{"id":3114,"date":"2022-03-24T09:45:12","date_gmt":"2022-03-24T03:45:12","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3114"},"modified":"2022-03-27T04:45:34","modified_gmt":"2022-03-26T22:45:34","slug":"gas-laws-2","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/gas-laws-2\/","title":{"rendered":"\u0997\u09cd\u09af\u09be\u09b8 \u09b8\u09c2\u09a4\u09cd\u09b0\u09b8\u09ae\u09c2\u09b9 – \u09a6\u09c1\u0987 (The Gas Laws)"},"content":{"rendered":"

\u0997\u09cd\u09af\u09be\u09b8 \u09b8\u09c2\u09a4\u09cd\u09b0\u09b8\u09ae\u09c2\u09b9 (The Gas Laws) <\/strong><\/h2>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u09ac\u09cb\u09b2\u09cd\u099f\u099c\u09ae\u09cd\u09af\u09be\u09a8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09ac\u09b2\u09a4\u09c7 \u0995\u09c0 \u09ac\u09c1\u099d?<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u0985\u09a3\u09c1 \u09aa\u09cd\u09b0\u09a4\u09bf \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u09c7\u09b0 \u09ae\u09be\u09a8\u0995\u09c7 \u09ac\u09cb\u09b2\u09cd\u099f\u099c\u09ae\u09cd\u09af\u09be\u09a8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u09ac\u09cb\u09b2\u09cd\u099f\u099c\u09ae\u09cd\u09af\u09be\u09a8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 k=\\frac{R}{N_{A}}<\/span><\/span><\/p>\n

\u00a0\\text { S.I. \u098f\u0995\u0995\u09c7 } k=\\frac{8.314 \/ k^{-1} \\text { mol }^{-1}}{6.022 \\times 10^{23} \\text { moleculemole }^{-1}}=1.38 \\times 10^{-23} J k^{-1} \\text { molecule }^{-1}<\/span><\/span><\/p>\n

Latm<\/span> \u098f\u0995\u0995\u09c7 k=\\frac{0.082 \\text { Latmk }^{-1} \\mathrm{~mol}-1}{6.022 \\times 10^{23} \\mathrm{moleculemole}^{-1}}=1.36 \\times 10^{-25} \\text { Latmk }^{-1} \\mathrm{molecule}^{-1}<\/span><\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u09a1\u09be\u09b2\u09cd\u099f\u09a8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09b8\u09c1\u09a4\u09cd\u09b0\u099f\u09bf \u0989\u09a6\u09be\u09b9\u09b0\u09a3\u09b8\u09b9 \u09ac\u09bf\u09ac\u09c3\u09a4 \u0995\u09b0\u0964<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u201c\u0995\u09cb\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u0989\u09b7\u09cd\u09a3\u09a4\u09be\u09af\u09bc \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09ac\u09bf\u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b9\u09c0\u09a8 \u098f\u0995\u09be\u09a7\u09bf\u0995 \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa -\u098f\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u0964\u201d \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0995\u09cb\u09a8 \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09aa\u09c3\u09a5\u0995\u09ad\u09be\u09ac\u09c7 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u0986\u09af\u09bc\u09a4\u09a8 \u098f\u0995\u09be\u0995\u09c0 \u09a6\u0996\u09b2 \u0995\u09b0\u09c7 \u09af\u09c7 \u099a\u09be\u09aa \u09aa\u09cd\u09b0\u09af\u09bc\u09be\u09c7\u0997 \u0995\u09b0\u09c7 \u09a4\u09be\u0995\u09c7 \u0990 \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09ac\u09b2\u09c7\u0964\u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 : \u0995\u09cb\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u0989\u09b7\u09cd\u09a3\u09a4\u09be\u09df \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09ac\u09bf\u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b9\u09c0\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u099a\u09be\u09aa <\/span>P<\/span> \u098f\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995\u099a\u09be\u09aa P_{1}, P_{2}, P_{3}, P_{n}<\/span><\/span> \u09b9\u09b2\u09c7, \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, \\mathbf{P}=\\mathbf{P}_{1}+\\mathbf{P}_{2}+\\mathbf{P}_{3}+\\ldots \\ldots . . \\mathbf{P}_{n}<\/span><\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09ac\u09b2\u09a4\u09c7 \u0995\u09bf \u09ac\u09c1\u099d?<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u0995\u09cb\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09b8\u09ae\u09c2\u09b9 \u09aa\u09c3\u09a5\u0995 \u09aa\u09c3\u09a5\u0995\u09ad\u09be\u09ac\u09c7 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3 \u0986\u09af\u09bc\u09a4\u09a8 \u09a6\u0996\u09b2 \u0995\u09b0\u09b2\u09c7 \u09af\u09c7 \u099a\u09be\u09aa \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u00a0 \u0995\u09b0\u09a4; \u09a4\u09be\u0995\u09c7 \u09b8\u0982\u09b6\u09cd\u09b2\u09bf\u09b7\u09cd\u099f \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u09a1\u09be\u09b2\u09cd\u099f\u09a8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09b8\u09c1\u09a4\u09cd\u09b0\u099f\u09bf \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u0964 (\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3) \u0985\u09a5\u09ac\u09be, \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u09af\u09c7 \u0995\u09cb\u09a8 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u0997\u09c1\u09b2\u09cb\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0<\/span> :<\/span> \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>T<\/span> \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc <\/span>V<\/span> \u0986\u09af\u09bc\u09a4\u09a8\u09c7\u09b0 \u09aa\u09be\u09a4\u09cd\u09b0\u09c7 \u09a4\u09bf\u09a8\u099f\u09bf \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 n_{1}, n_{2}, n_{3}<\/span><\/span>\u09ae\u09cb\u09b2 \u09ae\u09bf\u09b6\u09cd\u09b0\u09bf\u09a4 \u0995\u09b0\u09be \u09b9\u09b2\u09cb \u0964<\/span>\u00a0 <\/span>\u0989\u09aa\u09be\u09a6\u09be\u09a8 \u09a4\u09bf\u09a8\u099f\u09bf \u09aa\u09c3\u09a5\u0995\u09ad\u09be\u09ac\u09c7 <\/span>T<\/span> \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc <\/span>V<\/span> \u0986\u09af\u09bc\u09a4\u09a8 \u09a6\u0996\u09b2 \u0995\u09b0\u09c7\u00a0 <\/span>\\mathrm{P}_{1}, \\mathrm{P}_{2}, \\mathrm{P}_{3}<\/span><\/span>\u00a0\u099a\u09be\u09aa \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u00a0 \u0995\u09b0\u09c7, \u09a4\u09be\u09b9\u09b2\u09c7 \\mathbf{P}_{1}, \\mathbf{P}_{2}, \\mathbf{P}_{3}<\/span><\/span>\u00a0\u09b9\u09ac\u09c7 \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09a4\u09bf\u09a8\u099f\u09bf\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,<\/span><\/p>\n

