c`v ©weÁvb bdwbu t 6 · c`v_© av‡cwÿk zvc (jkg-1k ) c`v_© av‡cwÿk zvc (jkg-1k ) cvwb 4200...

c`v_©weÁvb

BDwbU 6 c„ôv # 113

BDwbU t 6

e¯‘i Dci Zv‡ci cÖfve

EFFECT OF HEAT ON SUBSTANCE f‚wgKv

Avgiv †iv‡` ùvov‡j kixi Mig nq, KviY kixi m~h© †_‡K Zvc cvq| cv‡Î cvwb wb‡q Dbv‡b DËß Ki‡j ev®ú

Drcbœ nq| Dbv‡bi Av¸b Zvc †`q| Zvc GK cÖKvi kw³| Zvc kw³i cÖfve Avgv‡ì Rxe‡b AZ¨šÍ ¸iæZ¡¡c~Y©|

Zv‡ci cÖfv‡e e¯‘i Ae¯’v cwieZ©b nq| c`v‡_©i AvqZ‡bi cwieZ©b nq| evqexq c`v‡_©i Pvc cwieZ©b nq|

Zv‡ci Gme cÖfve‡K Kv‡R jvwM‡q Avgiv Avgv‡ì eënvwiK I ˆ`bw›`b Rxeb‡K ¯”Q›` K‡i Zzwj| G BDwbUwU

Zvc, ZvcgvÎv, e ‘i Dci Zv‡ci cÖfve, KwVb, Zij, evqexq c`v‡_©i cÖmviY, e¯‘i Ae¯’vi cwieZ©b, Mjb,

ev®úxfeb, Mjb I ev®úxfe‡bi Dci Pv‡ci cÖfve, Gi cÖ‡qvM BZ¨vw` m¤ú‡K© we¯ÍvwiZ aviYv I Ávb AR©‡bi

mnvqK n‡e|

cvV-1 ZvcgvÎv I ZvcgvÎvi cwigvc (Heat and Measurement of Temparature)

D‡Ïk¨

GB cv‡Vi †k‡l Avcwb

1. Zvc I ZvcgvÎvi e¨vL¨v Ki‡Z cvi‡eb|

2. c`v‡_©i ZvcgvwÎK ag© e¨vL¨v Ki‡Z cvi‡eb|

3. ZvcgvÎvi wewfbœ †¯‹j e¨vL¨v Ki‡Z cvi‡eb|

4. dv‡ibnvBU, †mjwmqvm I †Kjwfb †¯‹‡ji g‡a¨ m¤úK© ¯’vcb Ki‡Z cvi‡eb|

6.1.1 Zvc I ZvcgvÎv (Heat and Temparature) GK LÛ eid nv‡Z wb‡j Avgiv VvÛv Abyfe Kwi| dzUšÍ cvwb‡Z nvZ w`‡j Amn¨ Mig Abyfe Kwi| GB

`yB Abyf~wZi AwfÁZv †_‡K Avgiv ewj ei‡d Ggb wKQz bvB hvi Afv‡e VvÛv Ges dzUšÍ cvwb‡Z Ggb wKQz Av‡Q

hvi cªfv‡e Mig Abyf‚Z nq| GB Abyf~wZi KviYB n‡”Q Zvc| Zvc GK cÖKvi kw³ hvi Afv‡e VvÛv Ges hvi

cÖfv‡e e¯‘ Mig nq| GK mgq weÁvbx‡ì aviYv wQj Zvc K¨vjwiK bv‡g GK cÖKvi m~² Zij ev evqexq c`v_©|

†Kv‡bv e¯‘‡Z K¨vjwiK Kg n‡j e¯‘ VvÛv Ges †ewk n‡j e¯‘ Mig nq| 1778 wLª: weÁvbx KvD›U ivg‡dvW©

Avwe®‹vi K‡ib, c`v‡_©i g‡a¨ AYymg~‡ni MwZi djB Zvc|

c`v‡_©i g‡a¨ AYy¸‡jv memg‡qB MwZkxj Ae¯’vq _v‡K| evB‡i †_‡K Ab¨ †Kv‡bv kw³ cÖ‡qvM Ki‡j GB MwZ

e„w× cvq| ZvB e¯‘ Mig nq| A_©vr Zvc n‡jv e¯‘i ev c`v‡_©i Af¨šÍi¯’ AYymg~‡ni MwZi m‡½ m¤úwK©Z GK

cÖKvi kw³ hv VvÛv I Mi‡gi Abyf‚wZ m„wó K‡i| Zvc kw³ Øviv KvR m¤úv`b nq| GB kw³‡K Ab¨ kw³‡Z

iƒcvšÍi Kiv hvq Avevi Ab¨ kw³I Zvc kw³‡Z iƒcvšÍwiZ nq| †hgb ê`y¨wZK evwZ‡Z we`y¨r kw³‡K Zvc kw³‡Z

Ges Zvc kw³‡K Av‡jvK kw³‡Z iƒcvšÍwiZ nq|

†Kv‡bv e¯‘‡K Zvc w`‡Z _vK‡j, hZ Zvc †`qv nq ZZ †ewk Mig nq| Mi‡gi gvÎv eySv‡bvi Rb¨ eënvi Kiv nq

DòZv ev ZvcgvÎv kãwU| `ÕywU e¯‘‡K ci¯ú‡ii Zvcxq ms¯ú‡k© Avb‡j G‡ì g‡a¨ Zv‡ci Av`vb cÖ vb N‡U|

GB Av`vb cÖ vb e¯‘i g‡a¨ Zv‡ci cwigv‡Yi Ici wbf©i K‡i bv| wbf©i K‡i e¯‘i Zvcxq Ae¯’vi Dci| e¯‘ `ywUi

Zvcxq Ae¯’v mgvb bv nIqv ch©šÍ Zvc GKwU †_‡K Ab¨wU‡Z (MigwU †_‡K VvÛvwU‡Z) cÖevwnZ nq| e¯‘i GB

Zvcxq Ae¯’vi bvg DòZv ev ZvcgvÎv|

GmGmwm †cÖvMÖvg


Zv‡ci msÁv : Zvc nj e¯‘i ev c`v‡_©i Af¨šÍi¯’ AYymg~‡ni MwZi m‡½ m¤úwK©Z GK cÖKvi kw³ hv VvÛv I

Mi‡gi Abyf‚wZ m„wó K‡i|

DòZv ev ZvcgvÎvi msÁv : ZvcgvÎv ev DòZv nj e¯‘i Zvcxq Ae¯’v hv H e¯‘ ‡_‡K Ab¨ e ‘‡Z Zvc cÖevn

wbqš¿Y K‡i|

Zv‡ci GKK : Zvc kw³i GKwU iƒc| ZvB kw³ Z_v Kv‡Ri GKKB Zv‡ci GKK| Zv‡ci SI GKK Ryj (J)|

GK mgq Zvc cwigv‡ci Rb¨ GKK aiv n‡Zv K¨vjwi| 1 MÖvg cvwbi ZvcgvÎv 1° C evov‡Z ev Kgv‡Z hZUv

Zv‡ci cÖ‡qvRb Zv‡K 1 K¨vjwi (Cal) aiv n‡Zv| 4.2 Ryj hvwš¿K kw³ 1 K¨vjwi Zv‡ci mgZzj¨| ZvB,

