NCERT Textbook - उष्मागतिकी Notes | EduRev

NCERT Hindi Textbooks (Class 6 to Class 12)

UPSC : NCERT Textbook - उष्मागतिकी Notes | EduRev

 Page 1


vè;k; 12
mQ"ekxfrdh
12-1 Hkwfedk
12-2 rkih; lkE;
12-3 mQ"ekxfrdh dk 'kwU; dksfV
fu;e
12-4 mQ"ek] vkarfjd mQtkZ rFkk dk;Z
12-5 mQ"ekxfrdh dk izFke fu;e
12-6 fof'k"V mQ"ek /kfjrk
12-7 mQ"ekxfrdh; voLFkk pj rFkk
voLFkk dk lehdj.k
12-8 mQ"ekxfrdh; izØe
12-9 mQ"ek batu
12-10 iz'khrd@mQ"ek iai
12-11 mQ"ekxfrdh dk f}rh; fu;e
12-12 mRØe.kh; o vuqRØe.kh; izØe
12-13 dkuksZ batu
lkjka'k
fopkj.kh; fo"k;
vH;kl
12.1 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
dks ijLij jxM+rs gSa rks gesa xjeh dh vuqHkwfr gksrh gS D;ksafd bl izfØ;k esa
fd;k x;k dk;Z mQ"ek mRiUu djrk gS A blosQ foijhr] Hkki batu esa ok"i dh
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
HkkSfrdh esa mQ"ek] rki] dk;Z vkfn dh vo/kj.kkvksa dks vf/d
lko/kuhiwoZd ifjHkkf"kr djus dh vko';drk iM+rh gS A ,sfrgkfld :i ls mQ"ek
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
osQ ja/zksa esa Hkjk jgrk gS A xje o BaMs fiaMksa osQ ikjLifjd laioZQ esa vkus ij ;g rjy
(ftls oSQykWfjd dgrs Fks) BaMs fiaM ls vis{kkÑr xje fiaM esa cgus yxrk gS !
;g fcyoqQy oSlk gh gS tSlk ml le; gksrk gS tc fHkUu&fHkUu m¡Qpkb;ksa rd
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
u gks tk,¡A blh osQ leku mQ"ek dh ^oSQykWfjd* /kj.kk esa mQ"ek ml le; rd
izokfgr gksrh jgrh gS tc rd fd ^oSQykWfjd ry* (vFkkZr~ rki) leku ugha
gks tkrs A
blh chp] mQ"ek dks mQtkZ osQ :i esa dfYir djus dh vk/qfud vo/kj.kk
osQ dkj.k blosQ (mQ"ek osQ) rjy Lo:i dks udkj fn;k x;k A bl laca/ esa
1798 esa csatkfeu FkkWelu (ftUgsa dkmUV jEiQksMZ Hkh dgrs gSa) us ,d egRoiw.kZ
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
Page 2


vè;k; 12
mQ"ekxfrdh
12-1 Hkwfedk
12-2 rkih; lkE;
12-3 mQ"ekxfrdh dk 'kwU; dksfV
fu;e
12-4 mQ"ek] vkarfjd mQtkZ rFkk dk;Z
12-5 mQ"ekxfrdh dk izFke fu;e
12-6 fof'k"V mQ"ek /kfjrk
12-7 mQ"ekxfrdh; voLFkk pj rFkk
voLFkk dk lehdj.k
12-8 mQ"ekxfrdh; izØe
12-9 mQ"ek batu
12-10 iz'khrd@mQ"ek iai
12-11 mQ"ekxfrdh dk f}rh; fu;e
12-12 mRØe.kh; o vuqRØe.kh; izØe
12-13 dkuksZ batu
lkjka'k
fopkj.kh; fo"k;
vH;kl
12.1 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
dks ijLij jxM+rs gSa rks gesa xjeh dh vuqHkwfr gksrh gS D;ksafd bl izfØ;k esa
fd;k x;k dk;Z mQ"ek mRiUu djrk gS A blosQ foijhr] Hkki batu esa ok"i dh
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
HkkSfrdh esa mQ"ek] rki] dk;Z vkfn dh vo/kj.kkvksa dks vf/d
lko/kuhiwoZd ifjHkkf"kr djus dh vko';drk iM+rh gS A ,sfrgkfld :i ls mQ"ek
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
osQ ja/zksa esa Hkjk jgrk gS A xje o BaMs fiaMksa osQ ikjLifjd laioZQ esa vkus ij ;g rjy
(ftls oSQykWfjd dgrs Fks) BaMs fiaM ls vis{kkÑr xje fiaM esa cgus yxrk gS !
;g fcyoqQy oSlk gh gS tSlk ml le; gksrk gS tc fHkUu&fHkUu m¡Qpkb;ksa rd
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
u gks tk,¡A blh osQ leku mQ"ek dh ^oSQykWfjd* /kj.kk esa mQ"ek ml le; rd
izokfgr gksrh jgrh gS tc rd fd ^oSQykWfjd ry* (vFkkZr~ rki) leku ugha
gks tkrs A
blh chp] mQ"ek dks mQtkZ osQ :i esa dfYir djus dh vk/qfud vo/kj.kk
osQ dkj.k blosQ (mQ"ek osQ) rjy Lo:i dks udkj fn;k x;k A bl laca/ esa
1798 esa csatkfeu FkkWelu (ftUgsa dkmUV jEiQksMZ Hkh dgrs gSa) us ,d egRoiw.kZ
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
mQ"ekxfrdh HkkSfrdh dh og 'kk[kk gS tks mQ"ek rFkk rki
dh vo/kj.kk ,oa mQ"ek osQ vU; izdkj dh mQtkZvksa esa varjk&
:ikUrj.k dk foospu djrh gS A mQ"ekxfrdh ,d LFkwy foKku
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`<+rkiwoZd
izekf.kr ugha fd;k x;k Fkk A mQ"ekxfrdh osQ o.kZu esa fudk;
osQ vis{kkÑr oqQN gh LFkwy pj lekfgr gksrs gSa tks lkekU;
vuqHko ij vk/kfjr gSa rFkk ftUgsa izR;{k :i esa ekik tk ldrk
gS A mnkgj.kkFkZ] fdlh xSl osQ lw{e o.kZu esa mldh jpuk djus
okys vxf.kr v.kqvksa osQ funsZ'kkadksa ,oa osxksa dk fu/kZj.k vko';d
gksrk gS A gkykafd xSlksa osQ v.kqxfr fl¼akr dk fooj.k cgqr foLr`r
ugha gS fiQj Hkh blesa v.kqvksa osQ osxks± dk fooj.k lekfgr gS A
blosQ foijhr fdlh xSl osQ mQ"ekxfrdh; fooj.k esa vkf.od
o.kZu iw.kZ :i ls udkj fn;k tkrk gS A mQ"ekxfrdh esa fdlh
xSl dh voLFkk nkc] vk;ru] rki] nzO;eku rFkk laxBu tSls
,sls LFkwy pjksa }kjk fu/kZfjr gksrh gS ftUgsa ge viuh bafnz;ksa ls
vuqHko djrs gSa vkSj eki ldrs gSa
*
A
;kaf=kdh ,oa mQ"ekxfrdh osQ chp Hksn vkiosQ efLr"d
esa HkyhHkkafr vk tkuk pkfg, A ;kaf=kdh esa gekjh #fp cyksa rFkk
cy vk?kw.kks± osQ izHkko esa xfr dj jgs d.kksa ,oa fi.Mksa esa gksrh
gS A mQ"ekxfrdh esa laiw.kZ fudk; dh xfr ij fopkj ugha fd;k
tkrk A bldh #fp fi.M dh vkafrjd LFkwy voLFkk esa gksrh
gS A tc canwd ls xksyh nkxrs gSa rc tks ifjorZu gksrk gS og
xksyh dh ;kaf=kd voLFkk  (fo'ks"kdj xfrt mQtkZ) esa ifjorZu
gksrk gS] mlosQ rki esa ugha A tc xksyh ydM+h esa /¡ldj #d
tkrh gS rks xksyh dh xfrt mQtkZ mQ"ek esa :ikarfjr gks tkrh
gS ftlls xksyh rFkk mlosQ pkjksa vksj dh ydM+h dh lrgksa dk
rki ifjofrZr gks tkrk gS A rki xksyh dh vkarfjd xfr (tks
vO;ofLFkr gS) dh mQtkZ ls lacaf/r gksrk gS u fd xksyh dh
laiw.kZ xfr ls A
12-2 rkih; lkE;
;kaf=kdh esa lkE;koLFkk ls rkRi;Z gS fd fudk; ij usV cká
cy o cy vk?kw.kZ 'kwU; gSa A mQ"ekxfrdh esa lkE;koLFkk dk
vFkZ fHkUu lanHkZ esa n`f"Vxkspj gksrk gS % fudk; dh voLFkk dks
ge ml le; lkE;koLFkk esa dgrs gSa tc fudk; dks vfHky{kf.kr
djus okys LFkwy pj le; osQ lkFk ifjofrZr ugha gksrs A
mnkgj.kkFkZ] fdlh i;kZoj.k ls iw.kZr% mQ"ekjks/h can n`<+ ik=k
esa Hkjh dksbZ xSl mQ"ekxfrd :i ls rc lkE;koLFkk esa gksxh
tc mlosQ nkc] vk;ru] rki] nzO;eku osQ ifjek.k rFkk laxBu
le; osQ lkFk ifjofrZr u gksa A
dksbZ fudk; lkE;koLFkk esa gS fd ugha O;kid :i esa
;g pkjksa vksj osQ ifjos'k rFkk ml nhokj dh izÑfr ij fuHkZj
djrk gS tks fudk; dks ifjos'k ls i`Fko~Q djrh gS A dYiuk
dhft, fd nks xSlsa A o B nks fHkUu&fHkUu ik=kksa esa Hkjh gSa A
iz;ksx }kjk gesa irk gS fd fdlh xSl osQ fn, gq, nzO;eku osQ
nkc o rki dks mlosQ nks Lora=k pjksa osQ :i esa pquk tk ldrk
gS A eku yhft, fd xSlksa osQ nkc o vk;ru Øe'k% (P
A
, V
A
)
rFkk (P
B
, V
B
) gSa A dYiuk dhft, fd igys nksuksa fudk;
ikl&ikl gSa ijarq mUgsa fdlh #¼ks"e nhokj (,d mQ"ekjks/h
nhokj) }kjk ,d nwljs ls i`Fko~Q j[kk x;k gS A bl nhokj osQ
dkj.k mQtkZ (mQ"ek) ,d ik=k ls nwljs ik=k esa ugha tk ikrh
gS A fudk;ksa dks Hkh 'ks"k ifjos'k ls blh izdkj dh #¼ks"e nhokj
ls i`Fko~Q j[krs gSa A bl O;oLFkk dk vkjs[kh; fp=k.k ¹12-1(a)º
esa fn;k x;k gS A ;gk¡ ;g ik;k x;k gS fd (P
A
, V
A
) osQ fdlh
Hkh laHkkfor ;qXe dk eku (P
B
, V
B
) osQ fdlh Hkh laHko ;qXe
osQ eku osQ lkFk lkE;koLFkk esa gksxk A iqu% dYiuk dhft, fd
#¼ks"e nhokj dks ,d mQ"ek&ikFkZ&nhokj ls izfrLFkkfir dj
fn;k x;k gS & ;g nhokj (mQ"ek) mQtkZ dks ,d fudk; ls
nwljs fudk; esa tkus nsrh gS A ,slk djus esa ;g ns[kk x;k gS
fd fudk;ksa A o B osQ LFkwy pj Lor% ml le; rd ifjofrZr
gksrs gSa tc rd fd nksuksa fudk; lkE;koLFkk dh fLFkfr izkIr
ugha dj ysrs A blosQ i'pkr~ mudh voLFkk esa dksbZ ifjorZu
ugha gksrk gS A bl fLFkfr dks fp=k ¹12-1(b)º esa n'kkZ;k x;k
gS A eku yhft, fd nksuksa xSlksa osQ nkc o vk;ru laca/h pj
ifjofrZr gksdj Øe'k% (P
A
', V '
A
) rFkk (P
B
', V '
B
) gks tkrs gSa
rkfd A o B dh u;h voLFkk,¡ iqu% ,d&nwljs dh lkE;koLFkk
esa gks tkrh gSa
**
 A ,d fudk; ls nwljs fudk; esa vc vkSj mQtkZ
dk izokg ugha gksrk A ,slh fLFkfr esa ge dgrs gSa fd fudk;
A, fudk; B osQ lkFk rkih; lkE; esa gS A
nks fudk;ksa osQ eè; dh lkE;koLFkk dh fLFkfr dks D;k
vfHkyf{kr djrh gS \ vki vius vuqHko ls mÙkj dk vuqeku
yxk ldrs gSa A rkih; lkE; esa] nks fudk;ksa osQ rki leku gksrs
gSa A ge tkusaxs fd mQ"ekxfrdh esa rki dh vo/kj.kk rd oSQls
ig¡qprs gSa \ mQ"ekxfrdh dk 'kwU; dksfV dk fu;e bldh vksj
laosQr djrk gS A
* mQ"ekxfrdh esa vU; ,sls pj Hkh fufgr gksrs gSa tks gekjh bafnz;ksa dks brus lqLi"V ugha gksrs (mnkgj.kkFkZ] ,aVªkWih] ,aFkkYih (laiw.kZ mQ"ek)] vkfn ftuosQ fo"k; esa vki
mPp d{kkvksa esa i<+saxs)] ¯drq ;s lHkh LFkwy pj gSa A
** ;g vko';d ugha gS fd nksuksa pj  cnysa A ,slk izfrca/ksa ij fuHkZj djrk gS A mnkgj.k osQ fy,] ;fn xSl fLFkj vk;ru okys ik=k esa Hkjh gks rks rkih; lkE; osQ fy,
osQoy xSlksa osQ nkc dks ifjofrZr gksuk pkfg, A
309 m"ekxfrdh
Page 3