\\begin{aligned}\n\nP_{1} V &=n_{1} R T \\\\\n\n\\therefore n_{1} &=\\frac{P_{1} V}{R T}\n\n\\end{aligned}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\\begin{aligned}\n\nP_{2} V &=n_{2} R T \\\\\n\n\\therefore n_{2} &=\\frac{P_{2} V}{R T}\n\n\\end{aligned}<\/span><\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\begin{aligned}\n\nP_{3} V &=n_{3} R T \\\\\n\n\\therefore n_{3} &=\\frac{P_{3} V}{R T}\n\n\\end{aligned}<\/span><\/span><\/p>\n

 <\/p>\n

\u098f\u0996\u09a8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa P_{m}<\/span><\/span>\u00a0\u098f\u09ac\u0982 \u09ae\u09cb\u099f\u00a0 \u09ae\u09c7\u09be\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>n<\/span> \u09b9\u09b2\u09c7,<\/span><\/p>\nP_{m} V=n R T<\/span>\n

\u09ac\u09be, <\/span>n==\\frac{P_{m} V}{R T}<\/span><\/span><\/p>\n

\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be,<\/span><\/p>\nn=n_{1}+n_{2}+n_{3}<\/span>\n\\therefore \\frac{P_{m} V}{R T}=\\frac{P_{1} V}{R T}+\\frac{P_{2} V}{R T}+\\frac{P_{3} V}{R T}+<\/span>\n\\text { \u09ac\u09be, } P_{m}=P_{1}+P_{2}+P_{3}+<\/span>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce, \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa, \u098f\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa\u09c7\u09b0 \u09af\u09cb\u0997\u09ab\u09b2\u09c7\u09b0\u00a0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u09a1\u09be\u09b2\u09cd\u099f\u09a8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b7\u09cd\u09a0\u09be \u0995\u09b0\u0964<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u09a1\u09be\u09b2\u09cd\u099f\u09a8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09bf\u09ac\u09c3\u09a4\u09bf \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa :<\/strong> \u201c\u0995\u09cb\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u0989\u09b7\u09cd\u09a3\u09a4\u09be\u09af\u09bc \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09ac\u09bf\u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b9\u09c0\u09a8 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u0964\u201d<\/span><\/p>\n

