mQ"ekxfrdh (Heat & Thermodynamics) PDF

vè;k; 11 mQ"ekxfrdh 11.1 Hkwfedk fiNys vè;k; esa geus nzO;ksa osQ rkih; xq.kksa dk vè;;u fd;kA bl vè;k; esa ge mu fu;eksa dk...

vè;k; 11 mQ"ekxfrdh 11.1 Hkwfedk fiNys vè;k; esa geus nzO;ksa osQ rkih; xq.kksa dk vè;;u fd;kA bl vè;k; esa ge mu fu;eksa dk vè;;u djsaxs tks Å"eh; ÅtkZ dks fu/kZfjr djrs gSaA ge mu izfØ;kvksa dk vè;;u djsaxs ftuesa dk;Z mQ"ek esa ifjofrZr gksrk gS] rFkk foykser% mQ"ek Hkh dk;Z esa ifjofrZr gksrh gS A 'khr ½rq esa tc ge gFksfy;ksa 11- 1 Hkwfedk dks ijLij jxM+rs gSa rks gesa xjeh dh vuqHkwfr gksrh gS D;ksafd bl izfØ;k esa 11- 2 rkih; lkE; fd;k x;k dk;Z mQ"ek mRiUu djrk gS A blosQ foijhr] Hkki batu esa ok"i dh 11- 3 mQ"ekxfrdh dk 'kwU; dksfV mQ"ek dk mi;ksx ykHkizn dk;Z dks laiUu djus esa vFkkZr~ fiLVu dks xfr nsus esa gksrk gS ftlosQ ifj.kkeLo:i jsyxkM+h osQ ifg, ?kwers gSaA fu;e HkkSfrdh esa mQ"ek] rki] dk;Z vkfn dh vo/kj.kkvksa dks vf/d 11- 4 mQ"ek] vkarfjd mQtkZ rFkk dk;Z lko/kuhiwod Z ifjHkkf"kr djus dh vko';drk iM+rh gS A ,sfrgkfld :i ls mQ"ek 11- 5 mQ"ekxfrdh dk izFke fu;e dh lVhd vo/kj.kk rd igq¡pus osQ fy, i;kZIr le; yxk A vk/qfud vo/kj.kk osQ iwoZ mQ"ek dks ,sls lw{e vn`'; rjy osQ :i esa le>k x;k tks fdlh inkFkZ 11- 6 fof'k"V mQ"ek /kfjrk osQ ja/zksa esa Hkjk jgrk gS A xje o BaMs fiaMksa osQ ikjLifjd laioZQ esa vkus ij ;g rjy 11- 7 mQ"ekxfrdh; voLFkk pj rFkk (ftls oSQykWfjd dgrs Fks) BaMs fiaM ls vis{kkÑr xje fiaM esa cgus yxrk gS ! voLFkk dk lehdj.k ;g fcyoqQy oSlk gh gS tSlk ml le; gksrk gS tc fHkUu&fHkUu m¡Qpkb;ksa rd 11- 8 mQ"ekxfrdh; izØe ikuh ls Hkjh nks Vafd;ksa dks ,d {kSfrt uy ls tksM+ fn;k tkrk gS A ty dk cgko ml le; rd fujarj cuk jgrk gS tc rd nksuksa Vafd;ksa esa ty osQ ry leku 11- 9 mQ"ekxfrdh dk f}rh; fu;e u gks tk,¡A blh osQ leku mQ"ek dh ^oSQykWfjd* /kj.kk esa mQ"ek ml le; rd 11- 10 mRØe.kh; o vuqRØe.kh; izØe izokfgr gksrh jgrh gS tc rd fd ^oSQykWfjd ry* (vFkkZr~ rki) leku ugha 11- 10 dkuksZ batu gks tkrs A blh chp] mQ"ek dks mQtkZ osQ :i esa dfYir djus dh vk/qfud vo/kj.kk lkjka'k osQ dkj.k blosQ (mQ"ek osQ) rjy Lo:i dks udkj fn;k x;k A bl laca/ esa fopkj.kh; fo"k; 1798 esa csatkfeu FkkWelu (ftUgsa dkmUV jEiQksMZ Hkh dgrs gSa) us ,d egRoiw.kZ vH;kl iz;ksx Hkh fd;k A bUgksaus ik;k fd ihry dh rksi esa Nsn djrs le; bruh vf/d mQ"ek mRiUu gksrh gS fd mlls ikuh mcy ldrk gS A blls