5Chapitre 1Introduction à la thermody-namique1.1. Le champ d’étude de la thermodynamiqueLa thermodynamique a pour objet l’étude de la matière (gaz, liquides, solides...) et lestransformations qu’elle subit. Ce sont en particulier les transferts thermiques (température)et mécaniques (par exemple compression) qui sont responsables de ces transformations detempérature, pression, volume ou changements de phase.1.1.1. HistoriqueLa première expérience réalisée en thermodynamique n’est pas récente, puisque 400 000ans avant notre ère l’Homo-erectus a appris à maîtriser le feu... Mais l’utilisation du feuest restée pendant très longtemps la seule application de la thermodynamique. Les progrèstechniques furent pourtant nombreux en mécanique ces derniers millénaires : les égyptiens ontpar exemple développé des systèmes de levage; les observations astronomiques ont motivé denombreuses recherches.Les premiers développements de la thermodynamique furent expérimentaux : l’observationd’une casserole chau¤ant sur le feu permet de constater que la vapeur est capable de pousserle couvercle pour évacuer la surpression. Il faut attendre 1629 pour voir apparaître la premièreieµmeturbine à vapeur. Le grand essor a lieu à la …n du XV III siècle et est lié aux débuts deieµmela révolution industrielle. Au XIX , l’utilisation plus rationnelle de l’énergie rend le déve-loppement de la thermodynamique primordial : il devient nécessaire de ne plus être tributairedes aléas ...
.- @e^mfqob . Fkqolar‘qflk Ý i^ qebojlavk^jfnrb I l_gb‘qfc bpq f‘f ab ‘^i‘ribo i^ clo‘b abp ‘el‘p pro i^ m^olf bk clk‘qflk ab i^ sfqbppb abp m^oqf‘ribp mlro bk aæarfob bkprfqb i^ mobppflk+ Mlro ‘bi^) ‘lkpfaæolkp rkb p ^‘b d −→ S %slfo roc drob .+.& rq _ i‘ribo i^ s^of^qflk ab i^ nr^kqfqæ ab jlrsbjbkq molslnræb pro i^ 8 fi c^ a ^ loa ‘^ m^oqf‘rib → m^%oobrmkoæppbbrkiqæ‘belp‘r)omi^rfpd‘rljmqboibklj_obab‘el‘ppbmolarfp^ikbpqÝmb‘k^ar^pkbqa d b t pp‘reoli‘^p − proc^‘b dS ob .+.