 \u09ac\u09bf\u09a6\u09cd\u09af\u09ae\u09be\u09a8 \u0964 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0985\u09ac\u09bf\u09b0\u09be\u09ae \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u0995\u09be\u09b0\u09a3\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u0995\u09cb\u09a8 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u09a8\u09be \u09b9\u09b2\u09c7\u0993 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7, \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09aa\u09c1\u09a8\u0983\u09ac\u09a8\u09cd\u099f\u09a8 \u0998\u099f\u09c7\u0964 \u09ab\u09b2\u09c7 \u0985\u09a8\u09ac\u09b0\u09a4 \u09a4\u09be\u09a6\u09c7\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u0998\u099f\u09c7\u0964 \u098f \u0995\u09be\u09b0\u09a3\u09c7 \u0995\u09cb\u09a8 \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u0995\u09b0\u09c7 \u09ac\u09b2\u09be \u09b8\u09ae\u09cd\u09ad\u09ac \u09a8\u09af\u09bc\u0964 \u09a4\u09ac\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u0997\u09a1\u09bc \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u09a4\u09bf\u09a8 \u09a7\u09b0\u09a3\u09c7\u09b0 \u0986<\/span>\u09a3\u09ac\u09bf\u0995 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u09af\u09c7\u09ae\u09a8 :<\/span><\/p>\n

    \n
  1. \u0997\u09a1\u09bc \u0997\u09a4\u09bf\u09ac\u09c7\u0997 : \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u0997\u09a4\u09bf\u09ac\u09c7\u0997\u09c7\u09b0 \u09aa\u09be\u099f\u09c0\u0997\u09a3\u09bf\u09a4\u09c0\u09df \u0997\u09a1\u09bc\u0995\u09c7 \u09b8\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0997\u09a1\u09bc \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u09a7\u09b0\u09bf, \u0995\u09cb\u09a8 \u09a8\u09ae\u09c1\u09a8\u09be\u09af\u09bc <\/span>N<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u0985\u09a3\u09c1 \u09ac\u09bf\u09a6\u09cd\u09af\u09ae\u09be\u09a8, \u09a4\u09be\u09a6\u09c7\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 \\mathrm{c}_{1}, \\mathrm{c}_{2}, \\mathrm{c}_{3}, \\mathrm{c}_{4}, \\ldots \\ldots \\ldots \\mathrm{c}_{n}<\/span> <\/span>\u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7- \u0997\u09a1\u09bc \u0997\u09a4\u09bf\u09ac\u09c7\u0997, c=\\frac{c_{1}+c_{2}+c_{3}+c_{4}+\\ldots \\ldots \\ldots+c_{n}}{N}<\/span><\/span><\/li>\n
  2. \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2 \u0997\u09a1\u09bc \u09ac\u09b0\u09cd\u0997\u09ac\u09c7\u0997 : \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u0997\u09dc \u09ae\u09be\u09a8\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2\u0995\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u099f\u09bf\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2-\u0997\u09a1\u09bc-\u09ac\u09f0\u09cd\u0997\u09ac\u09c7\u0997 \u09ac\u09c7\u0997 \u09ac\u09b2\u09be \u09b9\u09af\u09bc \u09ac\u09be <\/span>rms<\/span> \u09ac\u09c7\u0997 \u09ac\u09b2\u09c7 \u0964\u09a7\u09b0\u09bf, \u0995\u09cb\u09a8\u09cb \u09a8\u09ae\u09c1\u09a8\u09be\u09af\u09bc <\/span>N<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u0985\u09a3\u09c1 \u09ac\u09bf\u09a6\u09cd\u09af\u09ae\u09be\u09a8, \u09a4\u09be\u09a6\u09c7\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 \\mathrm{c}_{1}, \\mathrm{c}_{2}, \\mathrm{c}_{3}, \\mathrm{c}_{4}, \\ldots \\ldots \\ldots \\mathrm{c}_{n}<\/span><\/span>\u00a0\u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7,\u00a0<\/span><\/li>\n<\/ol>\n

    \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2-\u0997\u09a1\u09bc-\u09ac\u09f0\u09cd\u0997\u09ac\u09c7\u0997, c=\\sqrt{\\frac{c_{1}^{2}+c_{2}^{2}+c_{3}^{2}+\\ldots \\ldots \\ldots+c_{n}^{2}}{N}}<\/span><\/span><\/p>\n

      \n
    1. \u09b8\u09ae\u09cd\u09ad\u09be\u09ac\u09cd\u09af\u09a4\u09ae \u09ac\u09c7\u0997 : \u0995\u09cb\u09a8\u09cb \u09a8\u09ae\u09c1\u09a8\u09be\u09af\u09bc \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u0997\u09a4\u09bf\u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09af\u09c7 \u0997\u09a4\u09bf\u09ac\u09c7\u0997\u099f\u09bf \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u09ac\u09c7\u09b6\u09bf \u09b8\u0982\u0996\u09cd\u09af\u0995 \u0985\u09a3\u09c1\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09ac\u09bf\u09a6\u09cd\u09af\u09ae\u09be\u09a8 \u09a4\u09be\u0995\u09c7 \u09b8\u09ae\u09cd\u09ad\u09be\u09ac\u09cd\u09af \u09ac\u09be \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u09b8\u09ae\u09cd\u09ad\u09be\u09ac\u09cd\u09af\u09a4\u09ae \u09ac\u09c7\u0997 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u09a7\u09b0\u09bf, \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c0\u09af\u09bc \u09a8\u09ae\u09c1\u09a8\u09be\u09af\u09bc \u09e7 \u09b2\u0995\u09cd\u09b7 \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09e7\u09e6\u09e6 <\/span>cm\/s<\/span>; \u09eb \u09b2\u0995\u09cd\u09b7 \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 <\/span>300 <\/span>cm\/s<\/span>; <\/span>\u09ea<\/span> \u09b2\u0995\u09cd\u09b7 \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 <\/span>350 <\/span>cm\/s<\/span>;\u00a0<\/span><\/li>\n<\/ol>\n

      \u09e9 \u09b2\u0995\u09cd\u09b7 \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 <\/span>400 <\/span>cm\/s<\/span>; \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u09ac\u09c7\u09b6\u09bf \u09b8\u0982\u0996\u09cd\u09af\u0995 (\u09eb \u09b2\u0995\u09cd\u09b7) \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 <\/span>300 <\/span>cm\/s,<\/span> \u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b8\u09ae\u09cd\u09ad\u09be\u09ac\u09cd\u09af\u09a4\u09ae \u0997\u09a4\u09bf\u09ac\u09c7\u0997 <\/span>300 <\/span>cm\/s<\/span>.<\/span><\/p>\n