1 K¨vjwi = 4.2 Ryj|

ZvcgvÎvi GKK : ZvcgvÎvi SI GKK †Kjwfb| Z‡e ZvcgvÎvi †Kjwfb QvovI eûj cÖPwjZ `ywU GKK Av‡Q|

G¸‡jvi GKwU nj †mjwmqvm ev †mw›U‡MÖW Ges Ab¨wU dv‡ibnvBU|

Zvc I ZvcgvÎvi cv_©K¨

Zvc ZvcgvÎv

Zvc n‡jv e ‘i ev c`v‡_©i Af¨šÍi¯’ AYymg~‡ni

MwZi m‡½ m¤úwK©Z GK cÖKvi kw³ hv VvÛv I

Mi‡gi Abyf‚wZ m„wó K‡i|

ZvcgvÎv ev DòZv n‡jv e ‘i Zvcxq Ae¯’v hv H e¯‘

‡_‡K Ab¨ e¯‘‡Z Zvc cÖevn wbqš¿Y K‡i|

Zv‡ci SI GKK Ryj (J)| Zv‡ci Ab¨ GKwU

eënvwiK GKK K¨vjwi| GwU †gwUªK c×wZi

GKK| GL‡bv cywó weÁv‡b eëüZ nq|

ZvcgvÎv SI GKK †Kjwfb| G QvovI eûj cÖPwjZ `ywU

GKK nj †mjwmqvm ev †mw›U‡MÖW Ges dv‡ibnvBU|

Zvc cwigv‡ci hš¿ K¨vjwiwgUvi| ZvcgvÎv cwigv‡ci hš¿ _v‡g©vwgUvi|

Zv‡ci cÖevn Zv‡ci cwigv‡Yi Ici wbf©i K‡i bv | Zv‡ci cÖevn ZvcgvÎvi Ici wbf©i K‡i|

`ywU e ‘i Zv‡ci cwigvY GK n‡jI G‡ì ZvcgvÎvi

cwigvY wfbœ n‡Z cv‡i|

`ywU e ‘i ZvcgvÎv GK n‡jI G‡ì g‡a¨ Zv‡ci cwigvY

wfbœ n‡Z cv‡i|

6.1.2 c`v‡_©i ZvcgvwÎK ag© (Thermometric Properties of Matter)

Zvc cÖ‡qvM Ki‡j e¯‘i wKQz wKQz †fŠZ a‡g©i cwieZ©b nq| †hgb †Kv‡bv †Kv‡bv Zij c`v‡_©i AvqZb ev‡o, avZe

Zv‡ii ê`y¨wZK †iva ev‡o, evqexq c`v‡_©i Pvc I AvqZb ev‡o| †Kv‡bv †Kv‡bv c`v‡_©i eY© cwieZ©b nq| Zvc

cÖ‡qv‡M c`v‡_©i GBme †fŠZ ag©‡K Kv‡R jvwM‡q Zv‡ci gvÎv ev ZvcgvÎv cwigvc Kiv hvq Ges Zvcgvb hš¿

ˆZwi nq| †h me c`v‡_©i GB me ag© we‡ePbv K‡i ZvcgvcK hš¿ wbg©vY Kiv nq Zv‡ì ZvcwgwZK c`v_© e‡j|

Ges ZvcgvÎv cwigv‡ci Rb¨ c`v‡_©i †h me ag© Kv‡R jvMv‡bv nq Hme êwkó¨‡K ZvcgvwÎK ag© e‡j|

ZvcgvÎvi cwieZ©‡bi mv‡_ Zij c`v‡_©i AvqZ‡bi †h cwieZ©b nq Zvi Dci wfwË K‡i †h ZvcgvcK hš¿ ev

_v‡g©vwgUvi ˆZwi nq Zv‡K Zij _v‡g©vwgUvi e‡j| †hgb cvi` _v‡g©vwgUvi, Gj‡Kvnj _v‡g©vwgUvi| cvi` ev

Gj‡Kvnj‡K mylg e¨v‡mi ev cÖ ’‡”Q‡ì GKwU KuvP b‡ji g‡a¨ ivLv nq| G Ae¯’vq Zij ¯Í‡¤¢i AvqZb

ZvcgvÎvi mgvbycvwZK nq| G‡ÿ‡Î b‡ji g‡aï Zij ¯Í‡¤¢i D”PZv‡K ev ˆ`N© ‡K ZvcwgwZK ag© wnmv‡e we‡ePbv

Kiv nq|

Gfv‡e †Kv‡bv †Kv‡bv c`v‡_©i M¨v‡mi Pvc, †Kvb †Kvb c`v‡_©i ‰e`y¨wZK †iva, †Kv‡bv †Kv‡bv e¯‘i Zvc wewKiY

ag©‡K we‡ePbv K‡iI Zvcgvb hš¿ ev _v‡g©vwgUvi wbg©vY Kiv nq|

c`v_©weÁvb


6.1.3 ZvcgvÎvi wewfbœ †¯‹j (Different Scales of Temperature) †Kv‡bv e¯‘i ZvcgvÎv cwigv‡ci Rb¨ wbw`©ó †¯‹j I GKK cÖ‡qvRb| ZvcgvÎvi †¯‹j wba©vi‡Yi Rb¨ `ywU

ZvcgvÎv‡K w¯’i a‡i †bIqv n‡q‡Q| G‡ì ejv nq w¯’ivsK| eid‡K Zvc w`‡j ZvcgvÎv evo‡Z _v‡K| GK mgq

wbw`ó ZvcgvÎvq †cŠu‡Q eid Mj‡Z ïiæ K‡i Ges mg¯Í eid M‡j cy‡ivUv cvwb bv nIqv ch©šÍ ZvcgvÎvi †Kvb e„w×

ev cwieZ©b nq bv| weÁvbxiv G‡K GKwU w¯’iv•K wba©viY K‡i‡Qb| Avevi cvwb‡K Zvc w`‡Z _vK‡j cvwbi

ZvcgvÎv evo‡Z _v‡K, wKš‘ GK mgq ZvcgvÎvi e„w× †_‡g hvq cvwb dzU‡Z _v‡K, Ges cvwb ev®ú nIqv ïiæ nq|

mg¯Í cvwb ev®ú bv nIqv ch©šÍ dyUšÍ cvwbi ZvcgvÎv AcwiewZ©Z _v‡K| GwU‡K weÁvbxiv Avi GKwU w¯’iv•K

a‡i‡Qb| cÖ_gwU wb¤œ w¯’iv•K c‡iiwU EaŸ© w¯’iv•K |

AZGe cÖgvY Pv‡c †h ZvcgvÎvq eid M‡j cvwb nq Zv‡K wb¤œ w¯’iv•K e‡j| GB ZvcgvÎvq cvwb R‡g eid nq

e‡j G‡K wngv•K ev eidwe›`yI e‡j| Abyiƒcfv‡e cÖgvY Pv‡c dzUšÍ weï× cvwb †h ZvcgvÎvq Rjxq ev‡®ú cwiYZ

nq Zv‡K EaŸ© w¯’iv•K e‡j| G‡K õzUbv¼ ev ev®ú we› yI e‡j|

w¯’i we›`y ywUi gaëZx© ZvcgvÎvi eëavb‡K ZvcgvÎvi †¯‹‡ji †gŠwjK eëavb e‡j| †gŠwjK eëavb‡K bvbv

fv‡e fvM K‡i ZvcgvÎv cwigv‡ci wewfbœ †¯‹j ˆZwi n‡q‡Q| ZvcgvÎv cwigv‡ci enyj cÖPwjZ †¯‹j wZbwU:

†mjwmqvm, dv‡ibnvBU Ges †Kjwfb|

wPÎ t 6.1 wewfbœ ai‡bi ZvcgvÎvi †¯‹j

†mjwmqvm †¯‹‡ji wb¤œ w¯’iv¼ 0 wWMÖx, EaŸ© w¯’iv¼ 100 wWMÖx a‡i †gŠwjK eëavb‡K 100 fv‡M fvM Kiv nq (wPÎ

6.1)| cÖ‡Z¨K fvM‡K 1 wWMÖx †mjwmqvm (ms‡ÿ‡c 1C) ejv nq|

dv‡ibnvBU †¯‹‡ji wb¤œ w¯’iv¼ 32 wWMÖx, EaŸ© w¯’iv¼ 212 wWMÖx a‡i †gŠwjK eëavb‡K 180 fv‡M fvM Kiv nq

(wPÎ 6.1)| cÖ‡Z¨K fvM‡K 1 wWMÖx dvibnvBU (ms‡ÿ‡c 1 F) ejv nq|

†Kjwfb †¯‹‡j wb¤œ w¯’iv¼ 273 Ges Ea© w¯’iv¼ 373 a‡i †gŠwjK ˆ`N© ‡K 100 fv‡M fvM Kiv n‡q‡Q (wPÎ 6.1)|

cÖ‡Z¨K fvM‡K 1 †Kjwfb (ms‡ÿ‡c 1K) ejv nq| G‡ÿ‡Î wWMÖx ejv nq bv| †Kjwfb †¯‹jB ZvcgvÎv cwigv‡ci

AvšÍR©vwZK ev SI GKK|

GmGmwm †cÖvMÖvg


6.1.4 †mjwmqvm, dv‡ibnvBU I †Kjwfb †¯‹‡ji m¤úK©

Relation among Celsius, Fahrenheit and Kelvin Scales

†mjwmqvm, dv‡ibnvBU I †Kjwfb †¯‹‡ji m¤úK© wbY©‡qi Rb¨ GKwU _v‡gv©wgUvi AB †bqv n‡jv hvi wb¤œ w¯’iv¼

A Ges EaŸ© w¯’iv¼ B| GwU‡K †mjwmqvm, dv‡ibnvBU I †Kjwfb _v‡g©vwgUv‡ii cv‡k Ggbfv‡e ivLv n‡jv †hb

me¸‡jvi wb¤œ w¯’iv¼ Ges EaŸ© w¯’iv¼ `v‡Mi GKmv‡_ wg‡j hvq| aiv hvK, †Kv‡bv ZvcgvÎvq AB _v‡g©wgUv‡ii

cvi` kxl© hLb M Ae¯’v‡b Av‡m ZLb †mjwmqvm, dv‡ibnvBU I †Kjwfb †¯‹‡j h_vµ‡g C, F I K we›`y‡Z

Av‡m| AZGe Avgiv wjL‡Z cvwi,

MA C 0 F 32 K 273BA 100 0 212 32 373 273

- - -- - -

ev, C F 32 K 273100 180 100

- -

ev, C F 32 K 2735 9 5

- -

†mjwmqvm I dv‡ibnvBU †¯‹‡ji g‡a¨ m¤úK© n‡jvÑ

C F 325 9

-

ev, 9F C 325

wPÎ t 6.2 ZvcgvÎvi †¯‹j¸‡jvi g‡a¨ m¤úK©

MvwYwZK D`vniY 6.1

GKRb iæMxi ‡`‡ni ZvcgvÎv 104F | †mjwmqvm †¯‹‡j H ZvcgvÎ KZ n‡e ?

mgvavb t Avgiv Rvwb ,

C F 325 9

-

ev,

C 104 32 725 9 9

-

ev, C = 8 5 = 40

†`Iqv Av‡Q,

dv‡ibnvBU †¯‹‡j ZvcgvÎv, F = 104F †mjwmqvm ZvcgvÎv , C = ?

DËi t 40 C

c`v_©weÁvb


mvi-ms‡ÿc:

Zvc t GK cÖKvi kw³| c`v‡_©i g‡a¨ AYymg~‡ni MwZi djB Zvc, hv VvÛv I Mi‡gi Abyf‚wZ m„wó K‡i| Zv‡ci

GKK Ryj|

ZvcgvÎv t ZvcgvÎv ev DòZv nj e¯‘i Zvcxq Ae¯’v hv H e¯‘ ‡_‡K Ab¨ e¯‘‡Z Zvc cÖevn wbqš¿Y K‡i|

ZvcgvÎvi SI GKK †Kjwfb, Ab¨ GKK wWMÖx †mjwmqvm I wWMÖx dv‡ibnvBU|

wb¤œ w¯’iv¼ t cÖgvY Pv‡c †h ZvcgvÎvq eid M‡j cvwb nq Zv _v‡g©vwgUv‡ii wb¤œ w¯’ivsK| G‡K wngv¼ ev eid

we›`yI e‡j|

EaŸ© w¯’iv¼ t cÖgvY Pv‡c †h ZvcgvÎvq dzUšÍ weï× cvwb Rjxq ev‡®ú cwiYZ nq Zv _v‡g©vwgUv‡ii EaŸ© w¯’iv¼|

G‡K õzUbv¼ ev ev®ú we› yI e‡j|

†mjwmqvm, dv‡ibnvBU I †Kjwfb †¯‹‡ji m¤úK© t

C F 32 K 2735 9 5

- -

cv‡VvËi g~j¨vqb 6.1

mwVK DË‡ii cv‡k wUK () wPý w`b|

1| †h ZvcgvÎvq dzUšÍ weï× cvwb Rjxq ev‡®ú cwiYZ nq Zv‡K wK e‡j ?

(K) wb¤œ w¯’iv¼ (L) wngv¼

(M) ùzzUbv¼ (N) eid we› y

2| _v‡g©vwgUv‡ii wb¤œ w¯’iv¼ KZ ?

(K) wngv¼ ev ev¯ú we› y (L) cvwb †h ZvcgvÎvq eid nq

(M) ùzUbv¼ ev eid we› y (N) Dc‡ii †KvbwUB bq

3| †KvbwU c`v‡_©i ZvcgvwÎK ˆewkó¨ bq ?

(K) AvqZb (L) Pvc

(M) ˆe`y¨wZi †iva (N) ZvcgvÎv

4| ZvcgvÎv cwigv‡ci AvšÍR©vwZK GKK †KvbwU ?

(K) †mjwmqvm (L) dv‡ibnvBU

(M) †Kjwfb (N) wWMÖx †mjwmqvm

5| †Kjwfb †¯‹‡j cvwbi RgvUv¼ KZ ?