vè;k; 12
mQ"ekxfrdh
12-1 Hkwfedk
12-2 rkih; lkE;
12-3 mQ"ekxfrdh dk 'kwU; dksfV
fu;e
12-4 mQ"ek] vkarfjd mQtkZ rFkk dk;Z
12-5 mQ"ekxfrdh dk izFke fu;e
12-6 fof'k"V mQ"ek /kfjrk
12-7 mQ"ekxfrdh; voLFkk pj rFkk
voLFkk dk lehdj.k
12-8 mQ"ekxfrdh; izØe
12-9 mQ"ek batu
12-10 iz'khrd@mQ"ek iai
12-11 mQ"ekxfrdh dk f}rh; fu;e
12-12 mRØe.kh; o vuqRØe.kh; izØe
12-13 dkuksZ batu
lkjka'k
fopkj.kh; fo"k;
vH;kl
12.1 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
dks ijLij jxM+rs gSa rks gesa xjeh dh vuqHkwfr gksrh gS D;ksafd bl izfØ;k esa
fd;k x;k dk;Z mQ"ek mRiUu djrk gS A blosQ foijhr] Hkki batu esa ok"i dh
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
HkkSfrdh esa mQ"ek] rki] dk;Z vkfn dh vo/kj.kkvksa dks vf/d
lko/kuhiwoZd ifjHkkf"kr djus dh vko';drk iM+rh gS A ,sfrgkfld :i ls mQ"ek
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
osQ ja/zksa esa Hkjk jgrk gS A xje o BaMs fiaMksa osQ ikjLifjd laioZQ esa vkus ij ;g rjy
(ftls oSQykWfjd dgrs Fks) BaMs fiaM ls vis{kkÑr xje fiaM esa cgus yxrk gS !
;g fcyoqQy oSlk gh gS tSlk ml le; gksrk gS tc fHkUu&fHkUu m¡Qpkb;ksa rd
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
u gks tk,¡A blh osQ leku mQ"ek dh ^oSQykWfjd* /kj.kk esa mQ"ek ml le; rd
izokfgr gksrh jgrh gS tc rd fd ^oSQykWfjd ry* (vFkkZr~ rki) leku ugha
gks tkrs A
blh chp] mQ"ek dks mQtkZ osQ :i esa dfYir djus dh vk/qfud vo/kj.kk
osQ dkj.k blosQ (mQ"ek osQ) rjy Lo:i dks udkj fn;k x;k A bl laca/ esa
1798 esa csatkfeu FkkWelu (ftUgsa dkmUV jEiQksMZ Hkh dgrs gSa) us ,d egRoiw.kZ
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
mQ"ekxfrdh HkkSfrdh dh og 'kk[kk gS tks mQ"ek rFkk rki
dh vo/kj.kk ,oa mQ"ek osQ vU; izdkj dh mQtkZvksa esa varjk&
:ikUrj.k dk foospu djrh gS A mQ"ekxfrdh ,d LFkwy foKku
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`<+rkiwoZd
izekf.kr ugha fd;k x;k Fkk A mQ"ekxfrdh osQ o.kZu esa fudk;
osQ vis{kkÑr oqQN gh LFkwy pj lekfgr gksrs gSa tks lkekU;
vuqHko ij vk/kfjr gSa rFkk ftUgsa izR;{k :i esa ekik tk ldrk
gS A mnkgj.kkFkZ] fdlh xSl osQ lw{e o.kZu esa mldh jpuk djus
okys vxf.kr v.kqvksa osQ funsZ'kkadksa ,oa osxksa dk fu/kZj.k vko';d
gksrk gS A gkykafd xSlksa osQ v.kqxfr fl¼akr dk fooj.k cgqr foLr`r
ugha gS fiQj Hkh blesa v.kqvksa osQ osxks± dk fooj.k lekfgr gS A
blosQ foijhr fdlh xSl osQ mQ"ekxfrdh; fooj.k esa vkf.od
o.kZu iw.kZ :i ls udkj fn;k tkrk gS A mQ"ekxfrdh esa fdlh
xSl dh voLFkk nkc] vk;ru] rki] nzO;eku rFkk laxBu tSls
,sls LFkwy pjksa }kjk fu/kZfjr gksrh gS ftUgsa ge viuh bafnz;ksa ls
vuqHko djrs gSa vkSj eki ldrs gSa
*
A
;kaf=kdh ,oa mQ"ekxfrdh osQ chp Hksn vkiosQ efLr"d
esa HkyhHkkafr vk tkuk pkfg, A ;kaf=kdh esa gekjh #fp cyksa rFkk
cy vk?kw.kks± osQ izHkko esa xfr dj jgs d.kksa ,oa fi.Mksa esa gksrh
gS A mQ"ekxfrdh esa laiw.kZ fudk; dh xfr ij fopkj ugha fd;k
tkrk A bldh #fp fi.M dh vkafrjd LFkwy voLFkk esa gksrh
gS A tc canwd ls xksyh nkxrs gSa rc tks ifjorZu gksrk gS og
xksyh dh ;kaf=kd voLFkk  (fo'ks"kdj xfrt mQtkZ) esa ifjorZu
gksrk gS] mlosQ rki esa ugha A tc xksyh ydM+h esa /¡ldj #d
tkrh gS rks xksyh dh xfrt mQtkZ mQ"ek esa :ikarfjr gks tkrh
gS ftlls xksyh rFkk mlosQ pkjksa vksj dh ydM+h dh lrgksa dk
rki ifjofrZr gks tkrk gS A rki xksyh dh vkarfjd xfr (tks
vO;ofLFkr gS) dh mQtkZ ls lacaf/r gksrk gS u fd xksyh dh
laiw.kZ xfr ls A
12-2 rkih; lkE;
;kaf=kdh esa lkE;koLFkk ls rkRi;Z gS fd fudk; ij usV cká
cy o cy vk?kw.kZ 'kwU; gSa A mQ"ekxfrdh esa lkE;koLFkk dk
vFkZ fHkUu lanHkZ esa n`f"Vxkspj gksrk gS % fudk; dh voLFkk dks
ge ml le; lkE;koLFkk esa dgrs gSa tc fudk; dks vfHky{kf.kr
djus okys LFkwy pj le; osQ lkFk ifjofrZr ugha gksrs A
mnkgj.kkFkZ] fdlh i;kZoj.k ls iw.kZr% mQ"ekjks/h can n`<+ ik=k
esa Hkjh dksbZ xSl mQ"ekxfrd :i ls rc lkE;koLFkk esa gksxh
tc mlosQ nkc] vk;ru] rki] nzO;eku osQ ifjek.k rFkk laxBu
le; osQ lkFk ifjofrZr u gksa A
dksbZ fudk; lkE;koLFkk esa gS fd ugha O;kid :i esa
;g pkjksa vksj osQ ifjos'k rFkk ml nhokj dh izÑfr ij fuHkZj
djrk gS tks fudk; dks ifjos'k ls i`Fko~Q djrh gS A dYiuk
dhft, fd nks xSlsa A o B nks fHkUu&fHkUu ik=kksa esa Hkjh gSa A
iz;ksx }kjk gesa irk gS fd fdlh xSl osQ fn, gq, nzO;eku osQ
nkc o rki dks mlosQ nks Lora=k pjksa osQ :i esa pquk tk ldrk
gS A eku yhft, fd xSlksa osQ nkc o vk;ru Øe'k% (P
A
, V
A
)
rFkk (P
B
, V
B
) gSa A dYiuk dhft, fd igys nksuksa fudk;
ikl&ikl gSa ijarq mUgsa fdlh #¼ks"e nhokj (,d mQ"ekjks/h
nhokj) }kjk ,d nwljs ls i`Fko~Q j[kk x;k gS A bl nhokj osQ
dkj.k mQtkZ (mQ"ek) ,d ik=k ls nwljs ik=k esa ugha tk ikrh