\u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a8\u09c7\u09b0 \u099a\u09be\u09aa \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc :<\/strong> \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u0989\u09b7\u09cd\u09a3\u09a4\u09be\u09df \\mathbf{P}_{1}<\/span><\/span> \u099a\u09be\u09aa\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u098f\u0995\u099f\u09bf \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09df\u09a4\u09a8 V_{1}<\/span><\/span>\u098f\u09ac\u0982 \u0985\u09aa\u09b0 \u098f\u0995\u099f\u09bf \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0\u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09aa\u09b0\u09bf\u09ae\u09be\u09a3\u09c7 \u0986\u09af\u09bc\u09a4\u09a8 \u0993 \u099a\u09be\u09aa \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 V_{2} \u0993 P_{2}<\/span><\/span>\u00a0\u0964 \u0997\u09cd\u09af\u09be\u09b8 \u09aa\u09be\u09a4\u09cd\u09b0 \u09a6\u09c1\u099f\u09bf \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09c1\u09a8\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u0982\u09af\u09c1\u0995\u09cd\u09a4 \u0995\u09b0\u09c7 \u0997\u09cd\u09af\u09be\u09b8 \u09a6\u09c1\u099f\u09bf\u0995\u09c7 \u098f\u0995\u09a4\u09cd\u09b0\u09c7 \u09ae\u09bf\u09b6\u09cd\u09b0\u09bf\u09a4\u0995\u09b0\u09b2\u09c7 \u09ae\u09cb\u099f\u00a0 \u0986\u09af\u09bc\u09a4\u09a8 \u09b9\u09ac\u09c7 \\left(v_{1}+v_{2}\\right)<\/span><\/span>\u0964<\/span><\/p>\n

\"Gas<\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u09ae\u09bf\u09b6\u09cd\u09b0\u09bf\u09a4 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09aa\u09cd\u09b0\u09a5\u09ae \u0993 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u0986\u09df\u09a4\u09a8 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 P_{1}^{\\prime} \u0993 P_{2}^{\\prime}<\/span><\/span>\u00a0<\/span>\u098f\u09ac\u0982 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa P_{m}<\/span><\/span>\u00a0\u0964<\/span> \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ac\u09df\u09c7\u09b2 – \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 :<\/span><\/p>\nP_{1}^{\\prime}\\left(V_{1}+V_{2}\\right)=P_{1} V_{1} \\quad P_{2}^{\\prime}\\left(V_{1}+V_{2}\\right)=P_{2} V_{2}<\/span>\n\\therefore P_{1}^{\\prime}=\\frac{P_{1} v_{1}}{v_{1}+v_{2}} \\quad \\therefore P_{2}^{\\prime}=\\frac{P_{2} v_{2}}{v_{1}+v_{2}}<\/span>\n

\u0986\u09ac\u09be\u09b0 \u09a1\u09be\u09b2\u09cd\u099f\u09a8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, P_{m}=P_{1}^{\\prime}+P_{2}^{\\prime}<\/span><\/span><\/p>\n\\therefore P_{m}=\\frac{P_{1} v_{1}}{v_{1}+v_{2}}+\\frac{P_{2} v_{2}}{v_{1}+v_{2}}<\/span>\n

 <\/p>\n

\u09ac\u09be, P_{m}=\\frac{P_{1} v_{1}+P_{2} v_{2}}{v_{1}+v_{2}}<\/span><\/p>\n

 <\/p>\nP_{m}\\left(V_{1}+V_{2}\\right)=P_{1} V_{1}+P_{2} V_{2}<\/span>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u09ac\u09af\u09bc\u09c7\u09b2 – \u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u098f\u09ac\u0982 \u09a1\u09be\u09b2\u09cd\u099f\u09a8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09a6\u09c1\u0987 \u09ac\u09be \u09a4\u09a4\u09cb\u09a7\u09bf\u0995 \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09b8\u09be\u09ae\u0997\u09cd\u09b0\u09bf\u0995 \u099a\u09be\u09aa \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u09a1\u09be\u09b2\u09cd\u099f\u09a8\u09c7\u09b0\u00a0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0995\u09cb\u09a8 \u098f\u0995\u099f\u09bf \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u0989\u09aa\u09be\u09a6\u09be\u09a8\u099f\u09bf\u09b0 \u09ae\u09cb\u09b2 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6 \u0993 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa\u09c7\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/strong><\/h4>\n

\u0985\u09a5\u09ac\u09be,\u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0995\u09cb\u09a8 \u098f\u0995\u099f\u09bf \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b7\u09cd\u09a0\u09be \u0995\u09b0\u0964<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u09a7\u09b0\u09bf, \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09af\u09bc \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09ac\u09bf\u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b9\u09c0\u09a8 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u0986\u09af\u09bc\u09a4\u09a8<\/span> \u00a0<\/span>V<\/span> \u098f\u09ac\u0982 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u0997\u09c1\u09b2\u09cb\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa<\/span> \\mathbf{P}_{1}, \\mathbf{P}_{2}, \\mathbf{P}_{3}<\/span>\u00a0\u098f\u09ac\u0982 \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u0997\u09c1\u09b2\u09cb\u09b0 \u09aa\u09c3\u09a5\u0995 \u09aa\u09c3\u09a5\u0995 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 n_{1}, n_{2}, n_{3}<\/span><\/span>\u0964 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09c7 \u09aa\u09be\u0987;<\/span><\/p>\n=n_{1} R T<\/span>\n