(K) 0K (L) 32 K

(M) 273 K (N) - 273 K

GmGmwm †cÖvMÖvg


cvV-2 KwVb c`v‡_©i cÖmviY (Expansion of solids)

D‡Ïk¨


1. KwVb c`v‡_©i ˆ`N© cÖmviY e¨vL¨v Ki‡Z cvi‡eb|

2. KwVb c`v‡_©i †ÿÎ cÖmviY e¨vL¨v Ki‡Z cvi‡eb|

3. KwVb c`v‡_©i AvqZb cÖmviY e¨vL¨v Ki‡Z cvi‡eb|

6.2.1 KwVb c`v‡_©i cÖmviY (Expansion of Solids due to Heat) Avgiv Rvwb †Kv‡bv e¯‘‡Z Zvc cÖ‡qvM Ki‡j Zvi wewfbœ cÖfve cwijwÿZ nq, wewfbœ cwieZ©b N‡U|

†hgb- ZvcgvÎvi cwieZ©b, AvqZb cwieZ©b, Ae¯’vi cwieZ©b, evqexq c`v‡_©i †ÿ‡Î Pv‡ci cwieZ©b, Zwor

cwievnx c`v‡_©i †iv‡ai cwieZ©b, †PŠ¤K c`v‡_©i †PŠ¤K a‡g©i cwieZ©b BZ¨vw`|

mvaviYZ Zvc cÖ‡qv‡M c`v‡_©i AvqZb e„w× cvq (`yÕGKwU e¨wZµg Qvov)| Zv‡ci cÖfv‡e e¯‘i Aby¸‡jvi g‡aï

MwZ kw³ e„w× cvq| d‡j Gi AYy¸‡jvi Mo mvg¨ve¯’v evB‡ii w`‡K m‡i hvq Ges e¯‘ Zv‡ci cÖfv‡e m¤úÖmvwiZ

nq| GB cÖmviY e¯‘i me w`‡K N‡U e‡j Avgiv †`wL AvqZb e„w× cvq|

e¯‘i AvqZ‡bi wZbwU gvÎv ˆ`N© , cÖ ’ I D”PZv| ZvB Zv‡ci cÖfv‡e KwVb c`v‡_©i cÖmvi‡Yi e¨vcviwU wZb w`‡KB

we‡ePbv Ki‡Z nq| Ges wZb fv‡e GB e„w× ev cwieZ©b cwigvc Kiv nq, Zv nj,

1) ˆ`‡N© i cÖmviY,

2) Zjxq ev †ÿÎd‡ji cÖmviY

3) AvqZb cÖmviY|

GK UzK‡iv j¤v Zvi ev miæ iW‡K Zvc w`‡j Zvi AvqZb ev‡o e‡U wKš‘ Gi ˆ`‡N© i Zzjbvq cÖ ’ ev cÖ ’‡”Q‡ì

e„w× GZB Kg nq †h Zv Zvrch©c~Y© bq| AZ¨šÍ bMY¨| G †ÿ‡Î †Kej ˆ`‡N© i cÖmviY we‡ePbv Kiv nq| Avevi

GK LÛ wU‡bi cvZjv wmU ev cv‡Zi K_v fvev hvK| hvi ˆ`N© Ges cÖ ’ cÖvq mgvb| wKš‘ D”PZv ev cyiæZ¡ bMY¨|

G‡ÿ‡Î ˆ`N© Ges cÖ ’ Z_v †ÿÎdj ev ZjwUi e„w× we‡ePbvi cÖ‡qvRb nq| Abyiƒcfv‡e †Kvb †Kvb †ÿ‡Î e¯‘i

ˆ`N© , cÖ ’, D”PZv wZbwU gvÎvi cwieZ©bB Zvrch© c‚Y© n‡q I‡V| †m me †ÿ‡Î AvqZb cÖmviY MYbv Ki‡Z nq|

Zvc cÖ‡qv‡M me c`v‡_©i cÖmviY mgvb nq bv| cÖmvi‡Yi cwigvY c`v‡_©i †fŠZ a‡g©i GKwU| cixÿv K‡i †`Lv

†M‡Q wewfbœ KwVb c`v‡_©i cÖmviY wewfbœ| Zvc cÖ‡qv‡M GKB KwVb c`v‡_©i mKj w`‡KB mylg cÖmviY N‡U Ges

GB cÖmviY e¯‘i Avw` Ae¯’v I ZvcgvÎv e„w×i mvgvbycvwZK|

†hgb GKwU `‡Ûi ˆ`N© l0 GKK| ZvcgvÎv θ cwigvY e„w×i Rb¨ Gi ˆ`N© l cwigvY e„w× †cj|

G‡ÿ‡Î †`Lv hvq l l0 θ | [ Ô Õ mvgvbycvwZK wPý| cov nq Õproportional toÕ ev ÕmgvbycvwZKÕ ]|

6.2.2 ˆ`N© cÖmviY I ˆ`N© cÖmviY mnM ev ¸Yv¼ (Coefficient of Linear expansion) Av‡MB D‡jøL Kiv n‡q‡Q, †Kv‡bv †Kv‡bv †ÿ‡Î Avgv‡ì †Kej ˆ`‡N© i cÖmviY we‡ePbv Ki‡Z nq| Zvc cÖ‡qv‡M

KwVb e¯‘i ˆ`‡N© i mylg cÖmviY N‡U Ges GB cÖmviY e¯‘i Avw` ˆ`N© I ZvcgvÎv e„w×i ¸Yd‡ji mvgvbycvwZK|

†hgb GKwU `‡Ûi ˆ`N© l0 GKK| ZvcgvÎv θ1 †_‡K θ †e‡o θ2 nj| ZvcgvÎvi GB θ e„w×i Rb¨ Gi ˆ`N©

l cwigvY e„w× ‡cj|

c`v_©weÁvb


G‡ÿ‡Î †`Lv hvq l l0 θ |

ev, l = l0 θ ... ... ... ... .... (6.1)

GLv‡b GKwU MÖxK Aÿi (D”PviY Avjdv), GKwU mgvbycvwZK aªæeK| Gi gvb `ÛwUi

Dcv`v‡bi Dci wbf©i K‡i| G‡K mswkøó KwVb

c`v‡_©i ˆ`N© cÖmviY ¸YvsK ev ˆ`N© cÖmviY

mnM e‡j| G‡K MÖxK Aÿi (Avjdv) Øviv

cÖKvk Kiv nq|

wPÎ t 6.3 `‡Ûi ˆ`N © cÖmviY

(6.1) mgxKiY †_‡K †`Lv hvq †h,

0l

l =

ˆ`N© cmÖ viY

Avw` ˆ`N© ZvcgvÎvi ew„ ×

... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... (6.2)

Dc‡ii mgxKi‡Y ˆ`N© l0 =1m, ZvcgvÎvi e„w× θ =1K ai‡j, mvgvbycvwZK aªæeK = l nq| G

†_‡K ˆ`N© cÖmviY ¸Yv‡¼i wb¤œiƒc msÁv †`qv n‡q‡Q|

1m ˆ`‡N© i †Kv‡bv KwVb c`v‡_©i GKwU `‡Ûi ZvcgvÎv 1K e„w× Ki‡j H `‡Ûi ˆ`N© hZUzKz e„w× cvq Zv‡K H

`‡Ûi Dcv`v‡bi ˆ`N© cÖmviY ¸Yv¼ e‡j|

GKK: 6.2 bs mgxKi‡Yi Wvb cv‡ki ivwk¸‡jvi GKK ewm‡q ˆ`N© cÖmviY ¸Yv‡¼i GKK cvIqv hvq| GB GKK

nj K-1 ev cÖwZ †Kjwfb| jÿ¨ Kiæb ˆ`N© cÖmviY ¸Yv‡¼i gvb ˆ`‡N© i GK‡Ki Dci wbf©i K‡i bv|

Zvrch© t B¯úv‡Zi ˆ`N© cÖmviY ¸Yv¼ 1110-6 K-1 ej‡Z eySvq 1m ˆ`‡N© i GKLÛ B¯úvZ `‡Ûi ZvcgvÎv