gS A fudk;ksa dks Hkh 'ks"k ifjos'k ls blh izdkj dh #¼ks"e nhokj
ls i`Fko~Q j[krs gSa A bl O;oLFkk dk vkjs[kh; fp=k.k ¹12-1(a)º
esa fn;k x;k gS A ;gk¡ ;g ik;k x;k gS fd (P
A
, V
A
) osQ fdlh
Hkh laHkkfor ;qXe dk eku (P
B
, V
B
) osQ fdlh Hkh laHko ;qXe
osQ eku osQ lkFk lkE;koLFkk esa gksxk A iqu% dYiuk dhft, fd
#¼ks"e nhokj dks ,d mQ"ek&ikFkZ&nhokj ls izfrLFkkfir dj
fn;k x;k gS & ;g nhokj (mQ"ek) mQtkZ dks ,d fudk; ls
nwljs fudk; esa tkus nsrh gS A ,slk djus esa ;g ns[kk x;k gS
fd fudk;ksa A o B osQ LFkwy pj Lor% ml le; rd ifjofrZr
gksrs gSa tc rd fd nksuksa fudk; lkE;koLFkk dh fLFkfr izkIr
ugha dj ysrs A blosQ i'pkr~ mudh voLFkk esa dksbZ ifjorZu
ugha gksrk gS A bl fLFkfr dks fp=k ¹12-1(b)º esa n'kkZ;k x;k
gS A eku yhft, fd nksuksa xSlksa osQ nkc o vk;ru laca/h pj
ifjofrZr gksdj Øe'k% (P
A
', V '
A
) rFkk (P
B
', V '
B
) gks tkrs gSa
rkfd A o B dh u;h voLFkk,¡ iqu% ,d&nwljs dh lkE;koLFkk
esa gks tkrh gSa
**
 A ,d fudk; ls nwljs fudk; esa vc vkSj mQtkZ
dk izokg ugha gksrk A ,slh fLFkfr esa ge dgrs gSa fd fudk;
A, fudk; B osQ lkFk rkih; lkE; esa gS A
nks fudk;ksa osQ eè; dh lkE;koLFkk dh fLFkfr dks D;k
vfHkyf{kr djrh gS \ vki vius vuqHko ls mÙkj dk vuqeku
yxk ldrs gSa A rkih; lkE; esa] nks fudk;ksa osQ rki leku gksrs
gSa A ge tkusaxs fd mQ"ekxfrdh esa rki dh vo/kj.kk rd oSQls
ig¡qprs gSa \ mQ"ekxfrdh dk 'kwU; dksfV dk fu;e bldh vksj
laosQr djrk gS A
* mQ"ekxfrdh esa vU; ,sls pj Hkh fufgr gksrs gSa tks gekjh bafnz;ksa dks brus lqLi"V ugha gksrs (mnkgj.kkFkZ] ,aVªkWih] ,aFkkYih (laiw.kZ mQ"ek)] vkfn ftuosQ fo"k; esa vki
mPp d{kkvksa esa i<+saxs)] ¯drq ;s lHkh LFkwy pj gSa A
** ;g vko';d ugha gS fd nksuksa pj  cnysa A ,slk izfrca/ksa ij fuHkZj djrk gS A mnkgj.k osQ fy,] ;fn xSl fLFkj vk;ru okys ik=k esa Hkjh gks rks rkih; lkE; osQ fy,
osQoy xSlksa osQ nkc dks ifjofrZr gksuk pkfg, A
309 m"ekxfrdh
310 HkkSfrdh
12-3 mQ"ekxfrdh dk 'kwU; dksfV fu;e
dYiuk dhft, fd nks fudk; A o B ,d #¼ks"e nhokj ls
i`Fko~Q gSa A buesa ls izR;sd ,d rhljs fudk; C ls ,d lqpkyd
nhokj }kjk laioZQ esa gSa [fp=k 12-2(a)] A fudk;ksa dh voLFkk,¡
(vFkkZr~ muosQ LFkwy pj) rc rd ifjofrZr gksaxh tc rd A
o B nksuksa fudk; C osQ lkFk rkih; lkE; esa ugha vk tkrs gSa A
tc ,slk gks tk, rks dYiuk dhft, fd A o B osQ eè; dh
#¼ks"e nhokj ,d lqpkyd nhokj ls izfrLFkkfir dj nh tkrh
gS rFkk C dks A o B ls fdlh #¼ks"e nhokj ls i`Fko~Q dj fn;k
tkrk gS ¹fp=k 12-2(b)º A ,slk ns[kk tkrk gS fd A o B dh
voLFkk,¡ vc vkSj ugha cnyrha vFkkZr~ os nksuksa vc rkih;
lkE; esa gksrh gSa A ;g izs{k.k mQ"ekxfrdh osQ 'kwU; dksfV fu;e
dk vk/kj cuk A ;g fu;e crykrk gS fd ;fn nks fudk;
fdlh rhljs fudk; osQ lkFk i`Fko~Q&i`Fko~Q :i ls rkih;
lkE; esa gSa rks os ijLij Hkh rkih; lkE; esa gksrs gSa A ;gk¡
;g ckr è;ku esa j[kuh pkfg, fd mQ"ekxfrdh osQ izFke o
f}rh; fu;e dh vfHkO;fDr rFkk muosQ Øekadu osQ cgqr le;
ckn 1931 esa vkj-,p- iQkmyj us 'kwU; dksfV fu;e dk izfriknu
fd;k FkkA
'kwU; dksfV fu;e ls ;g laosQr feyrk gS fd tc nks fudk;
A o B ijLij rkih; lkE; esa gksrs gSa] rks ,slh dksbZ HkkSfrd jkf'k
gS tks nksuksa fudk;ksa osQ fy, leku eku j[krh gS A ;g mQ"ekxfrd
pj] ftldk eku rkih; lkE; okys fudk;ksa osQ fy, leku gksrk
gS] rki (T) dgykrk gS A vr% ;fn A o B lkE;koLFkk esa rhljs
fudk; C ls i`Fko~Q gSa rks T
A
 = T
C
 rFkkT
B
 = T
C
 A bldk rkRi;Z
;g gS fd T
A 
= T
B
 vFkkZr~ fudk; A o B Lo;a Hkh rkih; lkE;
esa gSa A
'kwU; dksfV fu;e osQ ekè;e ls geus fof/or rki dh
vo/kj.kk fodflr dh gS A gekjs lkeus iqu% ,d iz'u mRiUu
gksrk gS % fHkUu&fHkUu fiaMksa osQ rki osQ fy, ge vafdd ekuksa
dk fu/kZj.k oSQls djsa\ nwljs 'kCnksa esa] ge rki ekiØe oSQls
cuk,¡\ rkifefr bl ekSfyd iz'u ls laca/ j[krh gS ftlosQ
fo"k; esa ge vxys vuqHkkx esa vè;;u djsaxs A
fp=k 12-1 (a) (nks xSlksa osQ) fudk; A o B ,d #¼ks"e nhokj
ls i`Fko~Q gSa % bl nhokj ls mQ"ek vkj&ikj ugha tk ikrh A
(b) ;gh fudk; A o B ,d mQ"ek&ikFkZ nhokj ls i`Fko~Q
n'kkZ, x, gSa A ;g ,d pkyd nhokj gksrh gS ftlls mQ"ek
,d fudk; ls nwljs esa pyh tkrh gS A bl mnkgj.k esa
rkih; lkE; ;Fkksfpr le; esa izkIr gks tkrk gS A
12-4 mQ"ek] vkarfjd mQtkZ rFkk dk;Z
mQ"ekxfrdh osQ 'kwU; dksfV fu;e ls rki dh vo/kj.kk dh
mRifÙk gqbZ tks gekjs lkekU; Kku osQ vuqowQy gS A rki fdlh
fi.M dh m".krk dk |ksrd gS A tc nks fi.M mQ"eh; laioZQ
fp=k 12-2 (a) fudk; A o B tks ,d #¼ks"e nhokj ls i`Fko~Q gSa
tcfd buesa ls izR;sd ,d rhljs fudk; C ls ,d
lqpkyd nhokj }kjk laioZQ esa gS A (b) A o B osQ eè;
dh #¼ks"e nhokj dks fdlh lqpkyd nhokj ls izfrLFkkfir
fd;k x;k gS tcfd C dks A o B ls #¼ks"e nhokj ls
i`Fko~Q n'kkZ;k x;k gS A
(a)
(b)
(b)
(a)
Page 4