vf/d egRoiw.kZ rF; ;g izkIr gqvk fd iz;ksx esa mRiUu mQ"ek dk ifjek.k ml dk;Z ij fuHkZj djrk Fkk tks ?kksM+s fMªy dks ?kqekus esa djrs Fks u fd fMªy osQ iSusiu ij A oSQykWfjd Lo:i osQ vuqlkj vf/d iSuh fMªy dks ja/zksa ls vf/d mQ"ek rjy ckgj fudkyuk pkfg,] fdarq iz;ksx esa ;g lgh ugha ik;k x;k A izs{k.kksa dh lcls vf/d LokHkkfod O;k[;k ;g Fkh fd mQ"ek mQtkZ dk gh ,d :i gS rFkk iz;ksx ls Hkh ;g izekf.kr gks x;k fd mQtkZ ,d :i ls nwljs :i esa vFkkZr~ dk;Z ls mQ"ek esa :ikarkfjr gks tkrh gS A 2024-25 238 HkkSfrdh mQ"ekxfrdh HkkSfrdh dh og 'kk[kk gS tks mQ"ek rFkk rki esa Hkjh dksbZ xSl mQ"ekxfrd :i ls rc lkE;koLFkk esa gksxh dh vo/kj.kk ,oa mQ"ek osQ vU; izdkj dh mQtkZvksa esa varjk& tc mlosQ nkc] vk;ru] rki] nzO;eku osQ ifjek.k rFkk laxBu :ikUrj.k dk foospu djrh gS A mQ"ekxfrdh ,d LFkwy foKku le; osQ lkFk ifjofrZr u gksa A gS] D;ksafd ;g fdlh fudk; dh LFkwy izÑfr ij fopkj djrh gS u fd nzO; dh vkf.od lajpuk ij A okLro esa] blls lacaf/r vo/kj.kkvksa rFkk fu;eksa dk izfriknu 19oha 'krkCnh esa ml le; gqvk Fkk tc nzO; osQ vkf.od Lo:i dks n`us osQ fy, vkf.od fp=k izLrqr fd;k gS rFkkfi tgk¡ rd mQ"ekxfrdh dk laca/ gS] U fudk; dk osQoy ,d LFkwy pj gh gS A vkarfjd mQtkZ osQ laca/ esa ,d egRoiw.kZ rF; ;g gS fd ;g osQoy fudk; dh voLFkk ij fuHkZj djrh gS u fd bl ckr ij fd ;g voLFkk fdl izdkj izkIr gqbZ A fudk; dh vkarfjd mQtkZ U mQ"ekxfrdh; ^voLFkk pj* dk ,d mnkgj.k gS A bldk eku fudk; dh nh gqbZ voLFkk ij fuHkZj djrk gS u fd mlosQ bfro`fRRk (History) (vFkkZr~ ml fLFkfr rd igq¡pus osQ fy, vuqlj.k fd, x, iFk) ijA vr% fdlh xSl osQ fn, x, nzO;eku osQ fy, vkarfjd mQtkZ mldh fLFkfr ij fuHkZj djrh gS A ;g fLFkfr nkc] vk;ru o rki osQ fof'k"V ekuksa ls of.kZr gksrh fp=k 11-4 mQ"ek o dk;Z fdlh fudk; esa mQtkZ LFkkuakrj.k dh gS A ;g bl ckr ij fuHkZj ugha djrh fd xSl dh ;g fLFkfr nks fofHkUu fof/;k¡ gSa ftuls mldh vkarfjd mQtkZ esa fdl izdkj izkIr gqbZ A nkc] vk;ru] rki rFkk vkarfjd mQtkZ ifjorZu gksrk gS A (a) fudk; rFkk ifjos'k osQ chp fudk; (xSl) osQ mQ"ekxfrdh; voLFkk pj dgykrs gSa (vuqHkkx rkikarj osQ dkj.k mQ"ek dks mQtkZ osQ LFkkukarj.k osQ :i 11-7 ns[ksa) A ;fn xSl osQ vYiizHkkoh varjkf.od cyksa dh esa ifjHkkf"kr djrs gSa A (b) dk;Z mu lk/uksa (mnkgj.kkFkZ] fiLVu ls tqMs+ Hkkjksa dks mQij uhps djosQ fiLVu dks xfr mis{kk dj nsa rks xSl dh vkarfjd mQtkZ mlosQ v.kqvksa dh vusd nsuk) }kjk