{"id":2769,"date":"2022-03-24T16:37:08","date_gmt":"2022-03-24T16:37:08","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=2769"},"modified":"2023-06-18T11:30:12","modified_gmt":"2023-06-18T05:30:12","slug":"magnitude-of-gas-constant","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/magnitude-of-gas-constant\/","title":{"rendered":"\u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 \u098f\u09ac\u0982 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 (Magnitude of Gas Constant And The Variation of Density of a Gas with Temperature and Pressure)"},"content":{"rendered":"

\u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 <\/b>(Magnitude of Gas Constant)<\/b><\/h2>\n

\u09b8\u09b0\u09cd\u09ac\u099c\u09a8\u09c0\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 R<\/span><\/b>–<\/span>\u098f\u09b0 \u09ae\u09be\u09a8 <\/b>(Magnitude of universal Gas Constant <\/b>R<\/strong>) <\/b>: <\/b><\/h3>\n

\u098f\u0995 \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0995\u09c7 \u09b8\u09b0\u09cd\u09ac\u099c\u09a8\u09c0\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 (Gas Constant) <\/strong><\/span>\u09ac\u09be \u09ae\u09cb\u09b2\u09be\u09b0 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 <\/span>R<\/span><\/strong> \u09ac\u09b2\u09be \u09b9\u09df\u0964<\/span><\/p>\n

\u098f\u0995 \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af pV=RT<\/span><\/strong><\/span>\u00a0\u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09c7\u09b2\u09be\u09df \u09b8\u0995\u09b2 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09aa\u09cd\u09b0\u09af\u09cb\u099c\u09cd\u09af\u0964<\/span><\/p>\n

R=\\frac{p V}{T}=\\frac{p_{\\circ} V_{\\circ}}{T_{\\circ}}<\/span><\/b><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 <\/span>V<\/span> \u09b9\u099a\u09cd\u099b\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u099a\u09be\u09aa <\/span>p<\/span> \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be <\/span>T<\/span> \u09a4\u09c7 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u098f\u0995 \u09ae\u09cb\u09b2\u09c7\u09b0 \u0986\u09df\u09a4\u09a8\u0964<\/span><\/p>\n

\u098f\u0996\u09a8, \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u099a\u09be\u09aa, <\/span>p_{\\circ}=1.013 \\times 10^{5} \\mathrm{Nm}^{-2}<\/span><\/strong><\/p>\n

\u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be, <\/span>T_{\\circ}=273.15 \\mathrm{~K}<\/span><\/strong><\/p>\n

\u098f\u09ac\u0982 \u0985\u09cd\u09af\u09be\u09ad\u09cb\u0997\u09be\u09a1\u09cd\u09b0\u09cb\u09b0 \u0985\u09a8\u09c1\u0995\u09b2\u09cd\u09aa \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u098f\u0995 \u09ae\u09cb\u09b2 <\/span>22.4\u00a0<\/strong>liter<\/b>\u00a0\u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>22.4 \\times 10^{-3} \\mathrm{~m}^{3}<\/span><\/strong> \u0986\u09df\u09a4\u09a8 \u09a6\u0996\u09b2 \u0995\u09b0\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>V_{0}=22.4 \\times 10^{-3} \\mathrm{~m}^{3} \\mathrm{~mol}^{-1}<\/span><\/strong><\/p>\n

\u2234\\begin{aligned}\n\n\\therefore R=\\frac{p_{\\circ} V_{\\circ}}{T_{\\circ}} &=\\frac{\\left(1.013 \\times 10^{5} \\mathrm{Nm}^{-2}\\right) \\times\\left(22.4 \\times 10^{-3} \\mathrm{~m}^{3} \\mathrm{~mol}^{-1}\\right)}{273.15 \\mathrm{~K}} \\\\\n\n&=8.31 \\mathrm{JK}^{-1} \\mathrm{~mol}^{-1}\n\n\\end{aligned}<\/span><\/span><\/p>\n

\u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 K<\/b>–<\/span>\u098f\u09b0 \u09ae\u09be\u09a8 <\/b>(Magnitude of universal gas constant K) <\/b>: <\/span>(10.5)<\/span> \u098f\u09ac\u0982 <\/span>(10.9) <\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a4\u09c1\u09b2\u09a8\u09be \u0995\u09b0\u09c7 \u0986\u09ae\u09b0\u09be \u09a6\u09c7\u0996\u09bf,<\/span><\/h3>\n

K=n R=\\frac{m}{M} R<\/span><\/span><\/h3>\n

\u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 <\/span>K-<\/span>\u098f\u09b0 \u09ae\u09be\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ae\u09cb\u09b2\u09c7\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u098f\u09b0 \u09ad\u09b0 \u0993 \u0986\u09a3\u09ac\u09bf\u0995 \u09ad\u09b0\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7\u0964 \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 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 <\/span>R<\/span> \u098f\u09ac\u0982 <\/span>n<\/span> \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09b9\u09b2\u09cb nR<\/span><\/span>\u0964<\/span><\/p>\n