vè;k; 12
mQ"ekxfrdh
12-1 Hkwfedk
12-2 rkih; lkE;
12-3 mQ"ekxfrdh dk 'kwU; dksfV
fu;e
12-4 mQ"ek] vkarfjd mQtkZ rFkk dk;Z
12-5 mQ"ekxfrdh dk izFke fu;e
12-6 fof'k"V mQ"ek /kfjrk
12-7 mQ"ekxfrdh; voLFkk pj rFkk
voLFkk dk lehdj.k
12-8 mQ"ekxfrdh; izØe
12-9 mQ"ek batu
12-10 iz'khrd@mQ"ek iai
12-11 mQ"ekxfrdh dk f}rh; fu;e
12-12 mRØe.kh; o vuqRØe.kh; izØe
12-13 dkuksZ batu
lkjka'k
fopkj.kh; fo"k;
vH;kl
12.1 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
dks ijLij jxM+rs gSa rks gesa xjeh dh vuqHkwfr gksrh gS D;ksafd bl izfØ;k esa
fd;k x;k dk;Z mQ"ek mRiUu djrk gS A blosQ foijhr] Hkki batu esa ok"i dh
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
HkkSfrdh esa mQ"ek] rki] dk;Z vkfn dh vo/kj.kkvksa dks vf/d
lko/kuhiwoZd ifjHkkf"kr djus dh vko';drk iM+rh gS A ,sfrgkfld :i ls mQ"ek
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
osQ ja/zksa esa Hkjk jgrk gS A xje o BaMs fiaMksa osQ ikjLifjd laioZQ esa vkus ij ;g rjy
(ftls oSQykWfjd dgrs Fks) BaMs fiaM ls vis{kkÑr xje fiaM esa cgus yxrk gS !
;g fcyoqQy oSlk gh gS tSlk ml le; gksrk gS tc fHkUu&fHkUu m¡Qpkb;ksa rd
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
u gks tk,¡A blh osQ leku mQ"ek dh ^oSQykWfjd* /kj.kk esa mQ"ek ml le; rd
izokfgr gksrh jgrh gS tc rd fd ^oSQykWfjd ry* (vFkkZr~ rki) leku ugha
gks tkrs A
blh chp] mQ"ek dks mQtkZ osQ :i esa dfYir djus dh vk/qfud vo/kj.kk
osQ dkj.k blosQ (mQ"ek osQ) rjy Lo:i dks udkj fn;k x;k A bl laca/ esa
1798 esa csatkfeu FkkWelu (ftUgsa dkmUV jEiQksMZ Hkh dgrs gSa) us ,d egRoiw.kZ
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
mQ"ekxfrdh HkkSfrdh dh og 'kk[kk gS tks mQ"ek rFkk rki
dh vo/kj.kk ,oa mQ"ek osQ vU; izdkj dh mQtkZvksa esa varjk&
:ikUrj.k dk foospu djrh gS A mQ"ekxfrdh ,d LFkwy foKku
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`<+rkiwoZd
izekf.kr ugha fd;k x;k Fkk A mQ"ekxfrdh osQ o.kZu esa fudk;
osQ vis{kkÑr oqQN gh LFkwy pj lekfgr gksrs gSa tks lkekU;
vuqHko ij vk/kfjr gSa rFkk ftUgsa izR;{k :i esa ekik tk ldrk
gS A mnkgj.kkFkZ] fdlh xSl osQ lw{e o.kZu esa mldh jpuk djus
okys vxf.kr v.kqvksa osQ funsZ'kkadksa ,oa osxksa dk fu/kZj.k vko';d
gksrk gS A gkykafd xSlksa osQ v.kqxfr fl¼akr dk fooj.k cgqr foLr`r
ugha gS fiQj Hkh blesa v.kqvksa osQ osxks± dk fooj.k lekfgr gS A
blosQ foijhr fdlh xSl osQ mQ"ekxfrdh; fooj.k esa vkf.od
o.kZu iw.kZ :i ls udkj fn;k tkrk gS A mQ"ekxfrdh esa fdlh
xSl dh voLFkk nkc] vk;ru] rki] nzO;eku rFkk laxBu tSls
,sls LFkwy pjksa }kjk fu/kZfjr gksrh gS ftUgsa ge viuh bafnz;ksa ls
vuqHko djrs gSa vkSj eki ldrs gSa
*
A
;kaf=kdh ,oa mQ"ekxfrdh osQ chp Hksn vkiosQ efLr"d
esa HkyhHkkafr vk tkuk pkfg, A ;kaf=kdh esa gekjh #fp cyksa rFkk
cy vk?kw.kks± osQ izHkko esa xfr dj jgs d.kksa ,oa fi.Mksa esa gksrh
gS A mQ"ekxfrdh esa laiw.kZ fudk; dh xfr ij fopkj ugha fd;k
tkrk A bldh #fp fi.M dh vkafrjd LFkwy voLFkk esa gksrh
gS A tc canwd ls xksyh nkxrs gSa rc tks ifjorZu gksrk gS og
xksyh dh ;kaf=kd voLFkk  (fo'ks"kdj xfrt mQtkZ) esa ifjorZu
gksrk gS] mlosQ rki esa ugha A tc xksyh ydM+h esa /¡ldj #d
tkrh gS rks xksyh dh xfrt mQtkZ mQ"ek esa :ikarfjr gks tkrh
gS ftlls xksyh rFkk mlosQ pkjksa vksj dh ydM+h dh lrgksa dk
rki ifjofrZr gks tkrk gS A rki xksyh dh vkarfjd xfr (tks
vO;ofLFkr gS) dh mQtkZ ls lacaf/r gksrk gS u fd xksyh dh
laiw.kZ xfr ls A
12-2 rkih; lkE;
;kaf=kdh esa lkE;koLFkk ls rkRi;Z gS fd fudk; ij usV cká
cy o cy vk?kw.kZ 'kwU; gSa A mQ"ekxfrdh esa lkE;koLFkk dk
vFkZ fHkUu lanHkZ esa n`f"Vxkspj gksrk gS % fudk; dh voLFkk dks
ge ml le; lkE;koLFkk esa dgrs gSa tc fudk; dks vfHky{kf.kr
djus okys LFkwy pj le; osQ lkFk ifjofrZr ugha gksrs A
mnkgj.kkFkZ] fdlh i;kZoj.k ls iw.kZr% mQ"ekjks/h can n`<+ ik=k
esa Hkjh dksbZ xSl mQ"ekxfrd :i ls rc lkE;koLFkk esa gksxh
tc mlosQ nkc] vk;ru] rki] nzO;eku osQ ifjek.k rFkk laxBu
le; osQ lkFk ifjofrZr u gksa A
dksbZ fudk; lkE;koLFkk esa gS fd ugha O;kid :i esa
;g pkjksa vksj osQ ifjos'k rFkk ml nhokj dh izÑfr ij fuHkZj
djrk gS tks fudk; dks ifjos'k ls i`Fko~Q djrh gS A dYiuk
dhft, fd nks xSlsa A o B nks fHkUu&fHkUu ik=kksa esa Hkjh gSa A
iz;ksx }kjk gesa irk gS fd fdlh xSl osQ fn, gq, nzO;eku osQ
nkc o rki dks mlosQ nks Lora=k pjksa osQ :i esa pquk tk ldrk
gS A eku yhft, fd xSlksa osQ nkc o vk;ru Øe'k% (P
A
, V
A
)
rFkk (P
B
, V
B
) gSa A dYiuk dhft, fd igys nksuksa fudk;
ikl&ikl gSa ijarq mUgsa fdlh #¼ks"e nhokj (,d mQ"ekjks/h
nhokj) }kjk ,d nwljs ls i`Fko~Q j[kk x;k gS A bl nhokj osQ
dkj.k mQtkZ (mQ"ek) ,d ik=k ls nwljs ik=k esa ugha tk ikrh
gS A fudk;ksa dks Hkh 'ks"k ifjos'k ls blh izdkj dh #¼ks"e nhokj
ls i`Fko~Q j[krs gSa A bl O;oLFkk dk vkjs[kh; fp=k.k ¹12-1(a)º
esa fn;k x;k gS A ;gk¡ ;g ik;k x;k gS fd (P
A
, V
A
) osQ fdlh
Hkh laHkkfor ;qXe dk eku (P
B
, V
B
) osQ fdlh Hkh laHko ;qXe
osQ eku osQ lkFk lkE;koLFkk esa gksxk A iqu% dYiuk dhft, fd
#¼ks"e nhokj dks ,d mQ"ek&ikFkZ&nhokj ls izfrLFkkfir dj
fn;k x;k gS & ;g nhokj (mQ"ek) mQtkZ dks ,d fudk; ls
nwljs fudk; esa tkus nsrh gS A ,slk djus esa ;g ns[kk x;k gS
fd fudk;ksa A o B osQ LFkwy pj Lor% ml le; rd ifjofrZr
gksrs gSa tc rd fd nksuksa fudk; lkE;koLFkk dh fLFkfr izkIr
ugha dj ysrs A blosQ i'pkr~ mudh voLFkk esa dksbZ ifjorZu
ugha gksrk gS A bl fLFkfr dks fp=k ¹12-1(b)º esa n'kkZ;k x;k
gS A eku yhft, fd nksuksa xSlksa osQ nkc o vk;ru laca/h pj
ifjofrZr gksdj Øe'k% (P
A
', V '
A
) rFkk (P
B
', V '
B
) gks tkrs gSa
rkfd A o B dh u;h voLFkk,¡ iqu% ,d&nwljs dh lkE;koLFkk
esa gks tkrh gSa
**
 A ,d fudk; ls nwljs fudk; esa vc vkSj mQtkZ
dk izokg ugha gksrk A ,slh fLFkfr esa ge dgrs gSa fd fudk;
A, fudk; B osQ lkFk rkih; lkE; esa gS A
nks fudk;ksa osQ eè; dh lkE;koLFkk dh fLFkfr dks D;k
vfHkyf{kr djrh gS \ vki vius vuqHko ls mÙkj dk vuqeku
yxk ldrs gSa A rkih; lkE; esa] nks fudk;ksa osQ rki leku gksrs
gSa A ge tkusaxs fd mQ"ekxfrdh esa rki dh vo/kj.kk rd oSQls
ig¡qprs gSa \ mQ"ekxfrdh dk 'kwU; dksfV dk fu;e bldh vksj
laosQr djrk gS A
* mQ"ekxfrdh esa vU; ,sls pj Hkh fufgr gksrs gSa tks gekjh bafnz;ksa dks brus lqLi"V ugha gksrs (mnkgj.kkFkZ] ,aVªkWih] ,aFkkYih (laiw.kZ mQ"ek)] vkfn ftuosQ fo"k; esa vki
mPp d{kkvksa esa i<+saxs)] ¯drq ;s lHkh LFkwy pj gSa A
** ;g vko';d ugha gS fd nksuksa pj  cnysa A ,slk izfrca/ksa ij fuHkZj djrk gS A mnkgj.k osQ fy,] ;fn xSl fLFkj vk;ru okys ik=k esa Hkjh gks rks rkih; lkE; osQ fy,
osQoy xSlksa osQ nkc dks ifjofrZr gksuk pkfg, A
309 m"ekxfrdh
310 HkkSfrdh
12-3 mQ"ekxfrdh dk 'kwU; dksfV fu;e
dYiuk dhft, fd nks fudk; A o B ,d #¼ks"e nhokj ls
i`Fko~Q gSa A buesa ls izR;sd ,d rhljs fudk; C ls ,d lqpkyd
nhokj }kjk laioZQ esa gSa [fp=k 12-2(a)] A fudk;ksa dh voLFkk,¡