1K evo‡j Gi ˆ`N© 1110-6 m evo‡e|

aiv hvK θ1 GKK ZvcgvÎvq GKwU `‡Ûi ‰`N© l0 GKK| `ÛwU‡Z Zvc cÖ‡qv‡M ZvcgvÎv †e‡o θ2 nj Ges `‡Ûi

ˆ`N© nj l | Zvn‡j 6.2 mgxKiYwU n‡e

0l

l

)( 120

0

l

ll = ... (6.3)

AZGe, `‡Ûi P‚ovšÍ ˆ`N© )}(1{ 120 ll

A_ev, )1(0 ll ... ... .... ... ... ... ... ... ... ... ...... ... ... ... ... ... (6.4)

6.2.3 Zjxq ev †ÿÎ cÖmviY mnM ev ¸Yv¼ (Coefficient of surface expansion) †Kv‡bv †Kv‡bv †ÿ‡Î Avgv‡`i †Kej Zjxq cÖmviY we‡ePbv Ki‡Z nq| Zvc cÖ‡qv‡M KwVb e¯‘i Zj ev †ÿ‡Îi

mylg cÖmviY N‡U Ges GB †ÿÎ cÖmviY e¯‘ c„‡ôi Avw` †ÿÎdj I ZvcgvÎv e„w×i ¸Yd‡ji mgvbycvwZK|

†hgb GKwU cv‡Zi c„‡ôi Avw` †ÿÎdj A0 GKK| Gi ZvcgvÎv θ e„w×i Rb¨ †ÿÎdj A cwigvY e„w× †cj,

Ges P‚ovšÍ †ÿÎdj n‡jv A GKK|

G‡ÿ‡Î †`Lv hvq A A0 θ

P‚ovšÍ ˆ`N© - Avw` ˆ`N©

Avw` ‰`N© (P‚ovšÍ ZvcgvÎv - Avw` ZvcgvÎv)

GmGmwm †cÖvMÖvg


ev, A = A0 θ ... ... .... ... ... ... ... ... .. ... ... ... ... ... ... ... ... ... ... ... (6.5)

GLv‡b GKwU MÖxK Aÿi (D”PviY weUv), GKwU mgvbycvwZK aªæeK| Gi gvb cvZwUi Dcv`v‡bi Dci wbf©i

K‡i| G‡K mswkøó KwVb c`v‡_©i Zjxq ev †ÿÎ cÖmviY

¸Yv¼ ev †ÿÎ cÖmviY mnM e‡j| G‡K MÖxK Aÿi (weUv)

Øviv cÖKvk Kiv nq|

(6.5) mgxKiY †_‡K cvIqv hvq,

wPÎ t 6.4 cv‡Zi †ÿÎ cÖmviY

0

AA

= ... ... .... ... ... .... ... ... ... ... ... ... ... (6.6)

Dc‡ii mgxKi‡Y †ÿÎdj A0 =1m2, ZvcgvÎvi e„w× θ =1K ai‡j, mvgvbycvwZK aªæeK, = A nq| G

†_‡K †ÿÎ cÖmviY ¸Yv‡¼i wbgœiƒc msÁv †`qv n‡q‡Q|

1m2 †ÿÎd‡ji †Kv‡bv KwVb c`v‡_©i GKwU cv‡Zi ZvcgvÎv 1K e„w× Ki‡j H cv‡Zi †ÿÎdj hZUzKz e„w× cvq

Zv‡K H cv‡Zi ev H KwVb c`v‡_©i Dcv`v‡bi †ÿÎ ev Zjxq cÖmviY ¸Yv¼ e‡j|

GKK: 6.6 bs mgxKi‡Yi Wvb cv‡ki ivwk¸‡jvi GKK ewm‡q †ÿÎ cÖmviY ¸Yv‡¼i GKK cvIqv hvq| GB GKK

nj K-1 ev cÖwZ †Kjwfb| ˆ`N© cÖmviY ¸Yv‡¼i gZ †ÿÎ cÖmviY ¸Yv‡¼i gvb †ÿÎd‡ji gv‡bi ev GK‡Ki Dci

wbf©i K‡i bv|

Zvrch© t B¯úv‡Zi †ÿÎ cÖmviY ¸Yv¼ 2210-6 K-1 ej‡Z eySvq 1m2

†ÿÎd‡ji GK UzK‡iv B¯úv‡Zi cv‡Zi

ZvcgvÎv 1K evo‡j Gi †ÿÎdj 2210-6 m2 evo‡e|

aiv hvK θ1 GKK ZvcgvÎvq GKwU Z‡ji †ÿÎdj A0 GKK| cvZwU‡Z Zvc cÖ‡qv‡M ZvcgvÎv †e‡o θ2 nj Ges

cv‡Zi †ÿÎdj nj A Zvn‡j 6.6 bs mgxKiYwU n‡e

0

0 0 2 1

A AAA A

= ......... (6.7)

AZGe, cv‡Zi P‚ovšÍ †ÿÎdj 0 2 11{ - }A A

A_ev, 0 1A A ... ... .... ... ... ... ... ... ..... ... ... ... ... .... (6.8)

6.2.4 AvqZb cÖmviY mnM : (Coefficient of Volume expansion) †Kv‡bv †Kv‡bv †ÿ‡Î Avgv‡`i e¯‘i ˆ`N© , cÖ ’, D”PZv ev AvqZb we‡ePbv Ki‡Z nq| Zvc cÖ‡qv‡M KwVb e¯‘i

AvqZ‡bi mylg cÖmviY N‡U Ges GB AvqZb cÖmviY e¯‘i Avw` AvqZb I ZvcgvÎv e„w×i ¸Yd‡ji mvgvbycvwZK|

†hgb GKwU L‡Ûi Avw` AvqZb V0 GKK| Gi ZvcgvÎv θ e„w×i Rb¨ Gi AvqZb V cwigvY e„w× †cj, Ges

P‚ovšÍ AvqZb nj V GKK|

†¶Î cÖmviY

Avw` †¶Îdj ZvcgvÎvi e„w×

P‚ovšÍ †¶Îdj - Avw` †¶Îdj

Avw` †¶Îdj (P‚ovšÍ ZvcgvÎv - Avw` ZvcgvÎv)

c`v_©weÁvb


G‡ÿ‡Î †`Lv hvq V V0 θ |

ev, V = V0 θ ... ... .... ... ... ... ... ... ... ... ... ... ... ...... ... ... ... (6.9)

GLv‡b GKwU MÖxK Aÿi (D”PviY Mvgv), GKwU

mgvbycvwZK aªæeK| Gi gvb LÛwUi Dcv`‡bi Dci wbf©i

K‡i| G‡K mswkøó KwVb c`v‡_©i AvqZb cÖmviY ¸Yv¼ ev

AvqZb cÖmviY mnM e‡j| G‡K MÖxK Aÿi (Mvgv) Øviv

cÖKvk Kiv nq|

(6.9) mgxKiY †_‡K †`Lv hvq †h,

wPÎ 6.5 AvqZvKvi KwVb e¯‘i cÖmviY

0

VV

= ... ... .... ... ... ... ... ... ... ... ... (6.10)

Dc‡ii mgxKi‡Y AvqZb V0 =1m3, ZvcgvÎvi e„w× θ =1K ai‡j, mvgvbycvwZK aªæeK = V nq| G †_‡K