&+ I^ clo‘b pr_fb m^o ibp m^oqf‘r bpq − F → = dp − to → t dt a ^moåp ib qeæloåjb ab i^ nr^kqfqæ ab jlrsbjbkq) ^sb‘ dp − t → ot i^ s^of^qflk ab i^ nr^kqfqæ ab jlrsbjbkq qlq ib abp m^oqf‘ribp mbka^kq dt + Cfk^ibjbkq) i^ clo‘b pr_fb m^o i^ ^ m^olf bpq i lmmlpæb ab i^ clo‘b pr_fb m^o ibp m^oqf‘ribp %mofk‘fmb a ^‘qflk bq ab oæ^‘qflk&+ Ibp m^oqf‘ribp pr_fpp^kq rk ‘el‘ pro i^ m^olf plkq ibp m^oqf‘ribp pb aæmi^ä^kq prfs^kq (+ Oz ) ^sb‘ i^ sfqbppb v m pf i lk mobka ibp klq^qflkp ab i^ drob .+.+ Biibp obm^oqbkq bkprfqb a^kp i^ afob‘qflk ( − Oz ) ^sb‘ i^ sfqbppb v m + I^ s^of^qflk ab i^ nr^kqfqæ ab jlrsbjbkq ilop a rk pbri ‘el‘ bpq alk‘ d − p → = 2 ( mv m ) ( −−→ u z ) %0& Fi c^rq j^fkqbk^kq ‘ljmqbo ib klj_ob ab ‘el‘p pb molarfp^kq mbka^kq dt + Plfq n V i^ abkpfqæ m^oqf‘ri^fob+ Pbribp .,3 abp m^oqf‘ribp slkq a^kp i^ _lkkb afob‘qflk (+ Oz ) mlro ^iibo mbo‘rqbo i^ m^olf+ Ab mirp) mbka^kq dt ) ibp m^oqf‘ribp m^o‘lrobkq rkb afpq^k‘b l = v m dt 8 pbribp ibp m^oqf‘ribp pb pfqr^kq Ý rkb afpq^k‘b fkcæofbrob Ý l bq ^v^kq i^ _lkkb afob‘qflk slkq mbo‘rqbo i^ m^olf+ Fi v ^ alk‘ dN =16 n V ( ldS )=16 n V ( v m dtdS ) %1& m^oqf‘ribp mbo‘rq^kq i^ m^olf ab proc^‘b dS mbka^kq rk fkpq^kq dt + I^ s^of^qflk ab i^ nr^kqfqæ ab jlrsbjbkq qlq^ib pr_fb m^o ibp m^oqf‘ribp m^o qlrp ibp ‘el‘p ^v^kq br ifbr mbka^kq rk qbjmp dt plkq) ‘ljmqb qbkr abp obi^qflkp %0& bq %1& 7 dp − to → t = 2 ( mv m )16 n V ( v m dtdS ) ( −− u → z ) =13 n V mv 2 m dSdt ( −− u → z ) plfq rkb clo‘b − F → paroi → part = d − p → dt tot =13 n V mv 2 m dS ( −− u → z ) I^ clo‘b pr_fb m^o i^ m^olf bpq lmmlpæb 7 biib bpq alk‘ afofdæb prfs^kq u −→ z ) ‘ bpq*Ý*afob mbombkaf‘ri^fobjbkq Ý i^ m^olf bq sbop i buqæofbro+ Lo i^ mobppflk ‘fkæqfnrb bpq i^ clo‘b pr_fb m^o i^ m^olf m^o rkfqæ ab proc^‘b 7 P = FS =31 n V mv 2 m d Bk oæ^ifqæ) a^kp ib ‘^p ar jlaåib > ab i^ drob.+.) klrp ^roflkp l_qbkr ib oæpriq^q prfs^kq 7 P =13 n V mu 2 %2& ^sb‘ u i^ sfqbppb nr^ao^qfnrb jlvbkkb+ I^ pfjmif ‘^qflk ar jlaåib > bk jlaåib ? obsfbkq Ý ‘lkclkaob i^ sfqbppb jlvbkkb ^sb‘ i^ sfqbppb nr^ao^qfnrb jlvbkkb+ I^ obi^qflk %2& p æ‘ofq æd^ibjbkq) bk klq^kq V ib slirjb ab d^w ‘lkpfaæoæ bq N ib klj_ob ab m^oqf‘ribp qlq^i a^kp ‘b slirjb %^sb‘ n V = NV & 7 P V =31 Nmu 2 %3& I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J^kp+
.0 j^op /--1