      \u0997\u09a1\u09bc\u09ae\u09c1\u0995\u09cd\u09a4\u09aa\u09a5 : \u09aa\u09b0\u09aa\u09b0 \u09a6\u09c1\u099f\u09bf \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u0995\u09be\u09b2\u09c7 \u098f\u0995\u099f\u09bf \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1 \u09af\u09a4\u099f\u09be \u09b8\u09b0\u09b2 \u09b0\u09c8\u0996\u09bf\u0995 \u09aa\u09a5 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 \u0990 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u0995\u09c7 \u0990 \u0997\u09be\u09b8 \u0985\u09a3\u09c1\u09b0 \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09ac\u09b2\u09c7\u0964 \u09b8\u09ac \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u0995\u09c7 \u09ae\u09cb\u099f\u00a0 \u09b8\u0982\u0998\u09b0\u09cd\u09b7 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ad\u09be\u0997 \u0995\u09b0\u09b2\u09c7 \u09af\u09c7 \u0997\u09a1\u09bc \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u09a4\u09be\u0995\u09c7 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09ac\u09b2\u09c7 \u0964<\/span><\/p>\n

      \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09a7\u09b0\u09a3\u09c7\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2 \u0997\u09a1\u09bc \u09ac\u09b0\u09cd\u0997 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09ac\u09be RMS \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u09aa\u09c2\u09b0\u09cd\u09a3 \u0995\u09c7\u09a8 – \u09a4\u09be \u09ac\u09be\u0996\u09cd\u09af\u09be \u0995\u09b0\u0964<\/strong><\/h4>\n

      \u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2-\u0997\u09a1\u09bc-\u09ac\u09b0\u09cd\u0997 \u0997\u09a4\u09bf\u09ac\u09c7\u0997\u09c7\u09b0 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u099c\u09a8\u09c0\u09af\u09bc\u09a4\u09be : \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2-\u0997\u09a1\u09bc-\u09ac\u09b0\u09cd\u0997 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09b9\u099a\u09cd\u099b\u09c7 \u098f\u09ae\u09a8 \u098f\u0995\u099f\u09bf \u09ac\u09c7\u0997, \u09af\u09be \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09a7\u09b0\u09c7 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u09b9\u09bf\u09b8\u09c7\u09ac \u0995\u09b0\u09b2\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc; \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0997\u09a1\u09bc \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09a8\u09be \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u09b8\u09ae\u09cd\u09ad\u09be\u09ac\u09cd\u09af \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09b9\u09a4\u09c7 \u09b8\u09b0\u09be\u09b8\u09b0\u09bf \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u09a8\u09be\u0964 \u09a4\u09be\u0987, \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2-\u0997\u09a1\u09bc-\u09ac\u09b0\u09cd\u0997 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u09aa\u09c2\u09b0\u09cd\u09a3\u0964<\/span><\/p>\n

      \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995\u09ad\u09be\u09ac\u09c7 \u09a6\u09c7\u0996\u09be\u09a8\u09c7 \u09af\u09be\u09af\u09bc \u09af\u09c7, \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2-\u0997\u09a1\u09bc-\u09ac\u09b0\u09cd\u0997 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09c7 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c0\u09af\u09bc \u09a8\u09ae\u09c1\u09a8\u09be\u09af\u09bc \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf\u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc :<\/span><\/p>\n

      \u09a7\u09b0\u09bf, \u0995\u09cb\u09a8\u09cb \u0997\u09cd\u09af\u09be\u09b8\u09c0\u09af\u09bc \u09a8\u09ae\u09c1\u09a8\u09be\u09af\u09bc <\/span>n<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u0985\u09a3\u09c1 \u09ac\u09b0\u09cd\u09a4\u09ae\u09be\u09a8, \u09af\u09be\u09a6\u09c7\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 \\mathrm{c}_{1}, \\mathrm{c}_{2}, \\mathrm{c}_{3}, \\ldots \\ldots \\ldots \\mathrm{c}_{\\mathrm{n}}<\/span><\/span>\u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u09ad\u09b0 <\/span>m<\/span> \u0964<\/span><\/p>\n

      \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf =\\frac{1}{2} m c_{1}^{2}+\\frac{1}{2} m c_{2}^{2}+\\frac{1}{2} m c_{3}^{2}+\\ldots \\ldots \\ldots+\\frac{1}{2} m c_{n}^{2}<\/span><\/span><\/p>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span> =\\frac{1}{2} m\\left(c_{1}^{2}+c_{2}^{2}+c_{3}^{2}+\\cdots+c_{n}^{2}\\right)<\/span><\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(i)<\/span><\/p>\n

      \u0986\u09ac\u09be\u09b0, \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a8 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 <\/span>C<\/span> (\u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2 \u0997\u09a1\u09bc \u09ac\u09b0\u09cd\u09a3 \u0997\u09a4\u09bf\u09ac\u09c7\u0997) \u09a7\u09b0\u09be \u09b9\u09b2\u09c7 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf =\\frac{1}{2} m c^{2}<\/span><\/span><\/p>\n

      \u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>N<\/span> \u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u09b8\u09b0\u09cd\u09ac\u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf =N \\frac{1}{2} m c^{2}<\/span><\/span><\/p>\n

      =\\frac{1}{2} m \\cdot N\\left\\{\\sqrt{\\frac{c_{1}^{2}+c_{2}^{2}+c_{3}^{2}+\\cdots+c_{n}^{2}}{N}}\\right\\}^{2}<\/span><\/span><\/p>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\\frac{1}{2} m N \\times \\frac{c_{1}^{2}+c_{2}^{2}+c_{3}^{2}+\\cdots+c_{n}^{2}}{N}<\/span><\/span><\/p>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\\frac{1}{2} m\\left(c_{1}^{2}+c_{2}^{2}+c_{3}^{2}+\\cdots+c_{n}^{2}\\right)<\/span><\/span>\u2026\u2026\u2026\u2026\u2026(ii)<\/span><\/p>\n