\u09ac\u09be, P_{1}=\\frac{n_{1} R T}{V}<\/span> \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026……………(i)<\/span><\/p>\nP_{2} V=n_{2} R T<\/span>\n

\u09ac\u09be, P_{2}=\\frac{n_{2} R T}{V}<\/span> \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026……………(ii)<\/span><\/p>\nP_{3} V=n_{3} R T<\/span>\n

\u09ac\u09be, P_{3}=\\frac{n_{3} R T}{V}<\/span> \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026……………(iii)<\/span><\/p>\n

\u09a1\u09be\u09b2\u09cd\u099f\u09a8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7; \u0997\u09cd\u09af\u09be\u09b8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa,<\/span><\/p>\nP_{m}=P_{1}+P_{2}+P_{3}<\/span>\n=\\frac{n_{1} R T}{V}+\\frac{n_{2} R T}{V}+\\frac{n_{3} R T}{V}<\/span>\n

=\\frac{R T}{v}\\left(n_{1}+n_{2}+n_{3}+\\ldots \\ldots \\ldots \\ldots\\right.<\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.(iv)<\/p>\n

\u0995\u09bf\u09a8\u09cd\u09a4 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f \u00a0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>n<\/span> \u09b9\u09b2\u09c7,<\/span><\/p>\n

n=\\left(n_{1}+n_{2}+n_{3}+\\ldots \\ldots \\ldots \\ldots\\right)<\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.(v)<\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>iv)<\/span> \u098f <\/span>(<\/span>v)<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987;<\/span><\/p>\n

P_{m}=\\frac{R T}{V} \\cdot n<\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(vi)<\/p>\n

\u0986\u09ac\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>i)<\/span> \u0995\u09c7 <\/span>(<\/span>vi)<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ad\u09be\u0997 \u0995\u09b0\u09c7 \u09aa\u09be\u0987;<\/span><\/p>\n\\frac{P_{1}}{P_{m}}=\\frac{\\pi_{1} R T}{V} \\times \\frac{V}{\\pi R T}<\/span>\nP_{1}=\\frac{n_{1}}{n} \\cdot P_{m}<\/span>\n

\u098f\u0995\u0987\u09ad\u09be\u09ac\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc;<\/span><\/p>\nP_{2}=\\frac{n_{2}}{n} \\cdot P_{m}<\/span>\n

\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(viii)<\/p>\n

P_{3}=\\frac{n_{3}}{n} \\cdot P_{m}<\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(ix)<\/p>\n

\u0986\u09ac\u09be\u09b0 \u0995\u09cb\u09a8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0995\u09cb\u09a8 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 \u098f\u09ac\u0982 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u0995\u09c7 \u0989\u0995\u09cd\u09a4 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u099f\u09bf\u09b0 \u09ae\u09cb\u09b2 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6 \u09ac\u09b2\u09c7\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09af\u09c7 \u0995\u09cb\u09a8 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ae\u09cb\u09b2 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6,<\/span><\/p>\n

X=\\frac{\\text { \u0989\u09aa\u09be\u09a6\u09be\u09a8\u099f\u09bf\u09b0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be }}{\\text { \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ac \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ae\u09cb\u099f \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be }}<\/span><\/span><\/p>\n

\u0985\u09a4\u098f\u09ac, \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>vii), (viii)<\/span> \u0993<\/span> (<\/span>ix)<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc;<\/span><\/p>\n

P_{1}=x_{1} \\cdot P_{m}<\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 P_{2}=x_{2} P_{m}<\/span><\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 P_{3}=x_{3} P_{m}<\/span><\/span><\/p>\n

\u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09ad\u09be\u09ac\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc;<\/span><\/p>\n

P_{A}=x_{A} \\cdot P_{m}<\/span>\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(x)<\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0995\u09cb\u09a8 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa<\/span> =<\/span> \u0989\u09aa\u09be\u09a6\u09be\u09a8\u099f\u09bf\u09b0 \u09ae\u09cb\u09b2 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6 \u00d7<\/span>\u00a0\u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u099a\u09be\u09aa<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :<\/strong>\u00a0 \u09ae\u09cb\u09b2 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6 \u09ac\u09b2\u09a4\u09c7 \u0995\u09bf \u09ac\u09c1\u099d?<\/strong><\/span><\/p>\n