Pb‘qflk .+0 I^qeælofb ‘fkæqfnrb ar d^w m^oc^fq jlkl^qljfnrb .. Obj^onrb .+0 A ^moåp i^ obi^qflk %2& ab i^ mobppflk ‘fkæqfnrb) fi ^mm^o^ëq nrb ‘bqqb mobppflk bpq molmloqflkkbiib Ý i^ abkpfqæ m^oqf‘ri^fob ar d^w+ @bi^ pb ‘lkälfq ^fpæjbkq 7 p fi v ^ / clfp mirp ab m^oqf‘ribp) fi v ^ro^ / clfp mirp ab ‘el‘p) alk‘ i^ mobppflk alr_ib+ Ab jçjb) P bpq molmloqflkkbiib Ý i^ j^ppb abp m^oqf‘ribp 7 abp j^ppbp mirp fjmloq^kqbp cbolkq pr_fo abp clo‘bp mirp fjmloq^kqbp Ý i^ m^olf ilop ab ‘el‘p+ Bk k) i^ mobppflk bpq ^rppf molmloqflkkbiib Ý i^ sfqbppb ^r ‘^ abp m^oqf‘ribp+ ooæ
I^ mobppflk ^mm^o^ëq ‘ljjb rkb do^kabro j^‘olp‘lmfnrb 7 mlro jbprobo rkb mobppflk) fi pr§q ab jbprobo i^ clo‘b mobpp^kqb ar d^w p ^mmifnr^kq pro rkb proc^‘b S + Mlroq^kq i lofdfkb ab i^ mobppflk bpq _fbk jf‘olp‘lmfnrb 8 i^ obi^qflk P = (1 3) n V mu 2 obifb i^ mobppflk P j^‘olp‘lmfnrb %Ý d^r‘eb ab i æd^ifqæ& ^sb‘ abp do^kabrop jf‘olp‘lmfnrbp %Ý aolfqb ab i æd^ifqæ&+ Rkfqæp 7 A^kp ibp rkfqæp ar pvpqåjb fkqbok^qflk^i) i^ mobppflk p bumofjb bk M^p‘^i) klqæ P a 7 1 P a = 1 Nm − 2 J^fp ‘bqqb rkfqæ k bpq m^p ar qlrq ^a^mqæb ^ru mobppflkp ^j_f^kqbp 8 bk b bq) i^ mobppflk ^qjlpmeæofnrb Ý i^ proc^‘b ab i^ jbo bpq bk jlvbkkb ab 1 013 10 5 P a + Ib ^o lr i ^qjlpmeåob _ plkq ^ilop fkqolarfqp 7 1 bar = 10 5 P a 8 1 atm = 1 013 10 5 P a + .+0+1+ Aæ kfqflk ‘fkæqfnrb ab i^ qbjmæo^qrob I^ qbjmæo^qrob ‘fkæqfnrb a rk d^w m^oc^fq jlkl^qljfnrb bk ænrfif_ob qebojlavk^jfnrb pb aæ kfq ‘ljjb i^ jbprob ab i ækbodfb ‘fkæqfnrb jlvbkkb m^o ^qljb m^o i^ obi^qflk 7 ¿ 21 mv 2 À =32 B T k plfq bk‘lob 1 2 mu 2 =23 k B T %4& @b nrb pfdkf bnrb i^ qbjmæo^qrob bpq bk c^fq %Ý rkb ‘lkpq^kqb jriqfmif‘^qfsb 3 2 k B moåp& i ækbodfb ‘fkæqfnrb jlvbkkb abp ^qljbp+ k B bpq i^ ‘lkpq^kqb ab ?liqwj^kk 7 k B = 1 38 10 − 23 JK + I rkfqæ ab i^ qbjmæo^qrob bpq ib Hbisfk klqæb K + Obj^onrb .+1 I^ qbjmæo^qrob kb mbrq alk‘ m^p çqob kæd^qfsb) ‘^o rkb ækbodfb ‘fkæqfnrb kæd^qfsb k bpq m^p mlppf_ib+ Fi k bpq m^p klk mirp mlppf_ib a ^qqbfkaob ib wæol ^_plir % T = 0 K &) ‘b nrf pfdkf bo^fq nrb qlrp ibp ^qljbp plkq m^oc^fqbjbkq fjjl_fibp 7 i^ qbjmæo^qrob jfkfj^ib ^‘qrbiibjbkq ^qqbfkqb bpq 10 − 6 K + Obj^onrb .+2 >qqbkqflk) lk afq Hbisfk ) bq klk m^p abdoæ Hbisfk ffi Fi bpq qlrqbclfp rprbi a rqfifpbo ibp abdoæp @bipfrp %klqæp ◦ C &+ Rk æ‘^oq ab 1 ◦ C ‘loobpmlka Ý rk æ‘^oq ab 1 K 8 pbri ib wæol bpq aæ‘^iæ 7 0 ◦ C ‘loobpmlka Ý 273 15 K + I^ ‘lksbopflk bpq alk‘ 7 T ◦ C = T K − 273 15 I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J ^kp+ .0 j^op /--1