AvqZb cÖmviY ¸Yv‡¼i wbgœiƒc msÁv †`qv n‡q‡Q|

1m3 AvqZ‡bi †Kv‡bv KwVb c`v‡_©i GKwU AvqZvKvi L‡Ûi ZvcgvÎv 1K e„w× Ki‡j H LÛwUi AvqZb hZUzKz

e„w× cvq Zv‡K H c`v‡_©i Dcv`v‡bi AvqZb cÖmviY ¸Yv¼ e‡j|

GKK: 6.10 bs mgxKi‡Yi Wvb cv‡ki ivwk¸‡jvi GKK ewm‡q AvqZb cÖmviY ¸Yv‡¼i GKK cvIqv hvq| GB

GKK nj K-1 ev cÖwZ †Kjwfb| jÿ¨ Kiæb ˆ`N© I †ÿÎ cÖmviY ¸Yv‡¼i gZ AvqZb cÖmviY ¸Yv‡¼i gvb

AvqZ‡bi gv‡bi ev GK‡Ki Dci wbf©i K‡i bv|

B¯úv‡Zi AvqZb cÖmviY ¸Yv¼ 3310-6 K-1 ej‡Z eySvq 1m3

AvqZ‡bi GK LÛ B¯úv‡Zi ZvcgvÎv 1K evo‡j Gi AvqZb 3310-6 m3

evo‡e|

aiv hvK θ1 GKK ZvcgvÎvq GKwU avZe L‡Ûi AvqZb V0 GKK| LÛwU‡Z Zvc cÖ‡qv‡M ZvcgvÎv †e‡o θ2 nj

Ges L‡Ûi AvqZb V, Zvn‡j 6.10 bs mgxKiYwU n‡e

0

VV

0

0 2 1

--

V VV

= ...... .... ... (6.11)

AZGe, e¯‘i P‚ovšÍ AvqZb 0 2 11 { - }V V

A_ev, 0 1 V V ... ... .... ... ... .... ... ... ... ... ... ... ... ... ... ... (6.12)

AvqZb cÖmviY

Avw` AvqZb ZvcgvÎvi e„w×

P‚ovšÍ AvqZb - Avw` AvqZb

Avw` AvqZb (P‚ovšÍ ZvcgvÎv - Avw` ZvcgvÎv)

GmGmwm †cÖvMÖvg


6.2.5 ‰`N© cÖmviY ¸Yv¼, †ÿÎ cÖmviY ¸Yv¼ Ges AvqZb cÖmviY ¸Yv‡¼i m¤ú©K

(Relation among coefficients of linear, surface & volume expansion) aiv hvK abcd GKwU eM©vKvi mylg avZe cvZ (wPÎ 6.6)| hvi ˆ`N© I cÖ ’ Dfq w`‡K 0l GKK AZGe Gi

Z‡ji †ÿÎdj, A0 = 20l |

cvZwUi ZvcgvÎv θ K e„w× Kivq Gi

ˆ`N© cÖ ’ Dfq w`‡K mgvb cwigvY e„w×

cv‡e| aiv hvK e„w× †c‡q cÖ‡Z¨K w`‡K

ˆ`N© n‡jv l Ges †ÿÎdj n‡jv A, Zvn‡j bZzb †ÿÎdj n‡e , A = l2

|

6.6 bs wP‡Î Ae¯’vwU †`Lv‡bv n‡jv|

wPÎ t 6.6

mgxKiY 6.4 †_‡K -

)1(0 ll 2 22 2 2

01 1 2ol l l [ Dfq c‡ÿi eM© K‡i]

GLb mgxKi‡Y l2 = A Ges 20l = A0 ewm‡q Ges (θ)2

Gi gvb LyeB bMY¨ e‡j ev` w`‡j cvIqv hv‡e,

0 1 2{ }A A = 0 1A [ †h‡nZz, 0 1A A ; mgxKiY 6.8]

2 ev, = 2 ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (6.13)

A_©vr, †ÿÎ cÖmviY ¸Yv¼ ˆ`N© cÖmviY ¸Yv‡¼i wØ¸Y|

GKBfv‡e mgxKiY (6.4 Ges 6.12) †_‡K cÖgvY Kiv hvq AvqZb cÖmviY ¸Yv¼ ˆ`N© cÖmviY ¸Yv‡¼i wZb¸Y|

A_©vr =3 ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (6.14)

MvwYwZK D`vniY 6.2

30C ZvcgvÎvq GKwU Zvgvi Zv‡ii ˆ`N© 100m | 60C ZvcgvÎvq Gi ˆ`N© 100.05 m n‡j Zvgvi ˆ`N© i

cÖmviY ¸Yv¼ wbY©q Kiæb|

mgvavb :

Avgiv Rvwb

0l

l

30K100m0.05m

= 16.66610-6 K-1

DËi : 16.710-6 K-1

GLv‡b,

Avw` ZvcgvÎv, θ1 = 30C P‚ovšÍ ZvcgvÎv, θ2 = 60C ZvcgvÎvi e„w×, θ = (60-30) C= 30K Avw` ˆ`N© , l0 = 100 m P‚ovšÍ ˆ`N© , l = 100.05 m ˆ`N© e„w×, l = (100.05 - 100)m = .05m ˆ`N© cÖmviY ¸Yv¼, = ?

c`v_©weÁvb


MvwYwZK D`vniY 6.3

0C ZvcgvÎvq GKwU †jvnvi `‡Ûi ˆ`N© 1m | 50C ZvcgvÎvq Gi ˆ`N© KZ n‡e? (†jvnvi ˆ`N© cÖmviY

¸Yv¼ 11.610-6 K-1) mgvavb :

Avgiv Rvwb

0

0 )(l

ll

ev , )1(0 ll

= 1m (1+ 11.610-6 K-150K) = 1.0006m

DËi : 1.0006m

GLv‡b,

Avw` ZvcgvÎv, θ1 = 0C P‚ovšÍ ZvcgvÎv, θ2 = 50C ZvcgvÎvi e„w×, θ = (50-0) C= 50K Avw` ˆ`N© , l0 = 1 m ˆ`N© cÖmviY ¸Yv¼, = 11.610-6 K-1

P‚ovšÍ ˆ`N© , l = ?

MvwYwZK D`vniY 6.4

GKwU †jvnvi ˆZwi b‡ji ˆ`N© 300 m (0C ZvcgvÎvq) Gi ga¨ w`‡q Rjxq ev®ú cÖevwnZ n‡Z _vK‡j Gi ˆ`N©

KZ evo‡e? [†jvnvi ˆ`N© cÖmivY ¸Yv¼ 11.610-6 K-1]

mgvavb :

Avgiv Rvwb,

0l

l

ev , )α0 ll

= 300m(11.610-6 K-1)100K

= 0.0438m

DËi : 0.044m

GLv‡b,

Avw` ZvcgvÎv, θ1 = 0C P‚ovšÍ ZvcgvÎv, θ2 = 100C ZvcgvÎvi e„w×, θ = (100-0) C= 100K Avw` ˆ`N© , l0 = 300 m

ˆ`N© cÖmviY ¸Yv¼, = 11.610-6 K-1

ˆ`N© e„w×, l = ?

MvwYwZK D`vniY 6.5

GKwU mxmvi ¸wji AvqZb 0C DòZvq 2.5 cm3 Ges 100C DòZvq Gi AvqZb 0.02 cm3

cwigvY

e„w×cvq| mxmvi ˆ`N¨© cÖmviY ¸Yv¼ wbY©q Kiæb|

mgvavb :

Avgiv Rvwb, AvqZb cÖmviY ¸Yv¼

= 3

13

0

13

VV

ev , =

3

3

1 0.02cm3 2.5cm ×100K

GLv‡b,

Avw` ZvcgvÎv, θ1 = 0C P‚ovšÍ ZvcgvÎv, θ2 = 100C ZvcgvÎvi e„w×, θ = (100-0) C= 100K Avw` AvqZb, V0 = 2.5 cm3 AvqZb e„w×, V = 0.02 cm3 ˆ`N© cÖmviY ¸Yv¼, = ?