(vFkkZr~ muosQ LFkwy pj) rc rd ifjofrZr gksaxh tc rd A
o B nksuksa fudk; C osQ lkFk rkih; lkE; esa ugha vk tkrs gSa A
tc ,slk gks tk, rks dYiuk dhft, fd A o B osQ eè; dh
#¼ks"e nhokj ,d lqpkyd nhokj ls izfrLFkkfir dj nh tkrh
gS rFkk C dks A o B ls fdlh #¼ks"e nhokj ls i`Fko~Q dj fn;k
tkrk gS ¹fp=k 12-2(b)º A ,slk ns[kk tkrk gS fd A o B dh
voLFkk,¡ vc vkSj ugha cnyrha vFkkZr~ os nksuksa vc rkih;
lkE; esa gksrh gSa A ;g izs{k.k mQ"ekxfrdh osQ 'kwU; dksfV fu;e
dk vk/kj cuk A ;g fu;e crykrk gS fd ;fn nks fudk;
fdlh rhljs fudk; osQ lkFk i`Fko~Q&i`Fko~Q :i ls rkih;
lkE; esa gSa rks os ijLij Hkh rkih; lkE; esa gksrs gSa A ;gk¡
;g ckr è;ku esa j[kuh pkfg, fd mQ"ekxfrdh osQ izFke o
f}rh; fu;e dh vfHkO;fDr rFkk muosQ Øekadu osQ cgqr le;
ckn 1931 esa vkj-,p- iQkmyj us 'kwU; dksfV fu;e dk izfriknu
fd;k FkkA
'kwU; dksfV fu;e ls ;g laosQr feyrk gS fd tc nks fudk;
A o B ijLij rkih; lkE; esa gksrs gSa] rks ,slh dksbZ HkkSfrd jkf'k
gS tks nksuksa fudk;ksa osQ fy, leku eku j[krh gS A ;g mQ"ekxfrd
pj] ftldk eku rkih; lkE; okys fudk;ksa osQ fy, leku gksrk
gS] rki (T) dgykrk gS A vr% ;fn A o B lkE;koLFkk esa rhljs
fudk; C ls i`Fko~Q gSa rks T
A
 = T
C
 rFkkT
B
 = T
C
 A bldk rkRi;Z
;g gS fd T
A 
= T
B
 vFkkZr~ fudk; A o B Lo;a Hkh rkih; lkE;
esa gSa A
'kwU; dksfV fu;e osQ ekè;e ls geus fof/or rki dh
vo/kj.kk fodflr dh gS A gekjs lkeus iqu% ,d iz'u mRiUu
gksrk gS % fHkUu&fHkUu fiaMksa osQ rki osQ fy, ge vafdd ekuksa
dk fu/kZj.k oSQls djsa\ nwljs 'kCnksa esa] ge rki ekiØe oSQls
cuk,¡\ rkifefr bl ekSfyd iz'u ls laca/ j[krh gS ftlosQ
fo"k; esa ge vxys vuqHkkx esa vè;;u djsaxs A
fp=k 12-1 (a) (nks xSlksa osQ) fudk; A o B ,d #¼ks"e nhokj
ls i`Fko~Q gSa % bl nhokj ls mQ"ek vkj&ikj ugha tk ikrh A
(b) ;gh fudk; A o B ,d mQ"ek&ikFkZ nhokj ls i`Fko~Q
n'kkZ, x, gSa A ;g ,d pkyd nhokj gksrh gS ftlls mQ"ek
,d fudk; ls nwljs esa pyh tkrh gS A bl mnkgj.k esa
rkih; lkE; ;Fkksfpr le; esa izkIr gks tkrk gS A
12-4 mQ"ek] vkarfjd mQtkZ rFkk dk;Z
mQ"ekxfrdh osQ 'kwU; dksfV fu;e ls rki dh vo/kj.kk dh
mRifÙk gqbZ tks gekjs lkekU; Kku osQ vuqowQy gS A rki fdlh
fi.M dh m".krk dk |ksrd gS A tc nks fi.M mQ"eh; laioZQ
fp=k 12-2 (a) fudk; A o B tks ,d #¼ks"e nhokj ls i`Fko~Q gSa
tcfd buesa ls izR;sd ,d rhljs fudk; C ls ,d
lqpkyd nhokj }kjk laioZQ esa gS A (b) A o B osQ eè;
dh #¼ks"e nhokj dks fdlh lqpkyd nhokj ls izfrLFkkfir
fd;k x;k gS tcfd C dks A o B ls #¼ks"e nhokj ls
i`Fko~Q n'kkZ;k x;k gS A
(a)
(b)
(b)
(a)
311 m"ekxfrdh
esa yk, tkrs gSa rks blls mQ"ek osQ izokg dh fn'kk fu/kZfjr gksrh
gS A mQ"ek mPp rki okys fi.M ls fuEu rki okys fi.M dh
vksj izokfgr gksrh gS A tc rki leku gks tkrs gSa rks izokg #d
tkrk gS A ,slh fLFkfr esa nksuksa fi.M rkih; lkE; esa gksrs gSa A
ge ;g foLrkj ls i<+ pqosQ gSa fd Hkkafr&Hkkafr osQ fi.Mksa osQ
rki osQ fu/kZj.k osQ fy, rki ekiØe oSQls cuk, tkrs gSa A vc
ge mQ"ek rFkk rRlacaf/r jkf'k;ksa_ tSlsµvkarfjd mQtkZ rFkk dk;Z
dh vo/kj.kkvksa dk o.kZu djsaxs A
fdlh fudk; dh vkarfjd mQtkZ dh vo/kj.kk dks le>uk
dfBu ugha gS A ge tkurs gSa fd izR;sd LFkwy fudk; vla[;
v.kqvksa ls fufeZr gS A vkarfjd mQtkZ bu v.kqvksa dh fLFkfrt
o xfrt mQtkZvksa dk ;ksx gS A geus ;g fVIi.kh dh gS fd
mQ"ekxfrdh esa fudk; dh lexz :i ls xfrt mQtkZ izklafxd
ugha gksrh A bl izdkj] funsZ'k izsQe esa vkarfjd mQtkZ v.kq dh
xfrt o fLFkfrt mQtkZ osQ ;ksx osQ cjkcj gksrh gS ftlosQ lkis{k
fudk; dk nzO;eku&osaQnz fojkekoLFkk esa gksrk gS A bl izdkj]
blesa osQoy fudk; osQ v.kqvksa dh ;kn`fPNd xfr ls lacaf/r
(vO;ofLFkr) mQtkZ gh lekfgr gksrh gS A fudk; dh vkarfjd
mQtkZ dks U ls fpfÉr djrs gSa A
;|fi geus vkarfjd mQtkZ osQ vFkZ dks le>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
gS A ;g bl ckr ij fuHkZj ugha djrh fd xSl dh ;g fLFkfr
fdl izdkj izkIr gqbZ A nkc] vk;ru] rki rFkk vkarfjd mQtkZ
fudk; (xSl) osQ mQ"ekxfrdh; voLFkk pj dgykrs gSa (vuqHkkx
12-7 ns[ksa) A ;fn xSl osQ vYiizHkkoh varjkf.od cyksa dh
mis{kk dj nsa rks xSl dh vkarfjd mQtkZ mlosQ v.kqvksa dh vusd
;kn`fPNd xfr;ksa ls lac¼ xfrt mQtkZvksa osQ ;ksx osQ Bhd cjkcj
gksrh gS A vxys vè;k; esa ge i<+saxs fd fdlh xSl esa ;g xfr
osQoy LFkkuakrjh; gh ugha gksrh (blesa xfr ik=k osQ vk;ru
esa ,d fcanq ls nwljs fcanq osQ eè; gksrh gS)] oju~ blesa v.kq
dh ?kw.khZ rFkk daiu xfr Hkh gksrh gS (fp=k 12-3)A
fdlh fudk; dh vkarfjd mQtkZ esa fdu mik;ksa ls ifjorZu
fd, tk ldrs gSa \ lqfo/k dh n`f"V ls iqu% dYiuk dhft,
fd fp=k 12-4 osQ vuqlkj fudk; fdlh fn, x, nzO;eku dh
,d xSl gS tks ,d fl¯yMj esa Hkjh gS ftlesa xfr'khy fiLVu
yxk gS A vuqHko ;g crkrk gS fd xSl dh voLFkk (rFkk bl
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
tks xSl dh vis{kk mPp rki ij gS A rkikarj osQ dkj.k mQtkZ
(mQ"ek) xje fi.M ls xSl esa izokfgr gksxh A blls xSl dh
vkarfjd mQtkZ c<+ tk,xh A nwljk mik; gS fd fiLVu dks uhps
dh vksj nck;k tk, (vFkkZr~ fudk; ij dk;Z fd;k tk,) A
blesa Hkh xSl dh vkarfjd mQtkZ c<+ tkrh gS A fu%lansg ;s nksuksa
ckrsa foijhr fn'kk esa Hkh laHko gksrh gSa A ;fn pkjksa vksj osQ ifjos'k
dk rki de gS rks mQ"ek xSl ls ifjos'k esa izokfgr gksxh A blh
izdkj] xSl fiLVu dks mQij dh vksj /Ddk ns ldrh gS vkSj
ifjos'k ij dk;Z dj ldrh gS A la{ksi esa] mQ"ek vkSj dk;Z nks
fHkUu&fHkUu fof/;k¡ gSa ftuls mQ"eh; fudk; dh fLFkfr ifjofrZr
gksrh gS rFkk mldh vkarfjd mQtkZ esa ifjorZu gksrk gS A
mQ"ek ,oa vkarfjd mQtkZ dh /kj.kkvksa esa varj dks
lko/kuhiwoZd le>uk vko';d gS A mQ"ek fuf'pr :i ls
mQtkZ gS ijarq ;g mQtkZ ikjxeu esa gS A ;g ek=k 'kCnksa dk [ksy
ugha gS A nksuksa esa varj ewy egÙo dk gS A fdlh mQ"ekxfrdh
fudk; dh fLFkfr mldh vkarfjd mQtkZ ls vfHkyf{kr gksrh
gS u fd mQ"ek ls A bl izdkj dk izdFku fd ^fdlh nh
gqbZ voLFkk esa xSl esa mQ"ek dh oqQN ek=kk gksrh gS* mruk
gh fujFkZd gS ftruk fd ;g izdFku fd ^fdlh nh gqbZ fLFkfr
esa xSl esa oqQN dk;Z fufgr gksrk gS A*  blosQ foijhr] ^fdlh
nh gqbZ voLFkk esa xSl esa vkarfjd mQtkZ dh oqQN ek=kk gksrh
gS* iwjh rjg ls ,d lkFkZd izdFku gS A blh izdkj ls] ,sls izdFku
tSls ^fudk; dks ,d fuf'pr ek=kk dh mQ"ek nh xbZ gS*
;k ^fudk; }kjk ,d fuf'pr ek=kk dk dk;Z fd;k x;k*
iw.kZr% vFkZiw.kZ lkFkZd izdFku gSa A
la{ksi esa] mQ"ek o dk;Z mQ"ekxfrdh esa fLFkfr pj ugha
gksrs A ;s fdlh fudk; esa mQtkZ LFkkukarj.k dh fof/;k¡ gksrh
gSa ftlls mldh vkarfjd mQtkZ ifjofrZr gksrh gSA tks] tSlk fd
igys o.kZu dj pqosQ gSa] ,d voLFkk pj gksrk gS A
lk/kj.k Hkk"kk esa gesa izk;% mQ"ek rFkk vkarfjd mQtkZ esa
Hkze cuk jgrk gS A oqQN izkFkfed HkkSfrdh dh iqLrdksa esa
dHkh&dHkh bl Hksn dh mis{kk dj nh tkrh gS A rFkkfi mQ"ekxfrdh
dks HkyhHkkafr le>us osQ fy, ;g foHksn vko';d gS A
Page 5