      \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>i)<\/span> \u0993 <\/span>(<\/span>ii)<\/span> \u09a4\u09c1\u09b2\u09a8\u09be \u0995\u09b0\u09b2\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7, \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2 \u0997\u09a1\u09bc \u09ac\u09b0\u09cd\u0997 \u0997\u09a4\u09bf\u09ac\u09c7\u0997\u0995\u09c7 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09a7\u09b0\u09c7 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09be \u09b9\u09b2\u09c7 \u09a4\u09be \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

      \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09a8\u09bf\u09a3\u09c7\u0995 \u09b8\u09c2\u09a4\u09cd\u09b0\u0997\u09c1\u09b2\u09cb \u0989\u09aa\u09aa\u09be\u09a6\u09a8 \u0995\u09b0 :<\/strong><\/h4>\n

      (i) \u09ac\u09af\u09bc\u09c7\u09b2 \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0; (ii) \u099a\u09be\u09b0\u09cd\u09b2\u09b8 \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0; (ii) \u0985\u09cd\u09af\u09be\u09ad\u09cb\u0997\u09be\u09a1\u09cd\u09b0\u09cb \u09b8\u09c2\u09a4\u09cd\u09b0; (iv) \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae – \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u0964<\/strong><\/h3>\n

      \u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u09ac\u09df\u09c7\u09b2 \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 : <\/b>\u09ac\u09df\u09c7\u09b2 \u098f\u09b0\u00a0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09af\u09be\u09df\u09c0 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ad\u09b0\u09c7\u09b0 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09af\u09bc\u09a4\u09a8 \u098f\u09b0 \u0989\u09aa\u09b0 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u099a\u09be\u09aa\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09cd\u09a4\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce,<\/span><\/p>\nV \\propto \\frac{1}{P}<\/span>\n

      PV=K<\/p>\n

      \u0989\u0995\u09cd\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a4\u09be\u09aa\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09af\u09bc :<\/span><\/p>\nP V=\\frac{1}{3} m N c^{2}<\/span>\n

      =\\frac{2}{3} \\times N \\frac{1}{2} m c^{2}<\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(i)<\/span><\/p>\n

      \u0997\u09a4\u09bf \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u0985\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0, \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0997\u09a1\u09bc \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf <\/span>1<\/span>2<\/span>\u00a0m<\/span>c<\/span>2<\/span>\u00a0\u00a0<\/span>\u09aa\u09b0\u09ae \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce,<\/span><\/p>\n\\frac{1}{2} m c^{2} \\propto<\/span>\n

      \\text { \u09ac\u09be, } \\frac{1}{2} m c^{2}=K T<\/span> \u2026\u2026\u2026\u2026\u2026\u2026(ii)<\/span><\/p>\n

      \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>i)<\/span> \u0993 <\/span>(<\/span>ii)<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

      P V=\\frac{2}{3} N K T<\/span> \u2026\u2026\u2026\u2026\u2026\u2026(iii)<\/span><\/p>\n

      \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ad\u09b0\u09c7\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \\frac{2}{3} N K T<\/span><\/span>\u00a0<\/span>\u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>iii)<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

      PV=<\/span> \u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/span><\/p>\nV \\propto \\frac{1}{p}<\/span>\n

      \u098f\u099f\u09be\u0987 \u09ac\u09af\u09bc\u09c7\u09b2 -\u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u0964<\/span><\/p>\n

      (ii) \u099a\u09be\u09b0\u09cd\u09b2\u09b8 \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 : <\/b>\u099a\u09be\u09b0\u09cd\u09b2\u09b8 \u098f\u09b0 \u09b8\u09c1\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0 \u09b8\u09cd\u09a5\u09bf\u09b0 \u099a\u09be\u09aa\u09c7 \u09a8\u09bf\u09a6\u09bf\u09b7\u09cd\u099f \u09ad\u09b0\u09c7\u09b0 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09af\u09bc\u09a4\u09a8 \u09aa\u09b0\u09ae \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce,<\/span><\/p>\n

      V\u221dT<\/span><\/p>\n

      \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa \u0989\u0995\u09cd\u09a4 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf\u09a4\u09c7 \u0989\u09aa\u09a8\u09c0\u09a4 \u09b9\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc ; \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc,<\/span><\/p>\nP V=\\frac{1}{3} m N c^{2}<\/span>\n

      \u09ac\u09be, P V=\\frac{2}{3} \\times \\frac{1}{2} m N c^{2}<\/span><\/span>\u00a0\u2026\u2026\u2026\u2026\u2026(i)<\/span><\/p>\n

      \u0997\u09a4\u09bf \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u0985\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0, \u0997\u09cd\u09af\u09be\u09b8\u09be \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09c7\u09be\u099f \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf N \\cdot \\frac{1}{2} m c^{2}<\/span><\/span>\u00a0<\/span>\u09aa\u09b0\u09ae \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0985\u09a5\u09be\u09ce,<\/span><\/p>\nN \\cdot \\frac{1}{2} m c^{2} \\propto \\mathrm{T}<\/span>\n

      \u09ac\u09be, N \\cdot \\frac{1}{2} m c^{2}=K T<\/span><\/span>\u00a0\u2026\u2026\u2026\u2026\u2026\u2026(ii)<\/span><\/p>\n

      \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>i)<\/span> \u0993 <\/span>(<\/span>ii)<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

      \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09cd\u09a5\u09bf\u09b0 \u099a\u09be\u09aa\u09c7, <\/span>V=KT<\/span> ( \u098f\u0996\u09be\u09a8\u09c7 <\/span>K=\\frac{2 K}{3 P}=<\/span><\/span>\u00a0<\/span>\u09b8\u09cd\u09a5\u09bf\u09b0<\/span>\u00a0<\/span>\u09b8\u0982\u0996\u09cd\u09af\u09be )<\/span><\/p>\n

      \u2234V\u221dT<\/span><\/p>\n

      \u098f\u099f\u09be\u0987, \u099a\u09be\u09b0\u09cd\u09b2\u09b8 – \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u0964<\/span><\/p>\n

      (iii) \u0985\u09cd\u09af\u09be\u09ad\u09cb\u0997\u09be\u09a1\u09cd\u09b0\u09cb \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 : <\/b>\u0985\u09cd\u09af\u09be\u09ad\u09cb\u0997\u09be\u09a1\u09cd\u09b0\u09cb \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, \u098f\u0995\u0987 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u09b8\u09ae-\u0986\u09af\u09bc\u09a8\u09c7\u09b0 \u09b8\u0995\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7 \u09b8\u09ae\u09be\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u0995 \u0985\u09a3\u09c1 \u09a5\u09be\u0995\u09c7\u0964 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u0985\u09cd\u09af\u09be\u09ad\u09cb\u0997\u09be\u09a1\u09cd\u09b0\u09cb \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc :<\/span><\/p>\n

