{"id":711,"date":"2022-03-24T09:54:36","date_gmt":"2022-03-24T09:54:36","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=711"},"modified":"2022-04-04T01:06:51","modified_gmt":"2022-04-03T19:06:51","slug":"cp-and-cv-for-an-ideal-gas","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/cp-and-cv-for-an-ideal-gas\/","title":{"rendered":"\u098f\u0995\u099f\u09bf \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 CP \u0993 CV-\u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af | Difference between CP\u00a0and CV for an ideal gas"},"content":{"rendered":"\r\n

\u098f\u0995\u099f\u09bf \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a6\u09c1\u0987 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09be\u09aa\u09c7\u09b0(Difference between CP\u00a0and CV) \u09ae\u09a7\u09cd\u09af\u09c7 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af \u0995\u09b0\u09a4\u09c7 \u0997\u09bf\u09df\u09c7 \u09a4\u09be\u09aa \u0995\u09c1\u09aa\u09b0\u09bf\u09ac\u09be\u09b9\u09c0 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u0986\u09ac\u09a6\u09cd\u09a7 \u099a\u09cb\u0999 \u09b2\u0987\u0964 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u099a\u09cb\u0999 C\u0964 \u099a\u09cb\u0999\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u098f\u0995\u099f\u09bf \u09b9\u09be\u09b2\u0995\u09be \u0998\u09b0\u09cd\u09b7\u09a3\u09b6\u09c2\u09a8\u09cd\u09af \u0993 \u09ac\u09be\u09df\u09c1\u09a8\u09bf\u09b0\u09c1\u09a6\u09cd\u09a7 \u09aa\u09bf\u09b8\u09cd\u099f\u09a8 \u09ac\u09bf\u09a8\u09be \u09ac\u09be\u09a7\u09be\u09df \u099a\u09b2\u09be\u099a\u09b2 \u0995\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u09aa\u09bf\u09b8\u09cd\u099f\u09a8\u099f\u09bf D\u0964 \u09aa\u09bf\u09b8\u09cd\u099f\u09a8\u099f\u09bf\u0993 \u0995\u09c1\u09aa\u09b0\u09bf\u09ac\u09be\u09b9\u09c0 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u09a4\u09c8\u09b0\u09bf\u0964<\/span><\/p>\r\n\r\n\r\n\r\n

\r\n
\"Test\r\n
\u099a\u09bf\u09a4\u09cd\u09b0<\/figcaption>\r\n<\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n

\u098f\u0987 \u0986\u09ac\u09a6\u09cd\u09a7 \u099a\u09cb\u0999\u09c7 1 \u09ae\u09cb\u09b2 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u0997\u09cd\u09af\u09be\u09b8 \u09b2\u0987\u0964 \u098f\u0996\u09a8 \u0997\u09cd\u09af\u09be\u09b8\u099f\u09bf\u09b0 \u0986\u09df\u09a4\u09a8 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09b0\u09c7\u0996\u09c7 \u098f\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be dT \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u0995\u09b0\u09bf\u0964 \u09af\u09a6\u09bf \u09b8\u09cd\u09a5\u09bf\u09b0 \u0986\u09df\u09a4\u09a8\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09be\u09aa C_V<\/span> \u09b9\u09df, \u09a4\u09ac\u09c7 \u0997\u09cd\u09af\u09be\u09b8 \u0995\u09b0\u09cd\u09a4\u09c3\u0995 \u0997\u09c3\u09b9\u09c0\u09a4 \u09a4\u09be\u09aa\u00a0<\/span><\/p>\r\n\r\n\r\n\r\n

= \u09ad\u09b0 \\times<\/span> \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09be\u09aa \\times<\/span><\/span><\/span> \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af<\/span><\/p>\r\n\r\n\r\n\r\n

=<\/span> 1\\times C_V \\times dT<\/span><\/p>\r\n\r\n\r\n\r\n

=<\/span>C_VdT<\/span><\/p>\r\n\r\n\r\n\r\n

\u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u098f\u0995 \u0995\u09c7\u09b2\u09ad\u09bf\u09a8 \u09b9\u09b2\u09c7 \u0997\u09cd\u09af\u09be\u09b8 \u0995\u09b0\u09cd\u09a4\u09c3\u0995 \u0997\u09c3\u09b9\u09c0\u09a4 \u09a4\u09be\u09aa<\/span><\/p>\r\n\r\n\r\n\r\n