./ @e^mfqob . Fkqolar‘qflk Ý i^ qebojlavk^jfnrb .+0+2+ Bnr^qflk a æq^q a rk DMJ I^ obi^qflk %3& P V =31 Nmu 2 obifb i^ mobppflk Ý i^ sfqbppb nr^ao^qfnrb jlvbkkb+ I^ obi^qflk %4& 21 mu 2 =23 k B T obifb i^ qbjmæo^qrob Ý i^ sfqbppb nr^ao^qfnrb jlvbkkb+ Fi bpq ^ilop mlppf_ib a bk aæarfob rkb obi^qflk bkqob i^ qbjmæo^qrob bq i^ mobppflk 7 u 2 = 3 P V = 3 k B T N m m plfq P V = N k B T %5& nrf bpq i ænr^qflk a ^q ar d^w m^oc^fq jlkl^qljfnrb+ æq Obj^onrb .+3 I^ obi^qflk %5& bpq ^mmbiæb ænr^qflk a æq^q m^o‘b nr biib obifb ibp m^o^jåqobp a æq^q P ) V ) N bq T + Rkb ^rqob æ‘ofqrob ab i ænr^qflk a æq^q ar d^w m^oc^fq bpq plrsbkq rqfifpæb+ @ljjb N ) klj_ob ab m^oqf‘ribp) bpq qoåp do^ka %dækæo^ibjbkq ab i loaob ab 10 23 & bq k B qoåp mbqfq %ab i loaob ab 10 − 23 &) fi bpq mirp mo^qfnrb a rqfifpbo ibp do^kabrop R ) ‘lkpq^kqb abp d^w m^oc^fqp) bq n nr^kqfqæ ab j^qfåob) aæ kfbp ab i^ j^kfåob prfs^kqb+ Plfq a ^_loa N a i^ ‘lkpq^kqb a >sld^aol 7 N a = 6 02 10 23 %‘lkpq^kqb a >sld^aol aæ kfb a^kp ib pb‘lka^fob&+ Lk klqb n = NN a i^ nr^kqfqæ ab j^qfåob bumofjæb bk jlibp %pvj_lib mol & 8 lk klqb R = k B N a i^ ‘lkpq^kqb abp d^w m^oc^fqp %bk JK − 1 mol − 1 & 7 R = 8 314 JK − 1 mol − 1 I ænr^qflk ar d^w m^oc^fq absfbkq ^ilop 7 P V = nRT %6& Obj^ b .+4 Lk m^oib m^oclfp ab klj_ob ab jlibp ^r ifbr ab nr^kqfqæ ab j^qfåob onr mlro aæpfdkbo n ) ‘b nrf rk qbojb fjmolmob 7 ‘bi^ pbo^fq ænrfs^ibkq) m o bubjmib) Ý m^oibo ab ^ klj_ob ab jåqobp mlro aæpfdkbo rkb afpq^k‘b ffi
.+0+3+ Bkbodfb fkqbokb a rk DMJ I ækbodfb fkqbokb klqæb U a rk pvpqåjb bpq i^ pljjb ab qlrqbp ibp ækbodfbp jf‘olp‘lmfnrbp ar pvpqåjb 7 ibp ækbodfbp mlqbkqfbiibp a fkqbo^‘qflk jliæ‘rib*jliæ‘rib) ibp ækbodfbp a fkqbo^‘* qflk ^qljb*^qljb ^r pbfk ab ‘e^nrb jliæ‘rib ^fkpf nrb ibp ækbodfbp ‘fkæqfnrbp a ^dfq^qflk qebojfnrb+ Lo) m^o evmlqeåpb a^kp ib jlaåib ar d^w m^oc^fq) ibp ækbodfbp a fkqbo^‘qflkp bkqob abru m^oqf‘ribp plkq kriibp %slfo m^o^do^meb .+0+/&+ Ab mirp) pf ib d^w bpq jlkl^qljfnrb) fi .0 j^op /--1 I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J^kp+