      \u09a7\u09b0\u09be \u09af\u09be\u0995, \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f <\/span>T<\/span> \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u098f\u09ac\u0982 <\/span>P<\/span> \u099a\u09be\u09aa\u09c7 \u09aa\u09c3\u09a5\u0995 \u09aa\u09c3\u09a5\u0995 \u09a6\u09c1\u099f\u09bf \u0997\u09cd\u09af\u09be\u09b8 <\/span>A<\/span> \u0993 <\/span>B<\/span> \u098f\u0995\u0987 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f <\/span>V<\/span> \u0986\u09af\u09bc\u09a4\u09a8\u09c7 \u098f\u09a6\u09c7\u09b0 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 N_1<\/span><\/span>\u00a0<\/span> \u0993N_2<\/span><\/span>\u00a0\u09b8\u0982\u0996\u09cd\u09af\u0995 \u0985\u09a3\u09c1 \u09ac\u09bf\u09a6\u09cd\u09af\u09ae\u09be\u09a8\u0964 <\/span>A<\/span> \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u09ad\u09b0 m_1<\/span><\/span> \u098f\u09ac\u0982 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2 \u0997\u09a1\u09bc \u09ac\u09b0\u09cd\u0997 \u09ac\u09c7\u0997 c_1<\/span><\/span>\u00a0\u09b9\u09b2\u09c7 \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

      P V=\\frac{1}{3} m_{1} N_{1} c_{1}^{2}<\/span> \u2026\u2026\u2026\u2026\u2026(i)<\/span><\/p>\n

      \u0986\u09ac\u09be\u09b0 <\/span>B<\/span> \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u09ad\u09b0 m_2<\/span><\/span>\u098f\u09ac\u0982 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2 \u0997\u09a1\u09bc \u09ac\u09b0\u09cd\u0997 \u09ac\u09c7\u0997 c_2<\/span><\/span>\u00a0\u09b9\u09b2\u09c7 \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

      P V=\\frac{1}{3} m_{2} N_{2} c_{2}^{2}<\/span> \u2026\u2026\u2026\u2026\u2026\u2026\u2026(ii)<\/span><\/p>\n

      \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0997\u09cd\u09af\u09be\u09b8\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u099a\u09be\u09aa<\/span> P<\/span> \u098f\u09ac\u0982 \u0986\u09af\u09bc\u09a4\u09a8 <\/span>V<\/span> \u098f\u0995\u0987, \u09a4\u09be\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>i)<\/span> \u0993 <\/span>(<\/span>ii)<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n\\frac{1}{3} m_{1} N_{1} c_{1}^{2}=\\frac{1}{3} m_{2} N_{2} c_{2}^{2}<\/span>\n

      \u09ac\u09be, m_{1} N_{1} c_{1}^{2}=m_{2} N_{2} c_{2}^{2}<\/span><\/span>\u2026\u2026\u2026\u2026\u2026\u2026(iii)<\/span><\/p>\n

      \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ae\u09cd\u09af\u09be\u0995\u09cd\u09b8\u0993\u09af\u09bc\u09c7\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0985\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0 \u098f\u0995\u0987 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u0989\u09ad\u09af\u09bc \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0997\u09a1\u09bc \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u09ae\u09be\u09a8\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce,<\/span><\/p>\n\\frac{1}{2} m_{1} c_{1}^{2}=\\frac{1}{2} m_{2} c_{2}^{2}<\/span>\n

      \u09ac\u09be, m_{1} c_{1}^{2}=m_{2} c_{2}^{2}<\/span><\/span>\u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026(iv)<\/span><\/p>\n

      \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (<\/span>iii)<\/span> \u0995\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>iv)<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ad\u09be\u0997 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n\\mathbf{N}_{1}=\\mathbf{N}_{2}<\/span>\n

      \u0985\u09b0\u09cd\u09a5\u09be\u09ce, \u098f\u0995\u0987 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa \u09b8\u09ae\u09be\u09a8 \u0986\u09af\u09bc\u09a4\u09a8\u09c7\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u0985\u09a3\u09c1\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09b8\u09ae\u09be\u09a8\u0964 \u098f\u099f\u09bf\u0987 \u0985\u09cd\u09af\u09be\u09ad\u09cb\u0997\u09be\u09a1\u09cd\u09b0\u09cb \u09b8\u09c2\u09a4\u09cd\u09b0\u0964<\/span><\/p>\n

      (iv) \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae \u098f\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 : <\/b>\u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae -\u098f\u09b0 \u0997\u09cd\u09af\u09be\u09b8 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u09c1\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u099a\u09be\u09aa \u0993 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b9\u09be\u09b0 \u098f\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce,<\/span><\/p>\n

      r \\propto \\frac{1}{\\sqrt{d}}<\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026(i)<\/span><\/p>\n

      \u0989\u0995\u09cd\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09aa\u09cd\u09f0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc :<\/span><\/p>\n

      \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09b2\u09cb\u00a0 :<\/span><\/p>\n

      P V=\\frac{1}{3} m N c^{2}<\/span> \u2026<\/span>\u2026\u2026\u2026\u2026\u2026(ii)<\/span><\/p>\n

      \u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

      \\frac{m N}{V} c^{2}=3 P<\/span> \u2026\u2026\u2026\u2026\u2026\u2026\u2026(iii)<\/span><\/p>\n

      \u098f\u0996\u09be\u09a8\u09c7 <\/span>mN<\/span> \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a8\u09ae\u09c1\u09a8\u09be\u09df \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u09ad\u09b0 \u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc \u2013<\/span><\/p>\n

      \\frac{m N}{V}<\/span>=<\/span> \u0998\u09a8\u09a4\u09cd\u09ac <\/span>=d<\/span><\/p>\n

      \u09b8\u09c1\u09a4\u09b0\u09be\u0982, <\/span>(<\/span>iii)<\/span> \u09a8\u0982 \u09b9\u09a4\u09c7 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df,<\/span><\/p>\nd c^{2}=3 P<\/span>\n