vè;k; 12
mQ"ekxfrdh
12-1 Hkwfedk
12-2 rkih; lkE;
12-3 mQ"ekxfrdh dk 'kwU; dksfV
fu;e
12-4 mQ"ek] vkarfjd mQtkZ rFkk dk;Z
12-5 mQ"ekxfrdh dk izFke fu;e
12-6 fof'k"V mQ"ek /kfjrk
12-7 mQ"ekxfrdh; voLFkk pj rFkk
voLFkk dk lehdj.k
12-8 mQ"ekxfrdh; izØe
12-9 mQ"ek batu
12-10 iz'khrd@mQ"ek iai
12-11 mQ"ekxfrdh dk f}rh; fu;e
12-12 mRØe.kh; o vuqRØe.kh; izØe
12-13 dkuksZ batu
lkjka'k
fopkj.kh; fo"k;
vH;kl
12.1 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
dks ijLij jxM+rs gSa rks gesa xjeh dh vuqHkwfr gksrh gS D;ksafd bl izfØ;k esa
fd;k x;k dk;Z mQ"ek mRiUu djrk gS A blosQ foijhr] Hkki batu esa ok"i dh
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
HkkSfrdh esa mQ"ek] rki] dk;Z vkfn dh vo/kj.kkvksa dks vf/d
lko/kuhiwoZd ifjHkkf"kr djus dh vko';drk iM+rh gS A ,sfrgkfld :i ls mQ"ek
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
osQ ja/zksa esa Hkjk jgrk gS A xje o BaMs fiaMksa osQ ikjLifjd laioZQ esa vkus ij ;g rjy
(ftls oSQykWfjd dgrs Fks) BaMs fiaM ls vis{kkÑr xje fiaM esa cgus yxrk gS !
;g fcyoqQy oSlk gh gS tSlk ml le; gksrk gS tc fHkUu&fHkUu m¡Qpkb;ksa rd
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
u gks tk,¡A blh osQ leku mQ"ek dh ^oSQykWfjd* /kj.kk esa mQ"ek ml le; rd
izokfgr gksrh jgrh gS tc rd fd ^oSQykWfjd ry* (vFkkZr~ rki) leku ugha
gks tkrs A
blh chp] mQ"ek dks mQtkZ osQ :i esa dfYir djus dh vk/qfud vo/kj.kk
osQ dkj.k blosQ (mQ"ek osQ) rjy Lo:i dks udkj fn;k x;k A bl laca/ esa
1798 esa csatkfeu FkkWelu (ftUgsa dkmUV jEiQksMZ Hkh dgrs gSa) us ,d egRoiw.kZ
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
mQ"ekxfrdh HkkSfrdh dh og 'kk[kk gS tks mQ"ek rFkk rki
dh vo/kj.kk ,oa mQ"ek osQ vU; izdkj dh mQtkZvksa esa varjk&
:ikUrj.k dk foospu djrh gS A mQ"ekxfrdh ,d LFkwy foKku
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`<+rkiwoZd
izekf.kr ugha fd;k x;k Fkk A mQ"ekxfrdh osQ o.kZu esa fudk;
osQ vis{kkÑr oqQN gh LFkwy pj lekfgr gksrs gSa tks lkekU;
vuqHko ij vk/kfjr gSa rFkk ftUgsa izR;{k :i esa ekik tk ldrk
gS A mnkgj.kkFkZ] fdlh xSl osQ lw{e o.kZu esa mldh jpuk djus
okys vxf.kr v.kqvksa osQ funsZ'kkadksa ,oa osxksa dk fu/kZj.k vko';d
gksrk gS A gkykafd xSlksa osQ v.kqxfr fl¼akr dk fooj.k cgqr foLr`r
ugha gS fiQj Hkh blesa v.kqvksa osQ osxks± dk fooj.k lekfgr gS A
blosQ foijhr fdlh xSl osQ mQ"ekxfrdh; fooj.k esa vkf.od
o.kZu iw.kZ :i ls udkj fn;k tkrk gS A mQ"ekxfrdh esa fdlh
xSl dh voLFkk nkc] vk;ru] rki] nzO;eku rFkk laxBu tSls
,sls LFkwy pjksa }kjk fu/kZfjr gksrh gS ftUgsa ge viuh bafnz;ksa ls
vuqHko djrs gSa vkSj eki ldrs gSa
*
A
;kaf=kdh ,oa mQ"ekxfrdh osQ chp Hksn vkiosQ efLr"d
esa HkyhHkkafr vk tkuk pkfg, A ;kaf=kdh esa gekjh #fp cyksa rFkk
cy vk?kw.kks± osQ izHkko esa xfr dj jgs d.kksa ,oa fi.Mksa esa gksrh
gS A mQ"ekxfrdh esa laiw.kZ fudk; dh xfr ij fopkj ugha fd;k
tkrk A bldh #fp fi.M dh vkafrjd LFkwy voLFkk esa gksrh
gS A tc canwd ls xksyh nkxrs gSa rc tks ifjorZu gksrk gS og
xksyh dh ;kaf=kd voLFkk  (fo'ks"kdj xfrt mQtkZ) esa ifjorZu
gksrk gS] mlosQ rki esa ugha A tc xksyh ydM+h esa /¡ldj #d
tkrh gS rks xksyh dh xfrt mQtkZ mQ"ek esa :ikarfjr gks tkrh
gS ftlls xksyh rFkk mlosQ pkjksa vksj dh ydM+h dh lrgksa dk
rki ifjofrZr gks tkrk gS A rki xksyh dh vkarfjd xfr (tks
vO;ofLFkr gS) dh mQtkZ ls lacaf/r gksrk gS u fd xksyh dh
laiw.kZ xfr ls A
12-2 rkih; lkE;
;kaf=kdh esa lkE;koLFkk ls rkRi;Z gS fd fudk; ij usV cká
cy o cy vk?kw.kZ 'kwU; gSa A mQ"ekxfrdh esa lkE;koLFkk dk
vFkZ fHkUu lanHkZ esa n`f"Vxkspj gksrk gS % fudk; dh voLFkk dks
ge ml le; lkE;koLFkk esa dgrs gSa tc fudk; dks vfHky{kf.kr
djus okys LFkwy pj le; osQ lkFk ifjofrZr ugha gksrs A
mnkgj.kkFkZ] fdlh i;kZoj.k ls iw.kZr% mQ"ekjks/h can n`<+ ik=k
esa Hkjh dksbZ xSl mQ"ekxfrd :i ls rc lkE;koLFkk esa gksxh
tc mlosQ nkc] vk;ru] rki] nzO;eku osQ ifjek.k rFkk laxBu
le; osQ lkFk ifjofrZr u gksa A
dksbZ fudk; lkE;koLFkk esa gS fd ugha O;kid :i esa
;g pkjksa vksj osQ ifjos'k rFkk ml nhokj dh izÑfr ij fuHkZj
djrk gS tks fudk; dks ifjos'k ls i`Fko~Q djrh gS A dYiuk
dhft, fd nks xSlsa A o B nks fHkUu&fHkUu ik=kksa esa Hkjh gSa A
iz;ksx }kjk gesa irk gS fd fdlh xSl osQ fn, gq, nzO;eku osQ
nkc o rki dks mlosQ nks Lora=k pjksa osQ :i esa pquk tk ldrk
gS A eku yhft, fd xSlksa osQ nkc o vk;ru Øe'k% (P
A
, V
A
)
rFkk (P
B
, V
B
) gSa A dYiuk dhft, fd igys nksuksa fudk;
ikl&ikl gSa ijarq mUgsa fdlh #¼ks"e nhokj (,d mQ"ekjks/h
nhokj) }kjk ,d nwljs ls i`Fko~Q j[kk x;k gS A bl nhokj osQ
dkj.k mQtkZ (mQ"ek) ,d ik=k ls nwljs ik=k esa ugha tk ikrh
gS A fudk;ksa dks Hkh 'ks"k ifjos'k ls blh izdkj dh #¼ks"e nhokj
ls i`Fko~Q j[krs gSa A bl O;oLFkk dk vkjs[kh; fp=k.k ¹12-1(a)º
esa fn;k x;k gS A ;gk¡ ;g ik;k x;k gS fd (P
A
, V
A
) osQ fdlh
Hkh laHkkfor ;qXe dk eku (P
B
, V
B
) osQ fdlh Hkh laHko ;qXe
osQ eku osQ lkFk lkE;koLFkk esa gksxk A iqu% dYiuk dhft, fd
#¼ks"e nhokj dks ,d mQ"ek&ikFkZ&nhokj ls izfrLFkkfir dj
fn;k x;k gS & ;g nhokj (mQ"ek) mQtkZ dks ,d fudk; ls
nwljs fudk; esa tkus nsrh gS A ,slk djus esa ;g ns[kk x;k gS
fd fudk;ksa A o B osQ LFkwy pj Lor% ml le; rd ifjofrZr
gksrs gSa tc rd fd nksuksa fudk; lkE;koLFkk dh fLFkfr izkIr
ugha dj ysrs A blosQ i'pkr~ mudh voLFkk esa dksbZ ifjorZu
ugha gksrk gS A bl fLFkfr dks fp=k ¹12-1(b)º esa n'kkZ;k x;k
gS A eku yhft, fd nksuksa xSlksa osQ nkc o vk;ru laca/h pj
ifjofrZr gksdj Øe'k% (P
A
', V '
A
) rFkk (P
B
', V '
B
) gks tkrs gSa
rkfd A o B dh u;h voLFkk,¡ iqu% ,d&nwljs dh lkE;koLFkk
esa gks tkrh gSa
**
 A ,d fudk; ls nwljs fudk; esa vc vkSj mQtkZ
dk izokg ugha gksrk A ,slh fLFkfr esa ge dgrs gSa fd fudk;
A, fudk; B osQ lkFk rkih; lkE; esa gS A