\u0989\u09a4\u09cd\u09a4\u09b0 : <\/span>\u09ae\u09cb\u09b2 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6 :<\/strong> \u0995\u09cb\u09a8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0995\u09cb\u09a8 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u098f\u09ac\u0982 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09b8\u0995\u09b2 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u0995\u09c7 \u0990 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u099f\u09bf\u09b0 \u09ae\u09cb\u09b2 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6 \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u0995\u09cb\u09a8 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ae\u09cb\u09b2-\u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6\u00a0 =\\frac{\\text { \u0989\u09aa\u09be\u09a6\u09be\u09a8\u099f\u09bf\u09b0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be }}{\\text { \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ac \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ae\u09cb\u099f \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be }}<\/span><\/span><\/p>\n

 <\/p>\n

\u0997\u09be\u09a8\u09bf\u09a4\u09bf\u0995 \u09b0\u09c2\u09aa : \u0995\u09cb\u09a8 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be n_{1}, n_{2}, n_{3} \\ldots \\ldots . . n_{n}<\/span><\/span>\u098f\u09ac\u0982 \u09ae\u09bf\u09b6\u09cd\u09b0\u09a3\u09c7\u09b0 \u09ae\u09cb\u099f\u00a0 \u09ae\u09cb\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>n<\/span> \u09b9\u09b2\u09c7, \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u0989\u09aa\u09be\u09a6\u09be\u09a8\u099f\u09bf\u09b0 \u09ae\u09cb\u09b2 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6,<\/span><\/p>\nx_{1}=\\frac{n_{1}}{n_{1}+n_{2}+n_{3}+\\cdots+n_{n}}=\\frac{n_{1}}{n}<\/span>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u0993 \u09a8\u09bf\u0983\u09b8\u09b0\u09a3 \u09ac\u09b2\u09a4\u09c7 \u0995\u09bf \u09ac\u09c1\u099d?<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u09ac\u09cd\u09af\u09be\u09aa\u09a8 :<\/strong> \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u0995\u09cb\u09a8 \u0995\u09a0\u09bf\u09a8, \u09a4\u09b0\u09b2 \u09ac\u09be \u0997\u09cd\u09af\u09be\u09b8\u09c0\u09af\u09bc \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u09b8\u09cd\u09ac\u09a4\u0983\u09b8\u09cd\u09ab\u09c1\u09b0\u09cd\u09a4 \u0993 \u09b8\u09ae\u09ad\u09be\u09ac\u09c7 \u09aa\u09b0\u09bf\u09ac\u09cd\u09af\u09be\u09aa\u09cd\u09a4 \u09b9\u0993\u09af\u09bc\u09be\u09b0 \u09aa\u09cd\u09b0\u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u0995\u09c7 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u0995\u09a0\u09bf\u09a8 \u09ac\u09be \u09a4\u09b0\u09b2\u09c7\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09af\u09bc \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09aa\u09cd\u09b0\u09ac\u09a3\u09a4\u09be \u09ac\u09c7\u09b6\u09bf\u0964 \u0998\u09b0\u09c7 \u0995\u09cb\u09a8 \u09b8\u09c1\u0997\u09a8\u09cd\u09a7\u09bf \u09a6\u09cd\u09b0\u09ac\u09cd\u09af\u09c7\u09b0 \u09ac\u09cb\u09a4\u09b2 \u0996\u09c1\u09b2\u09b2\u09c7 \u09ac\u09be \u0998\u09b0\u09c7 \u0995\u09cb\u09a8 \u09b8\u09c1\u0997\u09a8\u09cd\u09a7\u09bf \u09ab\u09c1\u09b2 \u09b0\u09be\u0996\u09b2\u09c7 \u0998\u09b0\u09c7\u09b0 \u09b8\u09b0\u09cd\u09ac\u09a4\u09cd\u09b0-\u098f\u09b0 \u0997\u09a8\u09cd\u09a7 \u099b\u09a1\u09bc\u09bf\u09af\u09bc\u09c7 \u09aa\u09a1\u09bc\u09c7\u0964 \u09ac\u09be\u09af\u09bc\u09c1\u09a4\u09c7 \u09b8\u09c1\u0997\u09a8\u09cd\u09a7\u09bf \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8\u09c7\u09b0 \u098f\u099f\u09bf \u098f\u0995 \u0985\u09ad\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u0964<\/span><\/p>\n