GmGmwm †cÖvMÖvg


=

11 0.00008K3

= 2.6666666...10-6K-1

DËi : 2.6710-5K-1

mvi-ms‡ÿc:

ˆ`N© cÖmviY ¸Yv¼ t 1m ˆ`‡N© i †Kv‡bv KwVb c`v‡_©i GKwU `‡Ûi ZvcgvÎv 1K e„w× Ki‡j H `‡Ûi ˆ`N© hZUzKz

e„w× cvq Zv‡K H `‡Ûi Dcv`v‡bi ‰`N© cÖmviY ¸Yv¼ e‡j| Gi GKK K-1 ev cÖwZ †Kjwfb| GB gvb ˆ`‡N© i

GK‡Ki Dci wbf©i K‡i bv|

†ÿÎ cÖmviY ¸Yv¼ t 1m2 †ÿÎd‡ji †Kv‡bv KwVb c`v‡_©i GKwU cv‡Zi ZvcgvÎv 1K e„w× Ki‡j H cv‡Zi

†ÿÎdj hZUzKz e„w× cvq Zv‡K H cv‡Zi ev KwVb c`v‡_©i Dcv`v‡bi †ÿÎ ev Zjxq cÖmviY ¸Yv¼ e‡j| Gi GKK

K-1 ev cÖwZ †Kjwfb| GB gvb †ÿÎd‡ji GK‡Ki Dci wbf©i K‡i bv|

AvqZb cÖmviY ¸Yv¼ t 1m3 AvqZ‡bi †Kv‡bv KwVb c`v‡_©i GKwU e¯‘i ZvcgvÎv 1K e„w× Ki‡j H e¯‘i AvqZb

hZUzKz e„w× cvq Zv‡K H e ‘i ev KwVb c`v‡_©i Dcv`v‡bi AvqZb cÖmviY ¸Yv¼ e‡j| Gi GKK K-1 ev cÖwZ

†Kjwfb| GB gvb AvqZ‡bi GK‡Ki Dci wbf©i K‡i bv|

cv‡VvËi g~j¨vqb -6.2

mwVK DË‡ii cv‡k wUK ( ) wPý w`b|

1| ˆ`N© cÖmviY ¸Yv‡¼i GKK †KvbwU ?

(K) cÖwZ †Kjwfb (L) wgUvi cÖwZ †Kjwfb

(M) wgUvi (N) †Kjwfb

2| ˆ`N© cÖmviY ¸Yv¼ , †ÿÎ cÖmviY ¸Yv¼ Ges AvqZb cÖmviY ¸Yv¼ n‡j wb‡Pi †Kvb m¤úK©wU mwVK

bq?

(K) = 2 (L) = 3 (M) =2 (N) =

3| Zvc cÖ‡qv‡M †Kvb c`v‡_©i cÖmviY me †P‡q Kg nq?

(K) KwVb (L) Zij

(M) evqexq (N) ev®úxq

4| A¨vjywgwbqv‡gi AvqZb cÖmviY ¸Yv¼ 3310-6K-1 n‡j Gi ‰`N© cÖmviY ¸Yv¼ KZ?

(K) 3.310-6K-1 (L) 3310-5K-1 (M) 1110-6K-1 (N) 1.110-6K

c`v_©weÁvb


cvV-3 Zij c`v‡_©i cÖmviY (Expansion of Liquids)

D‡Ïk¨


1. Zij c`v‡_©i AvcvZ I cÖK…Z cÖmviY e¨vL¨v Ki‡Z cvi‡eb|

2. Zij c`v‡_©i AvcvZ I cÖK…Z cÖmvi‡Yi g‡a¨ m¤úK© ¯’vcb Ki‡Z cvi‡eb|

6.3.1 Zij c`v‡_©i cÖmviY (Expansion of Liquids due to Heat) Zvc cÖ‡qv‡M KwVb c`v‡_©i g‡Zv Zij c`v‡_©iI cÖmviY N‡U| KwVb c`v‡_©i mywbw`©ó AvKvi _vKvq Gi

wewfbœ cÖmviY ¯úófv‡e cÖwZfvZ nq| Gi ˆ`N© , †ÿÎdj Ges AvqZ‡bi cÖmviY m¤ú‡K© my¯úó aviYv mnR nq|

wKš‘ Zij c`v‡_©i wbw`©ó AvqZb _vK‡jI AvKvi ev ˆ`N© †bB| †h cv‡Î ivLv nq †mB cv‡Îi AvKvi aviY K‡i|

Zv‡ci cÖfv‡e Zij c`v‡_©i AvqZ‡bi cwieZ©bB †Kej cÖZxqgvb nq| ZvB Zij c`v‡_©i cÖmviY ej‡Z Gi

AvqZ‡bi cÖmviY‡KB eySvq|

cixÿv K‡i †`Lv †M‡Q GKB cwigvY Zvc cÖ‡qv‡M mg AvqZ‡bi KwVb c`v‡_©i Zzjbvq Zij c`v‡_©i AvqZ‡bi

cÖmviY †ewk nq| Avevi GKB cwigvY Zv‡c wewfbœ cÖKvi Zi‡ji cÖmvi‡Yi cwigvYI mgvb nq bv|

Zv‡c c`v‡_©i cªmviY ch©‡eÿ‡Yi Rb¨ H c`v_©‡K Zvc w`‡Z nq| Zij c`v_©‡K Zvc w`‡Z n‡j †Kv‡bv bv †Kv‡bv

cv‡Î wb‡q Zvc w`‡Z nq| cvÎ¸‡jv GKUz we‡kl AvKv‡ii n‡j cÖmviY my®úófv‡e ch©‡eÿY Kiv hvq| cvÎ¸‡jv

miæ j¤v Mjv wewkó Ges wb‡Pi w`‡K evj&e ev †MvjKvK…wZi n‡j DËg nq| wPÎ (6.7) G ai‡Yi cvÎ †`Lvb

n‡q‡Q|

wPÎ t 6.7 wewfbœ cv‡Î wewfbœ Zi‡ji cÖmviY

GKwU eo cv‡Îi g‡a¨ mgvb AvKvi I AvqZ‡bi

K‡qKwU j¤v Mjv wewkó evjevK…wZi cv‡Î wewfbœ

Zij c`v_© w`‡q GKB D”PZv ch©šÍ fwZ© K‡i

Lvovfv‡e `vuo Kwi‡q †`qv n‡q‡Q| eo cvÎwU‡Z Mig

cvwb Xvjv n‡q‡Q| Gi d‡j cÖwZwU cv‡Îi ZvcgvÎv

GKB nv‡i e„w× †c‡q‡Q| ZvcgvÎv e„w×i d‡j Zij

c`v_© AvqZ‡b e„w× †c‡q b‡ji g‡a¨ cÖ‡ek K‡i‡Q|

wKš‘ wewfbœ b‡ji g‡a¨ Zi‡ji D”PZv wewfbœ |

G †_‡K eySv hvq mgvb Zv‡c mgvb AvqZ‡bi wewfbœ Zij c`v‡_©i cÖmviY mgvb nq bv| Zij c`v_©‡K †h cv‡Î

wb‡q Zvc †`qv nq H cvÎwU Av‡M DËß nq| d‡j cvÎwUiI cÖmviY N‡U|

ZvB Zi‡ji †h cÖmviY `„k¨gvb nq Zv Zi‡ji cÖK…Z cÖmviY bq| A_P cvÎ‡K ev` w`‡q Zij c`v‡_© Zvc cÖ‡qvM

m¤¢e bq| G Rb¨ cv‡Îi cÖmviY we‡ePbv K‡i Zi‡ji cÖmviY wn‡me Ki‡Z nq| cv‡Îi cÖmvi‡Yi Dci wfwË K‡i