Pb‘qflk .+1 Klqflk ab mevpfnrb pq^qfpqfnrb ab ?liqwj^kk %E+M+& .0 k bufpqb m^p a fkqbo^‘qflk ^qljb*^qljb ^r pbfk a rkb m^oqf‘rib+ I ækbodfb fkqbokb U a rk pvp* qåjb ab N m^oqf‘ribp bq alk‘ pfjmibjbkq i^ pljjb abp ækbodfbp ‘fkæqfnrbp ab ‘e^‘rkb abp ^ f‘ribp 7 m oq N U = X 21 mv i 2 i =1 = N ¿ 21 mv 2 À 1 µ 2 mu 2 ¶ = N plfq U = 3 N k T = 3 n 2 B 2 RT %.-& Obj^onrb .+5 T bpq rk m^o^jåqob a æq^q fkqbkpfc bq n rk m^o^jåqob a æq q buqbkpfc 7 U bpq ^ alk‘ rk m^o^jåqob a æq^q buqbkpfc+ Obj onrb .+6 > ‘e^nrb qbjmæo^qrob T ‘loobpmlka rkb ækbodfb fkqbokb U + I ækbodfb fk* ^ qbokb a rk d^w m^oc^fq jlkl^qljfnrb kb aæmbka m^p ab i^ mobppflk+
.+1+ Klqflk ab mevpfnrb pq^qfpqfnrb ab ?liqwj^kk %E+M+& @b m^o^do^meb bpq qo fqæ bk ‘lrop ^ .+2+ Ibp ^rqobp rfabp bq me^pbp ‘lkabkpæbp .+2+.+ Aæ kfqflkp .+2+.+.+ I^ mobppflk Mi^älkp rkb m^olf pæm^o^qof‘b bkqob ib d^w bq ib sfab+ I^ mobppflk bpq aæ kfb ‘ljjb æq^kq i^ clo‘b m^o rkfqæ ab proc^‘b p ^mmifnr^kq pro ‘bqqb m^olf bq ‘oææb m^o ib d^w+ Obj^onrb .+.->qqbkqflk ffi Ab j^kfåob dækæo^ib) i^ mobppflk k bpq m^p ifæb rkfnrbjbkq ^ru ‘el‘p abp m^oqf‘ribp pro i^ m^olf) ‘ljjb ‘ bpq i^ ‘^p mlro ib d^w m^oc^fq+ @ljjb klr ^iilkp p ib slfo a^kp i^ prfqb ab ‘b ‘e^mfqob) i^ mobppflk bpq i^ pljjb ab i^ mobppflk ‘fkæqfnrb %arb ^ ru ‘el‘p& Ý i^nrbiib lk ^glrqb i^ mobppflk jliæ‘ri^fob %arb Ý i fkqbo^‘qflk abp m^oqf‘ribp bkqob biibp) fkqbo^‘qflk nrf ^ ^rppf rkb fk rbk‘b fkafob‘qb pro i^ clo‘b ab mlrppæb p ^mmifnr^kq pro i^ m^olf %slfo m^o bubjmib m^o^do^meb .+2+0+. &+
I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J ^kp+
.0 j^op /--1
@e^mfqob . Fkqolar‘qflk Ý i^ qebojlavk^jfnrb
.1 .+2+.+/+ I^ qbjmæo^qrob Mlro ib d^w m^oc^fq) i^ qbjmæo^qrob bpq molmloqflkkbiib Ý i ækbodfb ‘fkæqfnrb jf‘olp‘lmfnrb jlvbkkb a rkb m^oqf‘rib+ @ bpq ib ‘^p æd^ibjbkq mlro ibp ^rqobp rfabp+ .+2+.+0+ I ækbodfb fkqbokb I ækbodfb fkqbokb) klqæb U ) bpq i^ pljjb ab qlrqbp ibp ækbodfbp jf‘olp‘lmfnrbp ^r pbfk ar pvpqåjb 7 * ibp ækbodfbp ‘fkæqfnrbp a ^dfq^qflk qebojfnrb 8 * ibp ækbodfbp a fkqbo^‘qflk jliæ‘rib*jliæ‘rib 8 * ibp ækbodfbp a fkqbo^‘qflk ^qljb*^qljb r pbfk ab ‘e^nrb jliæ‘rib+ ^ @ljjb fi ^ æqæ sr moæ‘æabjjbkq) rk d^w m^oc^fq