      \u09ac\u09be, c^{2}=\\frac{3 P}{d}<\/span><\/span><\/p>\n

      \u09ac\u09be, =\\frac{\\sqrt{3 P}}{d}<\/span><\/span><\/p>\n

      \u09ac\u09be, c=\\sqrt{3 P} \\times \\frac{1}{\\sqrt{d}}<\/span><\/span>\u00a0\u2026\u2026\u2026\u2026\u2026\u2026(iv)<\/span><\/p>\n

      \u099a\u09be\u09aa \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a5\u09be\u0995\u09b2\u09c7,\\sqrt{3 P}\u00a0= \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 = K<\/span><\/span><\/p>\n

      \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>iv)<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

      c=K \\times \\frac{1}{\\sqrt{d}}<\/span> \u2026\u2026\u2026\u2026\u2026\u2026(v)<\/span><\/p>\n

      \u0985\u09b0\u09cd\u09a5\u09be\u09ce, C \\propto \\frac{1}{\\sqrt{d}}<\/span><\/span>\u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(vi)<\/span><\/p>\n

      \u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09a4 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b9\u09be\u09b0 <\/span>(<\/span>r)<\/span> \u098f\u09b0 \u0985\u09a3\u09c1\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7\u0964 \u0985\u09a3\u09c1\u09b0 \u09ac\u09c7\u0997 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09b0 \u09b8\u09be\u09a5\u09c7 \u09ac\u09cd\u09af\u09be\u09aa\u09a8\u09c7\u09b0<\/span><\/p>\n

      \u09b9\u09be\u09b0\u0993 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09af\u09bc\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce,<\/span><\/p>\n

      r\u221dC<\/span><\/p>\n

      \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>vi)<\/span> \u0995\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc<\/span><\/p>\nr \\propto \\frac{1}{\\sqrt{d}}<\/span>\n

      \u098f\u099f\u09bf\u0987 \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7 \u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b0\u09c2\u09aa\u0964 \u0985\u09a4\u098f\u09ac, \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09b9\u09a4\u09c7 \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09bf\u09a4 \u09b9\u09b2\u09cb \u0964<\/span><\/p>\n

      \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09b9\u09a4\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u0995\u09c7\u09ac\u09b2\u09ae\u09be\u09a4\u09cd\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2\u0964<\/strong><\/h4>\n

      \u0989\u09a4\u09cd\u09a4\u09b0 : <\/span>\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u0997\u09a4\u09c0\u09df \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u099a\u09cd\u099b\u09c7,<\/span><\/p>\nP V=\\frac{1}{3} m N c^{2}<\/span>\n

      \u09ac\u09be, P V=\\frac{2}{3} N \\times \\frac{1}{2} m c^{2}<\/span><\/span>\u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(i)<\/span><\/p>\n

      \u0986\u09ac\u09be\u09b0, <\/span>1<\/span> \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0985\u09a3\u09c1\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be<\/span> N =<\/span> \u0986\u09ad\u09cb\u0997\u09be\u09a1\u09cd\u09b0\u09cb \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>= N_{A}, \\text { \u098f\u09ac\u0982 } \\mathrm{PV}=\\mathrm{RT}<\/span><\/span><\/p>\n

      \u09b8\u09c1\u09a4\u09b0\u09be\u0982, <\/span>1<\/span> \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>i)<\/span> \u0995\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc,<\/span><\/p>\nR T=\\frac{2}{3} \\times N_{A} \\times \\frac{1}{2} m c^{2}<\/span>\n

      \u0986\u09ac\u09be\u09b0, <\/span> , \\frac{1}{2} m c^{2}<\/span><\/span>\u00a0\u00a0<\/span>\u09b9\u09b2\u09cb\u00a0 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u0997\u09a1\u09bc \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf<\/span><\/p>\n

      \\therefore R T=\\frac{2}{3} \\times N_{A} \\times<\/span><\/span>\u00a0\u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u0997\u09a1\u09bc \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf<\/span><\/p>\n

      \u09ac\u09be, <\/span>RT=\\frac{2}{3} \\times 1<\/span> <\/span>\u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf\u0964<\/span><\/p>\n

      \u0985\u09b0\u09cd\u09a5\u09be\u09ce, <\/span>1<\/span> \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf =\\frac{3}{2} R T<\/span><\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026(iii)<\/p>\n

      \u098f\u09ac\u0982 <\/span>n<\/span> \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf r \\propto \\frac{1}{\\sqrt{d}}<\/span><\/span>\u00a0\u2026\u2026\u2026\u2026\u2026\u2026(iv)<\/span><\/p>\n

      \u09af\u09c7\u09b9\u09c7\u09a4\u09c1, <\/span>R<\/span> \u098f\u0995\u099f\u09bf \u09a7\u09cd\u09b0\u09c1\u09ac\u0995, \u09a4\u09be\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>iii)<\/span> \u098f\u09ac\u0982 <\/span>(<\/span>iv)<\/span> \u09b9\u09a4\u09c7 \u09b8\u09cd\u09aa\u09b7\u09cd\u099f \u09af\u09c7, \u0997\u09cd\u09af\u09be\u09b8\u09c0\u09df \u0985\u09a3\u09c1\u09b0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4\u09bf \u0986\u09af\u09bc\u09a4\u09a8 \u09ac\u09be \u099a\u09be\u09aa\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u09a8\u09be\u0964 \u09b6\u09c1\u09a7\u09c1\u09ae\u09be\u09a4\u09cd\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2 \u098f\u09ac\u0982 \u09a4\u09be \u09aa\u09b0\u09ae \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964<\/span><\/p>\n

      \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09b9\u09a4\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2-\u0997\u09a1\u09bc-\u09ac\u09b0\u09cd\u0997 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09aa\u09b0\u09ae \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u098f\u09ac\u0982\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09ac\u09bf\u0995 \u09ad\u09b0\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964<\/strong><\/h4>\n

      \u0985\u09a5\u09ac\u09be, \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09ac \u09b9\u09a4\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, c=\\sqrt{\\frac{3 R T}{M}}<\/span><\/strong><\/p>\n

      \u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u0997\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09b9\u09b2\u09cb ,<\/span><\/p>\n

      P V=\\frac{1}{3} m N c^{2}<\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(v)<\/span><\/p>\n

      \u09ac\u09be, c^{2}=\\frac{3 P V}{m N}<\/span><\/span>\u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(vi)<\/span><\/p>\n