\u09a8\u09bf\u0983\u09b8\u09b0\u09a3 \u09ac\u09be \u0985\u09a8\u09c1\u09ac\u09cd\u09af\u09be\u09aa\u09a8 :<\/strong> \u099a\u09be\u09aa\u09c7\u09b0 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af\u09c7\u09b0 \u0995\u09be\u09b0\u09a3\u09c7 \u09b8\u09b0\u09c1\u099b\u09bf\u09a6\u09cd\u09b0 \u09aa\u09a5 \u09a6\u09bf\u09af\u09bc\u09c7 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09ac\u09c7\u09b0 \u09b9\u09af\u09bc\u09c7 \u0986\u09b8\u09be\u0995\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a8\u09bf\u0983\u09b8\u09b0\u09a3 \u09ac\u09be \u0985\u09a8\u09c1\u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09ac\u09b2\u09c7\u0964 \u0989\u099a\u09cd\u099a \u099a\u09be\u09aa\u09c7 \u0995\u09cb\u09a8 \u09b8\u09bf\u09b2\u09bf\u09a8\u09cd\u09a1\u09be\u09b0 \u09b0\u09be\u0996\u09be \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09bf\u09b2\u09bf\u09a8\u09cd\u09a1\u09be\u09b0\u09c7\u09b0 \u09b8\u09c1\u0995\u09cd\u09b7\u09cd\u09ae \u099b\u09bf\u09a6\u09cd\u09b0 \u09a6\u09bf\u09af\u09bc\u09c7 \u09ac\u09c7\u09b0 \u09b9\u09af\u09bc\u09c7 \u0986\u09b8\u09be \u09b9\u09b2\u09cb\u00a0 \u09a8\u09bf\u0983\u09b8\u09b0\u09a3 \u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b9\u09be\u09b0 \u09ac\u09be \u09a8\u09bf\u0983\u09b8\u09b0\u09a3 \u09b9\u09be\u09b0 \u09ac\u09b2\u09a4\u09c7 \u0995\u09bf \u09ac\u09c1\u099d?<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 : <\/span>\u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u098f\u0995\u0995 \u09b8\u09ae\u09af\u09bc\u09c7 \u09ac\u09cd\u09af\u09be\u09aa\u09bf\u09a4 \u09ac\u09be \u0985\u09a8\u09c1\u09ac\u09cd\u09af\u09be\u09aa\u09bf\u09a4 ( \u09a8\u09bf\u0983\u09b8\u09b0\u09bf\u09a4 ) \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09af\u09bc\u09a4\u09a8\u0995\u09c7 \u0990 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u099f\u09bf\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b9\u09be\u09b0 \u09ac\u09be \u09a8\u09bf\u0983\u09b8\u09b0\u09a3 \u09b9\u09be\u09b0 \u09ac\u09b2\u09c7\u0964 \u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b0\u09c2\u09aa : \u09a7\u09b0\u09bf, \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 <\/span>V<\/span> \u0986\u09af\u09bc\u09a4\u09a8 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09ac\u09be \u09a8\u09bf\u0983\u09b8\u09b0\u09a3\u09c7\u09b0 \u099c\u09a8\u09cd\u09af <\/span>t<\/span> \u09b8\u09ae\u09af\u09bc \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u099c\u09a8\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09ac\u09be \u09a8\u09bf\u0983\u09b8\u09b0\u09a3 \u09b9\u09be\u09b0 r=\\frac{v}{t}<\/span><\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09ac\u09bf\u09ac\u09c3\u09a4 \u0993 \u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be \u0995\u09b0\u0964<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 : <\/span>\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u09a5\u09ae\u09be\u09b8 \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae \u09e7\u09ee\u09e8\u09ef \u09b8\u09be\u09b2\u09c7 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09aa\u09b0\u09c0\u0995\u09cd\u09b7\u09be \u09a8\u09bf\u09b0\u09c0\u0995\u09cd\u09b7\u09be\u09b0 \u09aa\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u0982\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u098f\u0995\u099f\u09bf \u09b8\u09c2\u09a4\u09cd\u09b0 \u0989\u09a6\u09cd\u09ad\u09be\u09ac\u09a8 \u0995\u09b0\u09c7\u09a8\u0964 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09a8\u09be\u09ae\u09c7 \u09aa\u09b0\u09bf\u099a\u09bf\u09a4\u0964 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa :<\/span><\/p>\n

\u201c\u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \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\u201d<\/span><\/p>\n

\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b0\u09c2\u09aa : \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u09a7\u09b0\u09bf \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b9\u09be\u09b0 <\/span>r<\/span> \u098f\u09ac\u0982 \u0998\u09a8\u09a4\u09cd\u09ac <\/span>d<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0, r \\propto \\frac{1}{\\sqrt{d}}<\/span><\/span><\/p>\n

\u09af\u09a6\u09bf \u098f\u0995\u0987 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u09a6\u09c1\u099f\u09bf \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b9\u09be\u09b0 r_{1} \u0993 r_{2}<\/span><\/span> \u098f\u09ac\u0982 \u0998\u09a8\u09a4\u09cd\u09ac d_{1} \u0993 d_{2}<\/span><\/span>\u00a0\u09b9\u09af\u09bc\u0964 \u09a4\u09be\u09b9\u09b2\u09c7,<\/span><\/p>\n

r_{1} \\propto \\frac{1}{\\sqrt{d}_{1}}<\/span> <\/span>\u098f\u09ac\u0982<\/span>\u00a0<\/span> r_{2} \\propto \\frac{1}{\\sqrt{d_{2}}}<\/span><\/span><\/p>\n