mRiUu mQtkZ dk LFkkukarj.k gS ftuesa rkikarj ;kn`fPNd xfr;ksa ls lac¼ xfrt mQtkZvksa osQ ;ksx osQ Bhd cjkcj lekfgr ugha gksrk A 2024-25 m"ekxfrdh 241 fdlh fudk; dh vkarfjd mQtkZ esa fdu mik;ksa ls ifjorZu 11-5 mQ"ekxfrdh dk izFke fu;e fd, tk ldrs gSa \ lqfo/k dh n`f"V ls iqu% dYiuk dhft, ge ;g ns[k pqosQ gSa fd fdlh fudk; dh vkarfjd mQtkZ U fd fp=k 11-4 osQ vuqlkj fudk; fdlh fn, x, nzO;eku dh nks fof/;ksa ls mQtkZ LFkkukarj.k osQ dkj.k ifjofrZr gks ldrh ,d xSl gS tks ,d fl¯yMj esa Hkjh gS ftlesa xfr'khy fiLVu gS A ;s fof/;k¡ gSa % mQ"ek rFkk dk;Z A dYiuk dhft, fd yxk gS A vuqHko ;g crkrk gS fd xSl dh voLFkk (rFkk bl ∆Q = ifjos'k }kjk fudk; dks nh xbZ mQ"ek izdkj mldh vkarfjd mQtkZ) ifjofrZr djus osQ nks mik; gksrs gSa A ,d mik; gS fd fl¯yMj dks ml fi.M osQ laioZQ esa j[ksa ∆W = fudk; }kjk ifjos'k ij fd;k x;k dk;Z tks xSl dh vis{kk mPp rki ij gS A rkikarj osQ dkj.k mQtkZ ∆U = fudk; dh vkarfjd mQtkZ esa ifjorZu (mQ"ek) xje fi.M ls xSl esa izokfgr gksxh A blls xSl dh mQtkZ laj{k.k osQ lkekU; fu;e esa ;g var£ufgr gS fd vkarfjd mQtkZ c V1 rks W > 0_ rFkk V2 < V 1 V2 dV V – γ +1 osQ fy, W < 0 gksrk gS A bldk rkRi;Z ;g gS fd lerkih; = fu;rkad × ∫ Vγ V1 = fu;rkad ×1– γ V1 izlkj esa xSl mQ"ek vo'kksf"kr djosQ oqQN dk;Z laikfnr djrh gS tcfd lerkih; laihMu esa xSl ij ifjos'k }kjk dk;Z gksrk fu;rkad 1 – 1 = × (11.15) gS rFkk mQ"ek dk fu"dklu gksrk gS A 1– γ V 2 γ – 1 V1 γ – 1 11-8.3 #¼ks"e izØe lehdj.k (11-14)] ls fu;rkad P1 V1 γ gS vFkok P2 V2 γ #¼ks"e izØe esa fudk; dks ifjos'k ls mQ"ek#¼ dj nsrs gSa  P2V2 γ P1V1 γ  1 iQyLo:i vo'kksf"kr ;k fu"dkflr mQ"ek 'kwU; gksrh gS A ∴ W= ×  γ-1 − γ−1  1 – γ  V2 V1  lehdj.k (11-1) ls irk pyrk gS fd xSl }kjk laikfnr dk;Z osQ iQyLo:i vkarfjd mQtkZ de gks tkrh gS (vkSj bl izdkj 1 µR (T1 – T2 ) vkn'kZ xSl osQ fy, mldk rki) A ;gk¡ ge fcuk miifÙk osQ = 1– γ [P2V2 – P1V1] = γ –1 (11-16) bl rF; dk mYys[k dj jgs gSa (ftldk vki mPp d{kkvksa esa vè;;u djsaxs) fd vkn'kZ xSl osQ fy, #¼ks"e izØe esa tSlk visf{kr gS] ;fn #¼ks"e izØe esa dk;Z xSl }kjk laiUu γ PV = fu;rkad (11-13) gksrk gS (W > 0)] rc lehdj.k (11-16) ls T2>T1 A blosQ tgk¡ γ xSl dh nks fof'k"V mQ"ekvksa (lkekU; vFkok eksyj)] foijhr] ;fn dk;Z xSl ij laikfnr gksrk gS (W < 0) rks] gesa fLFkj nkc ij fof'k"V mQ"ek Cp rFkk fLFkj vk;ru ij fof'k"V T2 > T1 izkIr gksrk gS] vFkkZr~ xSl dk rki c