      1<\/span> \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0985\u09a3\u09c1\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>N =<\/span> \u0985\u09cd\u09af\u09be\u09ad\u09cb\u0997\u09be\u09a1\u09cd\u09b0\u09cb \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>=N_A<\/span> \u098f\u09ac\u0982 PV = RT<\/span><\/p>\n

      \u09b8\u09c1\u09a4\u09b0\u09be\u0982, <\/span>1<\/span> \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>ii)<\/span> \u0995\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc,<\/span><\/p>\nc^{2}=\\frac{3 R T}{m N_{A}}<\/span>\n

      \u09ac\u09be, c^{2}=\\frac{3 R T}{M}\\left(\\text { \u098f\u0996\u09be\u09a8\u09c7, } m N_{A}=M\\right.<\/span> <\/span>=<\/span>\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0<\/span>\u00a0<\/span>\u0986\u09a3\u09ac\u09bf\u0995<\/span>\u00a0<\/span>\u09ad\u09b0<\/span>\u00a0<\/span>)<\/span><\/p>\n

      \u09ac\u09be, c=\\frac{\\sqrt{3 R T}}{M}<\/span><\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(iii)<\/span><\/p>\n

      \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>iii)<\/span> \u09b9\u09a4\u09c7 \u09b8\u09cd\u09aa\u09b7\u09cd\u099f \u09af\u09c7, \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2-\u0997\u09a1\u09bc-\u09ac\u09b0\u09cd\u0997 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09af\u09bc\u09a4\u09a8 \u09ac\u09be \u099a\u09be\u09aa\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2 \u09a8\u09af\u09bc, \u09a4\u09be \u09b6\u09c1\u09a7\u09c1\u09ae\u09be\u09a4\u09cd\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09a3\u09ac\u09bf\u0995 \u09ad\u09b0\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2\u0964\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>iii)<\/span> \u09b9\u09a4\u09c7 \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc; \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2-\u0997\u09a1\u09bc-\u09ac\u09b0\u09cd\u0997 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u09aa\u09b0\u09ae \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u098f\u09ac\u0982 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09a3\u09ac\u09bf\u0995 \u09ad\u09b0\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964<\/span><\/p>\n

       <\/p>\n

      \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u0993 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af \u09b2\u09bf\u0996\u0964<\/strong><\/h4>\n

      \u0989\u09a4\u09cd\u09a4\u09b0 :<\/span><\/p>\n\n\n\n\n\n\n\n\n\n
      \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8<\/b><\/td>\n\u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8<\/b><\/td>\n<\/tr>\n
      \u09e7. \u09af\u09c7 \u09b8\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u09ac \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09b8\u09c2\u09a4\u09cd\u09b0 \u09b8\u09ae\u09c2\u09b9 <\/span>\u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7 \u09a4\u09be\u0995\u09c7 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u09ac\u09b2\u09c7\u0964 \u098f\u099f\u09bf \u098f\u0995\u099f\u09bf <\/span>\u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u09a7\u09be\u09b0\u09a3\u09be\u0964<\/span><\/td>\n\u09e7. \u09ac\u09be\u09b8\u09cd\u09a4\u09ac\u09c7 \u09af\u09c7 \u09b8\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df \u09a4\u09be\u09a6\u09c7\u09b0\u0995\u09c7 \u09ac\u09b8\u09cd\u09a4\u09ac <\/span>\u0997\u09cd\u09af\u09be\u09b8 \u09ac\u09b2\u09c7\u0964 \u09af\u09c7\u09ae\u09a8 \u2013 O_{2}, N_{2}, H_{2}<\/span><\/span>\u00a0\u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf<\/span><\/td>\n<\/tr>\n
      \u09e8. \u098f\u09a6\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09be \u09ac\u09bf\u0995\u09b0\u09cd\u09b7\u09a3 <\/span>\u09ac\u09b2 \u09a8\u09c7\u0987\u0964<\/span><\/td>\n\u09e8. \u098f\u09a6\u09c7\u09b0 \u0985\u09a8\u09c2\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09be \u09ac\u09bf\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2 <\/span>
      \n<\/span>\u00a0 \u00a0 \u0986\u099b\u09c7\u0964<\/span><\/td>\n<\/tr>\n
      \u09e9. \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0986\u09df\u09a4\u09a8 \u09aa\u09be\u09a4\u09cd\u09b0\u09c7\u09b0 \u0986\u09df\u09a4\u09a8\u09c7\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09df <\/span>\u09a8\u0997\u09a3\u09cd\u09af<\/span><\/td>\n\u09e9. \u0997\u09cd\u09af\u09be\u09b8\u09be\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0986\u09df\u09a4\u09a8 \u09aa\u09be\u09a4\u09cd\u09b0\u09c7\u09b0 \u0986\u09df\u09a4\u09a8\u09c7\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09df <\/span>\u09a8\u0997\u09a3\u09cd\u09af \u09a8\u09df \u0964<\/span><\/td>\n<\/tr>\n
      \u09ea. \u098f\u09b0\u09be <\/span>PV = nRT<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7\u0964<\/span><\/td>\n\u09ea. \u098f\u09b0\u09be \u09ad\u09cd\u09af\u09be\u09a8\u09a1\u09be\u09b0 \u0993\u09df\u09be\u09b2\u09cd\u200c\u09b8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7 \u00a0 \u00a0 <\/span>
      \n<\/span> \\left(P+\\frac{n^{2} a}{v^{2}}\\right)(v-n b)=n R T<\/span><\/span><\/td>\n<\/tr>\n
      \u09eb. \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09df \u098f\u09a6\u09c7\u09b0 \u0985\u09ad\u09cd\u09af\u09a8\u09cd\u09a4\u09b0\u09c0\u09a3 \u09b6\u0995\u09cd\u09a4\u09bf \u098f\u09b0 <\/span>
      \n<\/span>\u00a0 \u00a0 \u0986\u09df\u09a4\u09a8\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2 \u09a8\u09df\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce,(\u03b4U\/\u03b4V)_T=0<\/span><\/span><\/span><\/td>\n      		\u09eb. \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7, \\left(\\frac{\\delta U}{\\delta V}\\right)_{T} \\neq 0<\/span><\/span><\/td>\n<\/tr>\n
      \u09ec. \u09ac\u09be\u09b8\u09cd\u09a4\u09ac\u09c7 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u0986\u09a6\u09b0\u09cd\u09b6 \u0986\u099a\u09b0\u09a3 \u0995\u09b0\u09c7 \u09a8\u09be\u0964<\/span><\/td>\n\u09ec. \u0989\u099a\u09cd\u099a \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09df \u098f\u09ac\u0982 \u09a8\u09bf\u09ae\u09cd\u09a8\u099a\u09be\u09aa\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u0986\u09a6\u09b0\u09cd\u09b6 <\/span>\u0986\u099a\u09b0\u09a3 \u0995\u09b0\u09c7\u0964<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