jlkl^qljfnrb kb ‘lkqfbkq ^r‘rkb clo‘b a fkqbo^‘qflk fkqbokb 7 i ækbodfb fkqbokb U kb aæmbka alk‘ nrb ab i^ qbjmæo^qrob+ M^o ‘lkqob) mlro rk rfab nrbi‘lknrb) fi c^rq ^glrqbo ibp ækbodfbp a fkqbo^‘qflk bkqob ibp af æobkqbp m^oqf* ‘ribp 8 i ækbodfb fkqbokb U aæmbka alk‘ ^rppf ar slirjb V ar pvpqåjb+ Bk b bq) pf ib slirjb a rk pvpqåjb V bpq jlaf æ) i^ afpq^k‘b jlvbkkb bkqob ibp m^oqf‘ribp bpq jlaf æb) ‘b nrf ‘e^kdb alk‘ ibp ækbodfbp a fkqbo^‘qflk) alk‘ i ækbodfb fkqbokb U + .+2+.+1+ I^ ‘^m^‘fqæ ‘^ilof nrb Ý slirjb ‘lkpq^kq Bk ‘lk‘irpflk ab ‘b nrf sfbkq a çqob sr 7 * mlro rk d^w m^oc^fq jlkl^qljfnrb 7 U ( T ) 8 * mlro rk rfab nrbi‘lknrb 7 U ( T V ) + I^ ‘^m^‘fqæ ‘^ilofnrb Ý slirjb ‘lkpq^kq ) klqæb C V ) bpq ^ilop aæ kfb 7 C µ ∂∂UT ¶ V %..& V = I^ ‘^m^‘fqæ ‘^ilof nrb Ý slirjb ‘lkpq^kq bpq i ækbodfb Ý ^mmloqbo ^r pvpqåjb mlro ^rd* jbkqbo p^ qbjmæo^qrob a rk Hbisfk) nr^ka i bumæofbk‘b bpq b b‘qræb Ý slirjb ‘lkpq^kq+ Obj^onrb .+.. I fkaf‘b V bpq fkafpmbkp^ ib a^kp i^ aæ kfqflk %..&+ Bk b bq) i^ klq^qflk _ ( ∂U∂T ) p^kp fkaf‘b kb sbrq ofbk afob ffi Rkb aæofsæb m^oqfbiib %lr aæofsæb olkab & pfdkf b nrb i lk aæofsb U m^o o^mmloq Ý T bk d^oa^kq ibp ^rqobp do^kabrop ‘lkpq^kqbp) bk m^oqf‘rifbo f‘f bk d^oa^kq V bq P ‘lkpq^kqbp+ Lo Ý ‘^rpb ab i ænr^qflk a æq^q nrf bufpqb mlro qlrq pvpqåjb %‘ljjb i ænr^qflk ar d^w m^oc^fq m^o bubjmib&) ibp m^o^jåqobp P ) T bq V plkq obifæp+ Aæofsbo U m^o o^mmloq Ý T pfdkf b nrb i lk ‘^i‘rib i^ s^of^qflk ab U nr^ka lk c^fq s^ofbo T 8 lo fi bpq fjmlppf_ibp ab c^fob s^ofbo T bk d^oa^kq P bq V ‘lkpq^kqp Ý i^ clfp) Ý ‘^rpb ab i ænr^qflk a æq^q+ Fi c^rq ^ilop moæ‘fpbo pf ‘ bpq P lr pf ‘ bpq V nrb i lk d^oab ‘lkpq^kq nr^ka lk aæofsb m^o o^mmloq Ý T 7 µ ∂∂UT ¶ V 6 = µ ∂∂TU ¶ P %./& Ib qbojb ab d^r‘eb ab i bumobppflk %./& pfdkf b nrb i lk jbprob i^ s^of^qflk ab U nr^ka T s^ofb bk d^oa^kq V ‘lkpq^kq 7 P s^ofb ^ilop fjmif‘fqbjbkq %‘^o P = f ( T V ) &+ Ib pb‘lka jbj_ob ab i bumobppflk %./& pfdkf b nrb i lk æqrafb i^ s^of^qflk ab U nr^ka T s^ofb bk d^oa^kq P ‘lkpq^kq %bq alk‘ V s ofb fjmif‘fqbjbkq&+ Bumæofjbkq^ibjbkq) mlro æs^irbo ib mobjfbo ^ qbojb) fi c^rao^fq ‘e^r bo ib pvpqåjb a^kp rk oæ‘fmfbkq ^ru m^olfp ofdfabp %alk‘ V = cte 7 m^o bubjmib a^kp rk ^rql‘rfpbro& 8 i^ mobppflk ^rdjbkqbo^fq ^ilop mol_^_ibjbkq+ Mlro æs^irbo ib pb‘lka qbojb) fi c^rao^fq ‘e^r bo ib pvpqåjb Ý mobppflk ‘lkpq^kqb) alk‘ m^o bubjmib bk ib .0 j^op /--1 I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J^kp+