=<\/span>C_V\\times 1<\/span><\/p>\r\n\r\n\r\n\r\n

=C_V<\/span> \u099c\u09c1\u09b2 (J)<\/span><\/p>\r\n\r\n\r\n\r\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u09b8\u09cd\u09a5\u09bf\u09b0 \u099a\u09be\u09aa\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09be\u09aa C_P<\/span> \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09cd\u09a5\u09bf\u09b0 \u099a\u09be\u09aa\u09c7 1 \u09ae\u09cb\u09b2 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be 1 \u09a1\u09bf\u0997\u09cd\u09b0\u09bf \u09ac\u09be\u09dc\u09be\u09a4\u09c7 C_P<\/span> \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09a4\u09be\u09aa\u09c7\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8 \u09b9\u09ac\u09c7\u0964 \u0997\u09cd\u09af\u09be\u09b8\u09c7 \u09b8\u09b0\u09ac\u09b0\u09be\u09b9\u0995\u09c3\u09a4 \u098f\u0987 \u09a4\u09be\u09aa \u09a6\u09c1\u0987 \u09ad\u09be\u0997\u09c7 \u09ac\u09cd\u09af\u09df\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964 \u098f\u09b0 \u098f\u0995\u099f\u09bf \u0985\u0982\u09b6 C_V<\/span> \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09ac\u09be\u09dc\u09be\u09ac\u09c7 \u098f\u09ac\u0982 \u0985\u09aa\u09b0 \u0985\u0982\u09b6 \u09ac\u09be\u09b9\u09cd\u09af\u09bf\u0995 \u099a\u09be\u09aa P-\u098f\u09b0 \u09ac\u09bf\u09b0\u09c1\u09a6\u09cd\u09a7\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09df\u09a4\u09a8 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09a4\u09c7 \u0995\u09be\u099c \u0995\u09b0\u09ac\u09c7\u0964 \u09a7\u09b0\u09bf \u099a\u09be\u09aa\u09c7\u09b0 \u09ac\u09bf\u09b0\u09c1\u09a6\u09cd\u09a7\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0986\u09df\u09a4\u09a8 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09b0 \u09ab\u09b2\u09c7 \u09aa\u09bf\u09b8\u09cd\u099f\u09a8\u099f\u09bf x \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09ac\u09be\u0987\u09b0\u09c7 \u09b8\u09b0\u09c7 \u0997\u09c7\u09b2\u0964 \u0985\u09a4\u098f\u09ac \u0995\u09be\u099c\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 = \u09ac\u09b2 \\times<\/span> \u09b8\u09b0\u09a3<\/span><\/p>\r\n\r\n\r\n\r\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = \u099a\u09be\u09aa \\times<\/span><\/span> \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 \\times<\/span><\/span> <\/span> \u09b8\u09b0\u09a3 [\u2235 \u09ac\u09b2 = \u099a\u09be\u09aa \\times<\/span><\/span><\/span> \u0986\u09df\u09a4\u09a8]<\/span><\/p>\r\n\r\n\r\n\r\n

\u200c\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 =P \\times A \\times x<\/span>[k; \u098f\u0996\u09be\u09a8\u09c7 A= \u09aa\u09bf\u09b8\u09cd\u099f\u09a8 \u09ac\u09be \u099a\u09cb\u0999\u09c7\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2<\/span><\/p>\r\n\r\n\r\n\r\n

\u2234 \u0995\u09be\u099c =P.dV<\/span> \u099c\u09c1\u09b2 J; \u098f\u0996\u09be\u09a8\u09c7 dV= \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09bf\u09a4 \u0986\u09df\u09a4\u09a8 =A.x<\/span><\/p>\r\n\r\n\r\n\r\n

\u0985\u09a4\u098f\u09ac,<\/span> C_P=C_V+<\/span>\u0995\u09be\u099c\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3<\/span><\/p>\r\n\r\n\r\n\r\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u09ac\u09be, C_P=C_V+P.dV<\/span> —————- (1.6)<\/span><\/p>\r\n\r\n\r\n\r\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0(Ideal Gas) \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7<\/span><\/p>\r\n\r\n\r\n\r\n

\u09af\u09a6\u09bf \u099a\u09be\u09aa \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a5\u09be\u0995\u09c7, \u09a4\u09ac\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>1.16<\/span>–<\/span> \u0995\u09c7 \u09ac\u09cd\u09af\u09ac\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\r\n\r\n\r\n\r\n