nks fudk;ksa osQ eè; dh lkE;koLFkk dh fLFkfr dks D;k
vfHkyf{kr djrh gS \ vki vius vuqHko ls mÙkj dk vuqeku
yxk ldrs gSa A rkih; lkE; esa] nks fudk;ksa osQ rki leku gksrs
gSa A ge tkusaxs fd mQ"ekxfrdh esa rki dh vo/kj.kk rd oSQls
ig¡qprs gSa \ mQ"ekxfrdh dk 'kwU; dksfV dk fu;e bldh vksj
laosQr djrk gS A
* mQ"ekxfrdh esa vU; ,sls pj Hkh fufgr gksrs gSa tks gekjh bafnz;ksa dks brus lqLi"V ugha gksrs (mnkgj.kkFkZ] ,aVªkWih] ,aFkkYih (laiw.kZ mQ"ek)] vkfn ftuosQ fo"k; esa vki
mPp d{kkvksa esa i<+saxs)] ¯drq ;s lHkh LFkwy pj gSa A
** ;g vko';d ugha gS fd nksuksa pj  cnysa A ,slk izfrca/ksa ij fuHkZj djrk gS A mnkgj.k osQ fy,] ;fn xSl fLFkj vk;ru okys ik=k esa Hkjh gks rks rkih; lkE; osQ fy,
osQoy xSlksa osQ nkc dks ifjofrZr gksuk pkfg, A
309 m"ekxfrdh
310 HkkSfrdh
12-3 mQ"ekxfrdh dk 'kwU; dksfV fu;e
dYiuk dhft, fd nks fudk; A o B ,d #¼ks"e nhokj ls
i`Fko~Q gSa A buesa ls izR;sd ,d rhljs fudk; C ls ,d lqpkyd
nhokj }kjk laioZQ esa gSa [fp=k 12-2(a)] A fudk;ksa dh voLFkk,¡
(vFkkZr~ muosQ LFkwy pj) rc rd ifjofrZr gksaxh tc rd A
o B nksuksa fudk; C osQ lkFk rkih; lkE; esa ugha vk tkrs gSa A
tc ,slk gks tk, rks dYiuk dhft, fd A o B osQ eè; dh
#¼ks"e nhokj ,d lqpkyd nhokj ls izfrLFkkfir dj nh tkrh
gS rFkk C dks A o B ls fdlh #¼ks"e nhokj ls i`Fko~Q dj fn;k
tkrk gS ¹fp=k 12-2(b)º A ,slk ns[kk tkrk gS fd A o B dh
voLFkk,¡ vc vkSj ugha cnyrha vFkkZr~ os nksuksa vc rkih;
lkE; esa gksrh gSa A ;g izs{k.k mQ"ekxfrdh osQ 'kwU; dksfV fu;e
dk vk/kj cuk A ;g fu;e crykrk gS fd ;fn nks fudk;
fdlh rhljs fudk; osQ lkFk i`Fko~Q&i`Fko~Q :i ls rkih;
lkE; esa gSa rks os ijLij Hkh rkih; lkE; esa gksrs gSa A ;gk¡
;g ckr è;ku esa j[kuh pkfg, fd mQ"ekxfrdh osQ izFke o
f}rh; fu;e dh vfHkO;fDr rFkk muosQ Øekadu osQ cgqr le;
ckn 1931 esa vkj-,p- iQkmyj us 'kwU; dksfV fu;e dk izfriknu
fd;k FkkA
'kwU; dksfV fu;e ls ;g laosQr feyrk gS fd tc nks fudk;
A o B ijLij rkih; lkE; esa gksrs gSa] rks ,slh dksbZ HkkSfrd jkf'k
gS tks nksuksa fudk;ksa osQ fy, leku eku j[krh gS A ;g mQ"ekxfrd
pj] ftldk eku rkih; lkE; okys fudk;ksa osQ fy, leku gksrk
gS] rki (T) dgykrk gS A vr% ;fn A o B lkE;koLFkk esa rhljs
fudk; C ls i`Fko~Q gSa rks T
A
 = T
C
 rFkkT
B
 = T
C
 A bldk rkRi;Z
;g gS fd T
A 
= T
B
 vFkkZr~ fudk; A o B Lo;a Hkh rkih; lkE;
esa gSa A
'kwU; dksfV fu;e osQ ekè;e ls geus fof/or rki dh
vo/kj.kk fodflr dh gS A gekjs lkeus iqu% ,d iz'u mRiUu
gksrk gS % fHkUu&fHkUu fiaMksa osQ rki osQ fy, ge vafdd ekuksa
dk fu/kZj.k oSQls djsa\ nwljs 'kCnksa esa] ge rki ekiØe oSQls
cuk,¡\ rkifefr bl ekSfyd iz'u ls laca/ j[krh gS ftlosQ
fo"k; esa ge vxys vuqHkkx esa vè;;u djsaxs A
fp=k 12-1 (a) (nks xSlksa osQ) fudk; A o B ,d #¼ks"e nhokj
ls i`Fko~Q gSa % bl nhokj ls mQ"ek vkj&ikj ugha tk ikrh A
(b) ;gh fudk; A o B ,d mQ"ek&ikFkZ nhokj ls i`Fko~Q
n'kkZ, x, gSa A ;g ,d pkyd nhokj gksrh gS ftlls mQ"ek
,d fudk; ls nwljs esa pyh tkrh gS A bl mnkgj.k esa
rkih; lkE; ;Fkksfpr le; esa izkIr gks tkrk gS A
12-4 mQ"ek] vkarfjd mQtkZ rFkk dk;Z
mQ"ekxfrdh osQ 'kwU; dksfV fu;e ls rki dh vo/kj.kk dh
mRifÙk gqbZ tks gekjs lkekU; Kku osQ vuqowQy gS A rki fdlh
fi.M dh m".krk dk |ksrd gS A tc nks fi.M mQ"eh; laioZQ
fp=k 12-2 (a) fudk; A o B tks ,d #¼ks"e nhokj ls i`Fko~Q gSa
tcfd buesa ls izR;sd ,d rhljs fudk; C ls ,d
lqpkyd nhokj }kjk laioZQ esa gS A (b) A o B osQ eè;
dh #¼ks"e nhokj dks fdlh lqpkyd nhokj ls izfrLFkkfir
fd;k x;k gS tcfd C dks A o B ls #¼ks"e nhokj ls
i`Fko~Q n'kkZ;k x;k gS A
(a)
(b)
(b)
(a)
311 m"ekxfrdh
esa yk, tkrs gSa rks blls mQ"ek osQ izokg dh fn'kk fu/kZfjr gksrh
gS A mQ"ek mPp rki okys fi.M ls fuEu rki okys fi.M dh
vksj izokfgr gksrh gS A tc rki leku gks tkrs gSa rks izokg #d
tkrk gS A ,slh fLFkfr esa nksuksa fi.M rkih; lkE; esa gksrs gSa A
ge ;g foLrkj ls i<+ pqosQ gSa fd Hkkafr&Hkkafr osQ fi.Mksa osQ
rki osQ fu/kZj.k osQ fy, rki ekiØe oSQls cuk, tkrs gSa A vc
ge mQ"ek rFkk rRlacaf/r jkf'k;ksa_ tSlsµvkarfjd mQtkZ rFkk dk;Z
dh vo/kj.kkvksa dk o.kZu djsaxs A
fdlh fudk; dh vkarfjd mQtkZ dh vo/kj.kk dks le>uk
dfBu ugha gS A ge tkurs gSa fd izR;sd LFkwy fudk; vla[;
v.kqvksa ls fufeZr gS A vkarfjd mQtkZ bu v.kqvksa dh fLFkfrt
o xfrt mQtkZvksa dk ;ksx gS A geus ;g fVIi.kh dh gS fd
mQ"ekxfrdh esa fudk; dh lexz :i ls xfrt mQtkZ izklafxd
ugha gksrh A bl izdkj] funsZ'k izsQe esa vkarfjd mQtkZ v.kq dh
xfrt o fLFkfrt mQtkZ osQ ;ksx osQ cjkcj gksrh gS ftlosQ lkis{k
fudk; dk nzO;eku&osaQnz fojkekoLFkk esa gksrk gS A bl izdkj]
blesa osQoy fudk; osQ v.kqvksa dh ;kn`fPNd xfr ls lacaf/r
(vO;ofLFkr) mQtkZ gh lekfgr gksrh gS A fudk; dh vkarfjd
mQtkZ dks U ls fpfÉr djrs gSa A
;|fi geus vkarfjd mQtkZ osQ vFkZ dks le>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
gS A ;g bl ckr ij fuHkZj ugha djrh fd xSl dh ;g fLFkfr
fdl izdkj izkIr gqbZ A nkc] vk;ru] rki rFkk vkarfjd mQtkZ
fudk; (xSl) osQ mQ"ekxfrdh; voLFkk pj dgykrs gSa (vuqHkkx
12-7 ns[ksa) A ;fn xSl osQ vYiizHkkoh varjkf.od cyksa dh
mis{kk dj nsa rks xSl dh vkarfjd mQtkZ mlosQ v.kqvksa dh vusd
;kn`fPNd xfr;ksa ls lac¼ xfrt mQtkZvksa osQ ;ksx osQ Bhd cjkcj
gksrh gS A vxys vè;k; esa ge i<+saxs fd fdlh xSl esa ;g xfr
osQoy LFkkuakrjh; gh ugha gksrh (blesa xfr ik=k osQ vk;ru
esa ,d fcanq ls nwljs fcanq osQ eè; gksrh gS)] oju~ blesa v.kq
dh ?kw.khZ rFkk daiu xfr Hkh gksrh gS (fp=k 12-3)A
fdlh fudk; dh vkarfjd mQtkZ esa fdu mik;ksa ls ifjorZu
fd, tk ldrs gSa \ lqfo/k dh n`f"V ls iqu% dYiuk dhft,
fd fp=k 12-4 osQ vuqlkj fudk; fdlh fn, x, nzO;eku dh
,d xSl gS tks ,d fl¯yMj esa Hkjh gS ftlesa xfr'khy fiLVu
yxk gS A vuqHko ;g crkrk gS fd xSl dh voLFkk (rFkk bl