Pb‘qflk .+2 Ibp ^rqobp rfabp bq me^pbp ‘lkabkpæbp .2 mi^ä^kq a^kp rkb bk‘bfkqb æi^pqfnrb mi^‘æb a^kp i ^qjlpmeåob ab mobppflk ‘lkpq^kqb 7 fi bpq mlppf_ib nrb ib slirjb ^rdjbkqb ^ilop ilop ar ‘e^r ^db+ A^kp ib ‘^p ar d^w m^oc^fq jlkl^qljfnrb) ‘ljjb U = (3 2) nRT ) ^ilop 7 C V ( GP M ) = µ ∂∂TU ¶ V =23 nR Lk mbrq æd^ibjbkq aæ kfo rk C V j^ppfnrb klqæ c v nrf bpq ib C V m^o rkfqæ ab j^ppb 7 C V c v = m bq rk C V jli^fob ) nrf bpq rk C V m^o jlib klqæ C V m 7 C V m = C V n Rkfqæp 7 * C V bpq bk Glrib m^o Hbisfk % JK − 1 & 8 * c v bpq bk JK − 1 kg − 1 8 * C V m bpq bk JK − 1 mol − 1 %jçjb rkfqæ nrb R &+ A^kp ib ‘^p ar d^w m^oc^fq jlkl^qljfnrb 7 C V m ( GP M ) = (3 2) R .+2+/+ Ibp d^w m^oc^fqp mliv^qljfnrbp Ibp evmlqeåpbp ar d^w m^oc^fq mliv^qljfnrb plkq ibp prfs^kqbp 7 fi k v ^ m^p a fkqbo^‘qflk jliæ‘rib*jliæ‘rib 8 ibp jliæ‘ribp plkq ‘lkpfaæoæbp mlk‘qrbiibp bq i^ afpqof rqflk abp sfqbppbp bpq _ fplqolmb+ M^o ‘lkqob) fi v ^ abru ^qljbp m^o jliæ‘rib 7 fi c^rq alk‘ qbkfo ‘ljmqb ab i fkqbo^‘qflk ^qljb*^qljb ^r pbfk ab i^ jliæ‘rib+ Obmobklkp ^ilop ibp afsbop oæpriq^qp ar d^w m^oc^fq jlkl^qljfnrb mlro ibp dækæo^ifpbo ^r d^w m^oc^fq mliv^qljfnrb+ I^ mobppflk ‘fkæqfnrb %arb ^ru ‘el‘p pro i^ m^olf& bpq qlrglrop 7 = 1 n mu 2 P 3 V ^ qbj ^ ‘fkæqfnrb bpq qlrglrop aæ kfb m^o 7 I mæo qrob 21 mu 2 =32 k B T Fi c^rq pfjmibjbkq obj^onrbo nrb m bpq i^ j^ppb a rkb jliæ‘rib %bq klk m^p a rk ^qljb&+ I^ ilf ar d^w m^oc^fq jlkl^qljfnrb pb dækæo^ifpb alk‘ m^oc^fqbjbkq Ý qlrp ibp d^w m^o* c^fqp ) jçjb mliv^qljfnrbp 7 P V = nRT M^o ‘lkqob) a^kp i ækbodfb fkqbokb) fi c^rq ^glrqbo abp clojbp a ækbodfb klrsbiibp m^o o^mmloq ^r d^w m^oc^fq jlkl^qljfnrb arb Ý i^ moæpbk‘b abp ^qljbp a^kp ‘e^nrb jliæ‘rib %ækbodfbp ‘fkæqfnrbp ab olq^qflk ab i^ jliæ‘rib pro biib jçjb bq ækbodfbp a fkqbo^‘qflkp bkqob ibp ^qljbp&+ Lk ^ajbq nrb i lk ^ qlrglrop rkb obi^qflk ab i^ clojb U = nC V m T I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J ^kp+