\u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u099a\u09be\u09aa\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 <\/b>(Variation of Density of a Gas with Temperature and Pressure)<\/b><\/h2>\n

m<\/span> \u09ad\u09b0\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u0995\u09cb\u09a8\u09cb \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 p_{1}<\/span><\/span> \u099a\u09be\u09aa\u09c7 \u098f\u09ac\u0982 <\/span>T_{1}<\/span><\/span> \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09df \u09af\u09a6\u09bf \u0986\u09df\u09a4\u09a8 <\/span>V_{1}<\/span><\/span> \u098f\u09ac\u0982 \u0998\u09a8\u09a4\u09cd\u09ac \\rho_{1}<\/span><\/span> \u09b9\u09df \u098f\u09ac\u0982 \u0990 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 p_{2}<\/span><\/span> \u099a\u09be\u09aa\u09c7 \u098f\u09ac\u0982 T_{2}<\/span><\/span>\u00a0\u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09df \u0986\u09df\u09a4\u09a8 <\/span>V_{2}<\/span><\/span> \u098f\u09ac\u0982 \u0998\u09a8\u09a4\u09cd\u09ac <\/span>\\rho_{2}<\/span><\/span> \u09b9\u09df \u09a4\u09ac\u09c7<\/span><\/p>\n

\\rho_{1}=\\frac{m}{V_{1}}<\/span><\/p>\n

\u09ac\u09be, V_{1}=\\frac{m}{\\rho_{1}}<\/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 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u098f\u09ac\u0982,\\rho_{2}=\\frac{m}{V_{2}}<\/span><\/p>\n

\u09ac\u09be, V_{2}=\\frac{m}{\\rho_{2}}<\/span><\/span><\/p>\n

\u098f\u0996\u09a8, \\frac{p_{1} V_{1}}{T_{1}}=\\frac{p_{2} V_{2}}{T_{2}}<\/span> <\/span>\u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 V_{1}<\/span><\/span>–<\/span>\u098f\u09ac\u0982 <\/span>V_{2}<\/span><\/span>–<\/span>\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09df\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,<\/span><\/p>\n

\\frac{p_{1} m}{\\rho_{1} T_{1}}=\\frac{p_{2} m}{\\rho_{2} T_{2}}=<\/span>\u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/p>\n

\u09ac\u09be, \\frac{p_{1}}{\\rho_{1} T_{1}}=\\frac{p_{2}}{\\rho_{2} T_{2}}<\/span><\/span>=<\/span> \u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/span><\/p>\n

\u09ac\u09be, \\frac{\\rho_{1} T_{1}}{p_{1}}=\\frac{\\rho_{2} T_{2}}{p_{2}}=<\/span>\u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce, \\frac{\\rho T}{p}=<\/span><\/span>\u00a0\u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/span><\/p>\n

\u098f \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u099a\u09be\u09aa \u0993 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09be\u09a5\u09c7 \u0998\u09a8\u09a4\u09cd\u09ac\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7\u0964 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a5\u09be\u0995\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>T_{1}=T_{2}<\/span><\/b><\/span>\u00a0\u09b9\u09df \u09a4\u09ac\u09c7 <\/span>(1)<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df,<\/span><\/p>\n

\\frac{\\rho_{1}}{p_{1}}=\\frac{\\rho_{2}}{p_{2}}=\u09a7\u09cd\u09b0\u09c1\u09ac\u0995 <\/span><\/p>\n

\u09ac\u09be, \\rho=<\/span><\/span>\u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \\times<\/span> <\/span>\\rho<\/span><\/span><\/p>\n

\u09ac\u09be, \\rho \\propto p<\/span><\/strong><\/span><\/p>\n

\"Graph \"Graph<\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09cd\u09a5\u09bf\u09b0 \u099a\u09be\u09aa\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac \u098f\u09b0 \u09aa\u09b0\u09ae \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995<\/strong>\u0964 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\u09c7 <\/span>X-<\/span>\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u099a\u09be\u09aa <\/span>P<\/span> \u098f\u09ac\u0982 <\/span>Y-<\/span>\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 <\/span> \u09a8\u09bf\u09df\u09c7 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u0986\u0981\u0995\u09b2\u09c7 (\u09e7\u09e6.\u09ea \u0995) \u099a\u09bf\u09a4\u09cd\u09b0\u09c7\u09b0 \u09a8\u09cd\u09af\u09be\u09df \u09ae\u09c2\u09b2 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09ac\u09c7\u0964 \u0986\u09ac\u09be\u09b0 <\/span>X-<\/span>\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be <\/span>T<\/span> \u098f\u09ac\u0982 <\/span>Y-<\/span>\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac <\/span> \u09a8\u09bf\u09df\u09c7 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\u099f\u09bf (\u09e7\u09e6.\u09ea \u0996) \u099a\u09bf\u09a4\u09cd\u09b0\u09c7\u09b0 \u09a8\u09cd\u09af\u09be\u09df \u0986\u09df\u09a4\u09be\u0995\u09be\u09b0 \u0985\u09a7\u09bf\u09ac\u09c3\u09a4\u09cd\u09a4<\/strong> \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 (Magnitude of Gas Constant) \u09b8\u09b0\u09cd\u09ac\u099c\u09a8\u09c0\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 –\u098f\u09b0 \u09ae\u09be\u09a8 (Magnitude of universal Gas Constant R) : \u098f\u0995 \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0995\u09c7 \u09b8\u09b0\u09cd\u09ac\u099c\u09a8\u09c0\u09a8 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 (Gas Constant) \u09ac\u09be \u09ae\u09cb\u09b2\u09be\u09b0 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09ac\u09b2\u09be \u09b9\u09df\u0964 \u098f\u0995 \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[51,4242,3028,50],"tags":[2015,2016,2014,1977,1976,1978,1975,1979,1974,2017],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2769"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=2769"}],"version-history":[{"count":28,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2769\/revisions"}],"predecessor-version":[{"id":7843,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2769\/revisions\/7843"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=2769"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=2769"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=2769"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}