\u09ac\u09be, <\/span>\\frac{r_{1}}{r_{2}}=\\frac{\\sqrt{d_{2}}}{d_{1}}<\/span><\/span><\/p>\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 :\u00a0 \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u09c1\u09a4\u09cd\u09b0 \u09b9\u09a4\u09c7 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09a3\u09ac\u09bf\u0995 \u09ad\u09b0 \u0995\u09bf\u09ad\u09be\u09ac\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc ?<\/strong><\/h4>\n

\u0989\u09a4\u09cd\u09a4\u09b0 :<\/span> \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa :<\/strong><\/p>\n

\u201c\u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u0995\u09cb\u09a8\u09cb \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b9\u09be\u09b0 \u098f\u09b0 \u0998\u09a3\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2\u09c7\u09b0 \u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964\u201d<\/span><\/p>\n

\u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u0995\u09cb\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac <\/span>d<\/span> \u098f\u09ac\u0982 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b9\u09be\u09b0 <\/span>r<\/span> \u09b9\u09b2\u09c7 \u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995\u09ad\u09be\u09ac\u09c7 \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09a8\u09bf\u09ae\u09cd\u09a8\u09b0\u09c2\u09aa \u09a6\u09be\u0981\u09a1\u09bc\u09be\u09af\u09bc :\u00a0<\/span><\/p>\n

r \\propto \\frac{1}{\\sqrt{d}}<\/span><\/span><\/p>\n

\u0997\u09cd\u09b0\u09b9\u09be\u09ae\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09cb\u09b0\u09c2\u09aa \u0995\u09cb\u09a8\u09cb \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09a8\u09ac\u09bf\u0995 \u09ad\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc : \u09a7\u09b0\u09bf \u098f\u0995\u0987 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 d_{1} \\text { \u098f\u09ac\u0982} d_{2}<\/span><\/span>\u00a0\u0998\u09a8\u09a4\u09cd\u09ac \u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u09a6\u09c1\u099f\u09bf \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09ac\u09be \u09a8\u09bf\u0983\u09b8\u09b0\u09a3 \u09b9\u09be\u09b0 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 r_{1} \\text { \u098f\u09ac\u0982 } r_{2}<\/span><\/span>\u00a0\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u0997\u09cd\u09b0\u09be\u09b9\u09be\u09ae\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09aa\u09a8 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7,<\/span><\/p>\n

r_{1} \\propto \\frac{1}{\\sqrt{d}} \\text { \u09ac\u09be, } r_{1}=\\frac{K}{\\sqrt{d_{1}}}<\/span> \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(i)<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0, r_{2}=\\frac{1}{\\sqrt{d_{2}}} \\text { \u09ac\u09be, } r_{2}=\\frac{K}{\\sqrt{d_{2}}}<\/span><\/span>\u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(ii)<\/span><\/p>\n

\u0989\u09ad\u09af\u09bc \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span>K<\/span> \u098f\u0995\u099f\u09bf \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0964<\/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

\\frac{r_{1}}{r_{2}}=\\frac{\\frac{K}{\\sqrt{d_{1}}}}{\\frac{K}{\\sqrt{d_{2}}}} \\text { \u09ac\u09be, } \\frac{r_{1}}{r_{2}}=\\sqrt{\\frac{d_{2}}{d_{1}}}<\/span> \u2026\u2026\u2026\u2026\u2026\u2026(iii)<\/span><\/p>\n

\u09a7\u09b0\u09bf, \u098f\u0995\u0987 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u098f\u0995\u0987 \u09b8\u09b0\u09c1\u099b\u09bf\u09a6\u09cd\u09b0 \u09aa\u09a5\u09c7 \u0989\u09ad\u09af\u09bc \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09b8\u09ae-\u0986\u09af\u09bc\u09a4\u09a8 <\/span>(<\/span>V)<\/span> \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09a8\u09bf\u0983\u09b8\u09b0\u09a3\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 t_{1} \u0993 t_{2}<\/span><\/span>\u00a0\u09b8\u09ae\u09af\u09bc \u09b2\u09be\u0997\u09c7\u0964 \u09a4\u09be\u09b9\u09b2\u09c7,<\/span><\/p>\nr_{1}=\\frac{v}{t_{1}} \\text { \u098f\u09ac\u0982 } r_{2}=\\frac{v}{t_{2}}<\/span>\n

\\therefore \\frac{r_{1}}{r_{2}}=\\frac{t_{2}}{t_{1}}<\/span> \u2026\u2026\u2026\u2026\u2026(iv)<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>iii)<\/span> \u0993 <\/span>(<\/span>iv)<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