       <\/p>\n

      \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09b8\u09ae\u09c2\u09b9 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u09b9\u09a4\u09c7 \u09ac\u09bf\u099a\u09cd\u09af\u09c1\u09a4\u09bf\u09b0 \u0995\u09be\u09b0\u09a3\u09b8\u09ae\u09c2\u09b9 \u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be \u0995\u09b0\u0964<\/strong><\/h4>\n

      \u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09af\u09c7 \u09b8\u0995\u09b2 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af\u09c7\u09b0 \u0989\u09aa\u09b0 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u0995\u09b0\u09c7 <\/span>PV=nRT<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b7\u09cd\u09a0\u09be \u0995\u09b0\u09be \u09b9\u09af\u09bc\u09c7\u099b\u09c7 \u09a4\u09be\u09a4\u09c7 \u09a6\u09c1\u099f\u09bf \u09a4\u09cd\u09b0\u09c1\u099f\u09bf \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u09af\u09c7 \u0995\u09be\u09b0\u09a3\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7 \u09a8\u09be\u0964 \u09a4\u09be\u0987 \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u09ad\u09cd\u09af\u09be\u09a8\u09a1\u09be\u09b0 \u0993\u09af\u09bc\u09be\u09b2\u09b8 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u09a6\u09c1\u099f\u09bf \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09b8\u0982\u09b6\u09cb\u09a7\u09a8 \u0995\u09b0\u09c7\u09a8:<\/span><\/p>\n

      (i) \u0986\u09af\u09bc\u09a4\u09a8\u099c\u09a8\u09bf\u09a4 \u09a4\u09cd\u09b0\u09c1\u099f\u09bf \u09b8\u0982\u09b6\u09cb\u09a7\u09a8 : <\/b>\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u09ae\u09a4\u09c7, \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0986\u09af\u09bc\u09a4\u09a8,\u00a0<\/span><\/p>\n

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      (ii) \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09aa\u099c\u09a8\u09bf\u09a4 \u09a4\u09cd\u09b0\u09c1\u099f\u09bf \u09b8\u0982\u09b6\u09cb\u09a7\u09a8 :<\/b> \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u09ae\u09a4\u09c7, \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0995\u09cb\u09a8 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09be \u09ac\u09bf\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2 \u09a8\u09c7\u0987 \u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09a4\u09be \u09b8\u09a0\u09bf\u0995 \u09a8\u09af\u09bc\u0964 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0986\u09a8\u09cd\u09a4\u0983\u0986\u09a3\u09ac\u09bf\u0995 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2 \u09a8\u09be \u09a5\u09be\u0995\u09b2\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c0\u09af\u09bc \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u0995\u09c7 \u09a4\u09b0\u09b2\u09c7 \u09ac\u09be \u0995\u09a0\u09bf\u09a8\u09c7 \u09aa\u09b0\u09bf\u09a3\u09a4 \u0995\u09b0\u09be \u09af\u09c7\u09a4 \u09a8\u09be\u0964 <\/span>\u09a4\u09be\u099b\u09be\u09a1\u09bc\u09be \u099c\u09c1\u09b2-\u09a5\u09ae\u09b8\u09a8 \u09aa\u09b0\u09c0\u0995\u09cd\u09b7\u09be \u09b9\u09a4\u09c7\u0993 \u0986\u09a8\u09cd\u09a4\u0983\u0986\u09a3\u09ac\u09bf\u0995 \u0986\u0995\u09b0\u09cd\u09b7\u09a3\u09c7\u09b0 \u0985\u09b8\u09cd\u09a4\u09bf\u09a4\u09cd\u09ac\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc\u0964 \u098f\u0987 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u09c7\u09b0 \u0995\u09be\u09b0\u09a3\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u09af\u09c7 \u099a\u09be\u09aa \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u00a0 \u0995\u09b0\u09c7 \u09a4\u09be \u098f\u0995\u0987 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u0997\u09cd\u09af\u09be\u09b8\u099f\u09bf \u0986\u09a6\u09b0\u09cd\u09b6 \u09b9\u09b2\u09c7 \u09af\u09c7 \u099a\u09be\u09aa \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09a4 \u09a4\u09be\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u0995\u09ae\u0964 ( \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u0995\u09ae \u099a\u09be\u09aa \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u00a0 \u0995\u09b0\u09c7 )<\/span><\/p>\n

      \u09a4\u09be\u0987 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u099a\u09be\u09aa <\/span>= <\/span>P+<\/span> \u0986\u09a8\u09cd\u09a4\u0983\u0986\u09a3\u09ac\u09bf\u0995 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0964 \u09ad\u09cd\u09af\u09be\u09a8-\u09a1\u09be\u09b0 \u0993\u09af\u09bc\u09be\u09b2\u09b8 \u09a6\u09c7\u0996\u09be\u09a8 \u09af\u09c7, <\/span>n<\/span> \u09ae\u09cb\u09b2 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0986\u09a8\u09cd\u09a4\u0983\u0986\u09a3\u09ac\u09bf\u0995 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 <\/span>=\\frac{n^{2} a}{v^{2}}<\/span><\/span><\/p>\n

      \u0986\u09a8\u09cd\u09a4\u0983\u0986\u09a3\u09ac\u09bf\u0995 \u0986\u0995\u09b0\u09cd\u09b7\u09a3\u099c\u09a8\u09bf\u09a4 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09b9\u09b2\u09cb\u00a0 <\/span>‘a’, a<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09c7\u09b2\u09c7 \u0990 \u0997\u09cd\u09af\u09be\u09b8 \u09a4\u09b0\u09b2\u09c0\u0995\u09b0\u09a3 \u09b8\u09b9\u099c \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

      n<\/span> \u09ae\u09cb\u09b2 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u099a\u09be\u09aa <\/span>=<\/span> \\left(P+\\frac{n^{2} a}{v^{2}}\\right)<\/span><\/p>\n