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
tks xSl dh vis{kk mPp rki ij gS A rkikarj osQ dkj.k mQtkZ
(mQ"ek) xje fi.M ls xSl esa izokfgr gksxh A blls xSl dh
vkarfjd mQtkZ c<+ tk,xh A nwljk mik; gS fd fiLVu dks uhps
dh vksj nck;k tk, (vFkkZr~ fudk; ij dk;Z fd;k tk,) A
blesa Hkh xSl dh vkarfjd mQtkZ c<+ tkrh gS A fu%lansg ;s nksuksa
ckrsa foijhr fn'kk esa Hkh laHko gksrh gSa A ;fn pkjksa vksj osQ ifjos'k
dk rki de gS rks mQ"ek xSl ls ifjos'k esa izokfgr gksxh A blh
izdkj] xSl fiLVu dks mQij dh vksj /Ddk ns ldrh gS vkSj
ifjos'k ij dk;Z dj ldrh gS A la{ksi esa] mQ"ek vkSj dk;Z nks
fHkUu&fHkUu fof/;k¡ gSa ftuls mQ"eh; fudk; dh fLFkfr ifjofrZr
gksrh gS rFkk mldh vkarfjd mQtkZ esa ifjorZu gksrk gS A
mQ"ek ,oa vkarfjd mQtkZ dh /kj.kkvksa esa varj dks
lko/kuhiwoZd le>uk vko';d gS A mQ"ek fuf'pr :i ls
mQtkZ gS ijarq ;g mQtkZ ikjxeu esa gS A ;g ek=k 'kCnksa dk [ksy
ugha gS A nksuksa esa varj ewy egÙo dk gS A fdlh mQ"ekxfrdh
fudk; dh fLFkfr mldh vkarfjd mQtkZ ls vfHkyf{kr gksrh
gS u fd mQ"ek ls A bl izdkj dk izdFku fd ^fdlh nh
gqbZ voLFkk esa xSl esa mQ"ek dh oqQN ek=kk gksrh gS* mruk
gh fujFkZd gS ftruk fd ;g izdFku fd ^fdlh nh gqbZ fLFkfr
esa xSl esa oqQN dk;Z fufgr gksrk gS A*  blosQ foijhr] ^fdlh
nh gqbZ voLFkk esa xSl esa vkarfjd mQtkZ dh oqQN ek=kk gksrh
gS* iwjh rjg ls ,d lkFkZd izdFku gS A blh izdkj ls] ,sls izdFku
tSls ^fudk; dks ,d fuf'pr ek=kk dh mQ"ek nh xbZ gS*
;k ^fudk; }kjk ,d fuf'pr ek=kk dk dk;Z fd;k x;k*
iw.kZr% vFkZiw.kZ lkFkZd izdFku gSa A
la{ksi esa] mQ"ek o dk;Z mQ"ekxfrdh esa fLFkfr pj ugha
gksrs A ;s fdlh fudk; esa mQtkZ LFkkukarj.k dh fof/;k¡ gksrh
gSa ftlls mldh vkarfjd mQtkZ ifjofrZr gksrh gSA tks] tSlk fd
igys o.kZu dj pqosQ gSa] ,d voLFkk pj gksrk gS A
lk/kj.k Hkk"kk esa gesa izk;% mQ"ek rFkk vkarfjd mQtkZ esa
Hkze cuk jgrk gS A oqQN izkFkfed HkkSfrdh dh iqLrdksa esa
dHkh&dHkh bl Hksn dh mis{kk dj nh tkrh gS A rFkkfi mQ"ekxfrdh
dks HkyhHkkafr le>us osQ fy, ;g foHksn vko';d gS A
312 HkkSfrdh
fp=k 12-3  (a) tc ckWDl fojkekoLFkk esa gS rks xSl dh vkarfjd
mQtkZ U  mlosQ v.kqvksa dh xfrt o fLFkfrt mQtkZ osQ
;ksx osQ cjkcj gksrh gSA fofHkUu izdkj dh xfr;ksa
(LFkkukarjh;] ?kw.khZ] daiu) osQ dkj.k xfrt mQtkZ dks
U esa lekfgr fd;k tkrk gS A (b) ;fn ;gh lexz ckWDl
oqQN osx ls xfreku gS] rks ckWDl dh xfrt mQtkZ dks
U esa lfEefyr ugha djuk gS A
fp=k 12-4 mQ"ek o dk;Z fdlh fudk; esa mQtkZ LFkkuakrj.k dh
nks fofHkUu fof/;k¡ gSa ftuls mldh vkarfjd mQtkZ esa
ifjorZu gksrk gS A (a) fudk; rFkk ifjos'k osQ chp
rkikarj osQ dkj.k mQ"ek dks mQtkZ osQ LFkkukarj.k osQ :i
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
nsuk) }kjk mRiUu mQtkZ dk LFkkukarj.k gS ftuesa rkikarj
lekfgr ugha gksrk A
12-5 mQ"ekxfrdh dk izFke fu;e
ge ;g ns[k pqosQ gSa fd fdlh fudk; dh vkarfjd mQtkZ U
nks fof/;ksa ls mQtkZ LFkkukarj.k osQ dkj.k ifjofrZr gks ldrh
gS A ;s fof/;k¡ gSa % mQ"ek rFkk dk;Z A dYiuk dhft, fd
?Q = ifjos'k }kjk fudk; dks nh xbZ mQ"ek
?W = fudk; }kjk ifjos'k ij fd;k x;k dk;Z
?U = fudk; dh vkarfjd mQtkZ esa ifjorZu
mQtkZ laj{k.k osQ lkekU; fu;e esa ;g var£ufgr gS fd
?Q = ?U + ?W (12.1)
bldk rkRi;Z ;g gS fd tks mQtkZ (?Q) fudk; dks nh tkrh
gS] mldk oqQN va'k fudk; dh vkarfjd mQtkZ esa o`f¼ djrk
gS (?U) rFkk 'ks"k ifjos'k ij fd;k x;k dk;Z (?W) gS A lehdj.k
(12-1) dks mQ"ekxfrdh osQ izFke fu;e osQ :i esa tkuk
tkrk gS A ;g mQtkZ laj{k.k dk osQoy lkekU; fu;e gS ftls
fdlh Hkh ml fudk; ij ykxw fd;k tk ldrk gS ftlesa ifjos'k
dks vFkok ifjos'k ls mQ"ek LFkkukarj.k ij è;ku fn;k tkrk gS A
eku yhft, fd ge lehdj.k (12-1) dks oSdfYid
:i esa izLrqr djrs gSa]
?Q – ?W = ?U (12.2)
vc eku yhft, fd fudk; fdlh vkjafHkd voLFkk ls
vafre voLFkk esa dbZ izdkj ls vkrk gS A mnkgj.kkFkZ] xSl dh
voLFkk (P
1
, V
1
) ls ifjofrZr djosQ (P
2
, V
2
) dj nh tk, rks
ge igys xSl osQ nkc dks fLFkj j[kdj mlosQ vk;ru dks V
1
ls V
2
  esa ifjofrZr djrs gSa vFkkZr~ igys ge voLFkk (P
1
, V
2
)
esa tk ldrs gSa vkSj fiQj xSl osQ vk;ru dks fLFkj j[krs gq,
blosQ nkc dks P
1
 ls P
2
 esa ifjofrZr djrs gSa A blls xSl (P
2
,
V
2
) voLFkk esa igq¡p tkrh gS A fodYir% ge igys vk;ru dks
fLFkj j[k ldrs gSa vkSj fiQj ncko fLFkj j[krs gSaA pwafd U ,d
voLFkk pj gS] ?U  osQoy izkjafHkd o vafre voLFkkvksa ij
fuHkZj djsxk u fd ml iFk ij ftlls xSl ,d voLFkk ls nwljh
voLFkk esa igq¡prh gS A ;|fi] ?Q rFkk ?W  nksuksa] lkekU;r;k]
ml iFk ij fuHkZj djrs gSa ftlls xSl izkjafHkd voLFkk ls vafre
voLFkk esa tkrh gS A mQ"ekxfrdh osQ izFke fu;e] lehdj.k
(12.2)] ls ;g Li"V gS fd la;kstu ?Q – ?W  iFk ij fuHkZj
ugha djrk A blls irk pyrk gS fd ;fn dksbZ fudk; ,slh izfØ;k
viukrk gS ftlesa ?U = 0 (mnkgj.kkFkZ] vkn'kZ xSl dk lerkih;
izlkj] vuqHkkx 12-8 nsf[k,)] rks
?Q = ?W
vFkkZr~ fudk; dks nh xbZ mQ"ek fudk; }kjk ifjos'k ij dk;Z
djus esa iw.kZ :i ls mi;ksx esa vk tkrh gS A
;fn fudk; fl¯yMj esa Hkjh xSl gS rFkk fl¯yMj esa
xfr'khy fiLVu yxk gS rks fiLVu dks xfr nsus esa xSl dks dk;Z
djuk iM+rk gS A pwafd cy dks nkc × {ks=kiQy osQ :i esa ifjHkkf"kr
djrs gSa rFkk {ks=kiQy × foLFkkiu dks vk;ru dgrs gSa rks fLFkj
Read More
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

Objective type Questions

,

mock tests for examination

,

Extra Questions

,

Sample Paper

,

Semester Notes

,

ppt

,

NCERT Textbook - उष्मागतिकी Notes | EduRev

,

MCQs

,

past year papers

,

NCERT Textbook - उष्मागतिकी Notes | EduRev

,

pdf

,

Exam

,

Free

,

shortcuts and tricks

,

Viva Questions

,

NCERT Textbook - उष्मागतिकी Notes | EduRev

,

study material

,

Important questions

,

Summary

,

practice quizzes

,

Previous Year Questions with Solutions

,

video lectures

;