\\frac{t_{2}}{t_{1}}=\\frac{r_{1}}{r_{2}}=\\sqrt{\\frac{d_{2}}{d_{1}}}<\/span>\u2026\u2026\u2026\u2026(v)<\/span><\/p>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, \u0997\u09cd\u09af\u09be\u09b8 \u09a6\u09c1\u099f\u09bf\u09b0 \u0986\u09a8\u09ac\u09bf\u0995 \u09ad\u09b0 <\/span>M<\/span>1<\/span> \u0993 <\/span>M<\/span>2<\/span> \u0964 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be <\/span>(<\/span>T)<\/span> \u0993 \u099a\u09be\u09aa <\/span>(<\/span>P)<\/span> \u098f \u0989\u09ad\u09af\u09bc \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ae\u09cb\u09b2\u09be\u09b0\u00a0 \u0986\u09af\u09bc\u09a4\u09a8 <\/span>V<\/span> \u09b9\u09b2\u09c7 \u0998\u09a8\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be \u09b9\u09a4\u09c7 \u09aa\u09be\u0987 :<\/span><\/p>\nd_{1}=\\frac{M_{1}}{v} \u0993\u00a0 d_{2}=\\frac{M_{2}}{v}<\/span>\n

\\therefore \\frac{d_{2}}{d_{1}}=\\frac{M_{2}}{M_{1}}<\/span>\u2026\u2026\u2026\u2026\u2026\u2026(vi)<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac, \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>v)<\/span> \u0993 <\/span>(<\/span>vi)<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09df,<\/span><\/p>\n

\\frac{t_{2}}{t_{1}}=\\frac{r_{1}}{r_{2}}=\\sqrt{\\frac{M_{2}}{M_{1}}}<\/span> <\/span> \u2026\u2026\u2026\u2026\u2026\u2026(vii)<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (vii) \u09b9\u09a4\u09c7 \u09b8\u09b0\u09b2\u09c0\u0995\u09b0\u09a3\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc,<\/span><\/p>\n

M_{2}=\\left(\\frac{r_{1}}{r_{2}}\\right)^{2} \\times M_{1}<\/span> \u2026\u2026\u2026\u2026\u2026\u2026(viii)<\/span><\/p>\n

M_{2}=\\left(\\frac{t_{2}}{t_{1}}\\right)^{2} \\times M_{1}<\/span> \u2026\u2026\u2026\u2026\u2026\u2026(ix)<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09a6\u09c1’\u099f\u09bf \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09cd\u09af\u09aa\u09a8 \u09b9\u09be\u09b0 \u09ac\u09be \u09ac\u09cd\u09af\u09be\u09aa\u09a8\u09c7\u09b0 \u09b8\u09ae\u09af\u09bc \u098f\u09ac\u0982 \u09af\u09c7 \u0995\u09cb\u09a8 \u098f\u0995\u099f\u09bf \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09a8\u09ac\u09bf\u0995 \u09ad\u09b0 \u099c\u09be\u09a8\u09be \u09a5\u09be\u0995\u09b2\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>viii)<\/span> \u09ac\u09be <\/span>(<\/span>ix)<\/span> \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09c7 \u0985\u09aa\u09b0 \u0997\u09cd\u09af\u09be\u09b8\u099f\u09bf\u09b0 \u0985\u09a8\u09bf\u09ac\u09bf\u0995 \u09ad\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0997\u09cd\u09af\u09be\u09b8 \u09b8\u09c2\u09a4\u09cd\u09b0\u09b8\u09ae\u09c2\u09b9 (The Gas Laws) \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u09ac\u09cb\u09b2\u09cd\u099f\u099c\u09ae\u09cd\u09af\u09be\u09a8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09ac\u09b2\u09a4\u09c7 \u0995\u09c0 \u09ac\u09c1\u099d? \u0989\u09a4\u09cd\u09a4\u09b0 : \u0985\u09a3\u09c1 \u09aa\u09cd\u09b0\u09a4\u09bf \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u09c7\u09b0 \u09ae\u09be\u09a8\u0995\u09c7 \u09ac\u09cb\u09b2\u09cd\u099f\u099c\u09ae\u09cd\u09af\u09be\u09a8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u09ac\u09cb\u09b2\u09cd\u099f\u099c\u09ae\u09cd\u09af\u09be\u09a8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u00a0 Latm \u098f\u0995\u0995\u09c7 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u09a1\u09be\u09b2\u09cd\u099f\u09a8\u09c7\u09b0 \u0986\u0982\u09b6\u09bf\u0995 \u099a\u09be\u09aa \u09b8\u09c1\u09a4\u09cd\u09b0\u099f\u09bf \u0989\u09a6\u09be\u09b9\u09b0\u09a3\u09b8\u09b9 \u09ac\u09bf\u09ac\u09c3\u09a4 \u0995\u09b0\u0964 \u0989\u09a4\u09cd\u09a4\u09b0 : \u201c\u0995\u09cb\u09a8<\/p>\n

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