      \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09e8\u099f\u09bf \u09a4\u09cd\u09b0\u09c1\u099f\u09bf \u09b8\u0982\u09b6\u09cb\u09a7\u09a8 \u0995\u09b0\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09af\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b7\u09cd\u09a0\u09be \u0995\u09b0\u09be \u09b9\u09af\u09bc \u09a4\u09be\u0995\u09c7 \u09ad\u09cd\u09af\u09be\u09a8-\u09a1\u09be\u09b0-\u0993\u09af\u09bc\u09be\u09b2\u09b8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

      \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09a8\u09bf\u09ae\u09b0\u09c2\u09aa :<\/span><\/p>\n\\left(P+\\frac{n^{2} a}{v^{2}}\\right)(v-n b)=n R T<\/span>\n

      \u098f\u0995 \u09ae\u09cb\u09b2 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7, <\/span>n=1<\/span> \u09b9\u09b2\u09c7, (\u09af\u09c7\u09ae\u09a8 <\/span>44<\/span>g CO_2<\/span><\/span>\u00a0<\/span>, 32g O_2<\/span><\/span>\u00a0\u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf)\u0964<\/span><\/p>\n\\left(P+\\frac{a}{v^{2}}\\right)(v-n b)=R T<\/span>\n

      \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u0995\u09cb\u09a8 \u09b6\u09b0\u09cd\u09a4\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09b8\u09ae\u09c2\u09b9 \u0986\u09a6\u09b0\u09cd\u09b6 \u0986\u099a\u09b0\u09a3 \u0995\u09b0\u09c7 \u09a4\u09be \u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be \u0995\u09b0\u0964<\/strong><\/h4>\n

      \u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> n<\/span> \u09ae\u09cb\u09b2 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09cd\u09b0\u09af\u09cb\u099c\u09cd\u09af \u09ad\u09cd\u09af\u09be\u09a8\u09a1\u09be\u09b0 \u0993\u09af\u09bc\u09be\u09b2\u09b8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa,<\/span><\/p>\n

      \\left(P+\\frac{n^{2} a}{v^{2}}\\right)(v-n b)=n R T<\/span> \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(i)<\/span><\/p>\n

      \u0989\u099a\u09cd\u099a \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u09a8\u09bf\u09ae\u09cd\u09a8\u099a\u09be\u09aa\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09be\u09b8\u09b8\u09ae\u09c2\u09b9 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ae\u09a4 \u0986\u099a\u09b0\u09a3 \u0995\u09b0\u09c7\u0964 \u0995\u09be\u09b0\u09a3,<\/span><\/p>\n

      i. \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09af\u09a4 \u09ac\u09c7\u09b6\u09c0 \u09b9\u09af\u09bc \u098f\u09ac\u0982 \u099a\u09be\u09aa \u09af\u09a4 \u0995\u09ae \u09b9\u09af\u09bc, \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09af\u09bc\u09a4\u09a8 \u09a4\u09a4 \u09ac\u09c7\u09b6\u09c0 \u09b9\u09af\u09bc\u0964 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09af\u09bc\u09a4\u09a8 \u09ac\u09c7\u09b6\u09c0 \u09b9\u09b2\u09c7 \u098f\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09af\u09bc \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0986\u09af\u09bc\u09a4\u09a8 \u09a8\u0997\u09a3\u09cd\u09af \u09b9\u09af\u09bc\u0964 \u098f \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0995\u09be\u09b0\u09cd\u09af\u0995\u09b0 \u0986\u09af\u09bc\u09a4\u09a8 \u0989\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n

      \u00a0<\/span>\u2234<\/span> \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09e7\u09ae \u099f\u09bf \u09a6\u09c2\u09b0\u09c0\u09ad\u09c2\u09a4 \u09b9\u09af\u09bc\u0964 \u09a4\u09be\u0987 (i) \u09a8\u0982 \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7, <\/span>V-nb \u2248 V <\/span>\u09a7\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n

      ii. \u0986\u09ac\u09be\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09af\u09bc\u09a4\u09a8 \u09af\u09a4 \u09ac\u09c7\u09b6\u09bf \u09b9\u09af\u09bc, \u0985\u09a3\u09c1\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09a4\u09a4 \u09ac\u09c7\u09b6\u09bf \u09b9\u09af\u09bc\u0964 \u0989\u099a\u09cd\u099a \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u09a8\u09bf\u09ae\u09cd\u09a8\u099a\u09be\u09aa\u09c7 \u098f\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09aa\u09be\u09b0\u09b8\u09cd\u09aa\u09b0\u09bf\u0995\u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2 \u098f\u09a4\u0987 \u09b9\u09cd\u09b0\u09be\u09b8 \u09aa\u09be\u09af\u09bc \u09af\u09c7, \u0986\u09a8\u09cd\u09a4\u0983\u0986\u09a8\u09ac\u09bf\u0995 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u099c\u09a8\u09bf\u09a4 \u09b0\u09be\u09b6\u09bf \\frac{n^{2} a}{v^{2}<\/span><span style="font-weight: 400;"><\/span><\/span> – \u0995\u09c7 \u0989\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u0985\u09b0\u09cd\u09a5\u0982 (i) \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u09a7\u09b0\u09be P+\\frac{n^{2} a}{v^{2}\u2248P<\/span> \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n

      \u098f\u09ad\u09be\u09ac\u09c7 \u0997\u09a4\u09bf\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09e8\u09af\u09bc \u0995\u09cd\u09b0\u099f\u09bf\u0993 \u09a6\u09c2\u09b0 \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

      \u0989\u099a\u09cd\u099a \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u09a8\u09bf\u09ae\u09cd\u09a8 \u099a\u09be\u09aa\u09c7 \u09ad\u09cd\u09af\u09be\u09a8-\u09ad\u09be\u09b0-\u0993\u09af\u09bc\u09be\u09b2\u09b8 \u09b8\u09ae\u09c0\u0995\u09a3\u099f\u09bf\u0995\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc,<\/span><\/p>\n

      PV=nRT<\/span> \u09af\u09be \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

      \u0985\u09a4\u098f\u09ac \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc, \u0989\u0995\u09cd\u09a4 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u09a8\u09bf\u09ae\u09cd\u09a8\u099a\u09be\u09aa\u09c7 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0997\u09cd\u09af\u09be\u09b8\u09c7 \u0986\u09a6\u09b0\u09cd\u09b6 \u09ae\u09a4 \u0986\u099a\u09b0\u09a3 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

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