PdV+VdP=RdT+TdR<\/span><\/span><\/p>\r\n\r\n\r\n\r\n

PdV+V\\times 0=RdT+T\\times 0<\/span>———— [\u2235 \u09b8\u09cd\u09a5\u09bf\u09b0 \u099a\u09be\u09aa\u09c7 dP=0 \u098f\u09ac\u0982 R \u09a7\u09cd\u09b0\u09c1\u09ac \u09b0\u09be\u09b6\u09bf \u09b9\u0993\u09df\u09be\u09df, dR=0 \u098f\u09ac\u0982 \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf dT=1K]<\/span><\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be, <\/span>PdV=RdT=R<\/span><\/p>\r\n\r\n\r\n\r\n

\u2234<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>1.6<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\r\n\r\n\r\n\r\nC_P=C_V+R<\/span>\r\n\r\n\r\n\r\n

C_P-C_V=R<\/span> —————————- (1.7)<\/span><\/p>\r\n\r\n\r\n\r\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a6\u09c1\u0987 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09be\u09aa\u09c7\u09b0 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af(Difference between CP\u00a0and CV for an ideal gas) \u09ac\u09be \u0985\u09a8\u09cd\u09a4\u09b0\u09ab\u09b2 \u0997\u09cd\u09af\u09be\u09b8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 R-\u098f\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/span><\/p>\r\n\r\n\r\n\r\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 R \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995, \u09b8\u09c1\u09a4\u09b0\u09be\u0982 C_P>C_V<\/span>\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09cd\u09a5\u09bf\u09b0 \u099a\u09be\u09aa\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ae\u09cb\u09b2\u09be\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09be\u09aa \u09b8\u09cd\u09a5\u09bf\u09b0 \u0986\u09df\u09a4\u09a8\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ae\u09cb\u09b2\u09be\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09be\u09aa \u0985\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u09ac\u09dc\u0964 R-\u098f\u09b0 \u09ae\u09be\u09a8 8.314 JK^{-1}mol^{-1}<\/span> \u09ac\u09b8\u09bf\u09df\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (1.7) \u09b9\u09a4\u09c7 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df,<\/span>C_P-C_V=8.314 J K^{-1}mol^{-1}<\/span><\/p>\r\n\r\n\r\n\r\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (1.16) \u09a5\u09c7\u0995\u09c7 \u09aa\u09be\u0987,<\/span> \\frac{C_P}{C_V}-1=\\frac{R}{C_V}<\/span><\/span><\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be, <\/span>\\gamma -1 =\\frac{R}{C_V}<\/span> \\Big(\\because \\frac{C_P}{C_V}=\\gamma \\Big)<\/span><\/span><\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be, C_V=\\frac{R}{\\gamma -1}<\/span><\/span><\/p>\r\n","protected":false},"excerpt":{"rendered":"

\u098f\u0995\u099f\u09bf \u0986\u09a6\u09b0\u09cd\u09b6 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09a6\u09c1\u0987 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09be\u09aa\u09c7\u09b0(Difference between CP\u00a0and CV) \u09ae\u09a7\u09cd\u09af\u09c7 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af \u0995\u09b0\u09a4\u09c7 \u0997\u09bf\u09df\u09c7 \u09a4\u09be\u09aa \u0995\u09c1\u09aa\u09b0\u09bf\u09ac\u09be\u09b9\u09c0 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u0986\u09ac\u09a6\u09cd\u09a7 \u099a\u09cb\u0999 \u09b2\u0987\u0964 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u099a\u09cb\u0999 C\u0964 \u099a\u09cb\u0999\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u098f\u0995\u099f\u09bf \u09b9\u09be\u09b2\u0995\u09be \u0998\u09b0\u09cd\u09b7\u09a3\u09b6\u09c2\u09a8\u09cd\u09af \u0993 \u09ac\u09be\u09df\u09c1\u09a8\u09bf\u09b0\u09c1\u09a6\u09cd\u09a7 \u09aa\u09bf\u09b8\u09cd\u099f\u09a8 \u09ac\u09bf\u09a8\u09be \u09ac\u09be\u09a7\u09be\u09df \u099a\u09b2\u09be\u099a\u09b2 \u0995\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u09aa\u09bf\u09b8\u09cd\u099f\u09a8\u099f\u09bf<\/p>\n

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