ZvB Zi‡ji yai‡Yi cÖmviY cvIqv hvq; Zvn‡jv-

1. cÖK…Z cÖmviY

2. AvcvZ cÖmviY

GmGmwm †cÖvMÖvg


Zij c`v_©‡K cv‡Î bv †i‡L DËß Kiv m¤¢e n‡j Zi‡ji †h cÖmviY cvIqv hv‡e Zv‡K Zi‡ji cÖK…Z cÖmviY e‡j|

cv‡Î †i‡L Zij c`v_© DËß Kiv nq e‡j cv‡Îi cÖmviY we‡qvM K‡i †h cÖmivY cvIqv hvq ZvB Zi‡ji cÖK…Z

cÖmviY|

cv‡Îi cÖmviY we‡ePbv bv K‡i AvcvZ `„wó‡Z cvÎ¯’ Zi‡ji †h cÖmviY `„ó nq A_©vr cv‡Îi mv‡c‡ÿ Zi‡ji †h

cÖmviY cvIqv hvq Zv‡K Zi‡ji AvcvZ cÖmviY e‡j|

6.3.2 cÖK…Z cÖmviY I AvcvZ cÖmvi‡Yi m¤úK©

(Relation between Real and Apparent Expansion of Liquids) wPÎ 6.8 †`Lyb| GKwU miæ j¤v Mjv d¬v‡· A `vM ch©šÍ cvwb †bqv n‡jv wPÎ [6.8(K)]| GLb d¬v‡· Zvc cÖ‡qvM

Kiv n‡j cÖ_‡g d¬v·wU Zvc MÖnY Ki‡e Ges d¬v·wU cÖmvwiZ n‡e| Zi‡ji AvqZb G Ae¯’vq evo‡e bv, Zi‡ji

Dcwi Zj cv‡Îi Mjvq A `vM †_‡K wb‡P †b‡g B `v‡M Avm‡e| wPÎ [6.8(L)] A_©vr cvÎwU AB cwigvY cÖmvwiZ

n‡e| cvÎ DËß nIqvi c‡i Avi Zvc MªnY Ki‡e bv |

(K) (L) (M)

wPÎ t 6.8 cv‡Îi mv‡c‡ÿ Zi‡ji cÖmviY

cvÎ DËß n‡j, Gevi cvwb‡Z Zvc

mÂvwiZ n‡e| Ges Gch©v‡q cvwbi Dcwi

Z‡ji D”PZv evo‡e| aiv hvK P‚ovšÍ

Ae¯’vq cvwbi Dcwi Z‡ji Ae¯’vb nj

C| Zij cÖmvwiZ n‡q A `vM AwZµg

K‡i C `vM ch©šÍ D‡V G‡m‡Q wPÎ

6.8(M)| AvcvZ `„wó‡Z g‡b nq Zi‡ji

cÖmviY A `vM ‡_‡K C `vM ch©šÍ| wKš‘

cÖK…Z c‡ÿ Zi‡ji DcwiZj B †_‡K C `v‡M †cŠu‡Q‡Q, A_©vr Zi‡ji cÖK…Z e„w×

N‡U BC|

myZivs BC = Vr = Zi‡ji cÖK…Z cÖmviY

AC = Va = Zi‡ji AvcvZ cÖmviY

BA = Vg = cv‡Îi cÖmviY

wPÎ 6.8 jÿ¨ Kiæb| Zvn‡j, Avgiv cvB

BC =AC + BA ev, Vr = Va + Vg ... ... .... ... ... ... ... ...... ... ... ... ... ... ... ... ... (6.15)

A_©vr cÖK…Z cÖmviY = AvcvZ cÖmviY + cv‡Îi cÖmviY

Zij c`v_© cv‡Îi ‡P‡q †ewk cÖmvwiZ n‡j Z‡eB Zi‡ji AvcvZ cÖmviY `„k¨gvb nq| wKš‘ Zij c`v_© †_‡K

cvÎwU †ewk cÖmvwiZ n‡j Zi‡ji †Kv‡bv cÖmviY †Zv `„k¨gvb n‡eB bv Dciš‘ †`Lv hv‡e ZijwU Zv‡c AvqZb

K‡g msKzwPZ n‡q †M‡Q| hw` Zij Ges cvÎ mg cwigvY ev‡o Zv n‡j cv‡Îi g‡a¨ Zi‡ji AvqZb AcwiewZ©Z

_vK‡e| G‡ÿ‡ÎI †Kvb AvcvZ cÖmviY †`Lv hv‡e bv|

c`v_©weÁvb


6.3.3 Zij c`v‡_©i cÖmviY mnM ev ¸Yv¼ (Coefficient of Expansion of liquids) †h‡nZz Zij c`v‡_©i `yÕai‡Yi cÖmviY we‡ePbv Kiv nq ZvB Gi cÖmviY ¸Yv¼I `yB cÖKvi| h_v- cÖK…Z

cÖmviY ¸Yv¼ Ges AvcvZ cÖmviY ¸Yv¼|

Zij c`v‡_©i cÖK…Z cªmviY ¸Yv¼, r (Coefficient of Real Expansion of liquids)

aiv hvK ZvcgvÎv θ e„w×i Rb¨ V0 GKK AvqZ‡bi †Kv‡bv Zi‡ji cÖK…Z cÖmviY Vr nj| G‡ÿ‡Î †`Lv hvq

Vr V0 θ ev, Vr = r V0 θ ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (6.16) GLv‡b r GKwU mgvbycvwZK aªæeK| Gi gvb Zi‡ji cÖK…wZi Dci wbf©i K‡i| G‡K Zij c`v‡_©i cÖK…Z cÖmviY

¸Yv¼ ev cÖK…Z cÖmviY mnM e‡j|

r 0

rVV

= ... ... .... ... ... ...... ... ... ... ... ... (6.17)

Dc‡ii mgxKi‡Y AvqZb V0 =1m3, ZvcgvÎvi e„w× θ =1K ai‡j, mvgvbycvwZK aªæeK

r = Vr nq| G †_‡K AvqZb cÖmviY ¸Yv‡¼i wbgœiƒc msÁv †`qv hvq|

1m3 AvqZ‡bi †Kv‡bv Zij c`v‡_©i ZvcgvÎv 1K e„w× Ki‡j H Zij c`v‡_©i AvqZ‡bi †h cÖK…Z cÖmviY N‡U

Zv‡K H Zij c`v‡_©i cÖK…Z cÖmviY ¸Yv¼ e‡j| G‡K r Øviv cÖKvk Kiv nq|

GKK: 6.17 bs mgxKi‡Yi Wvb cv‡ki ivwk¸‡jvi GKK ewm‡q AvqZb cÖmviY ¸Yv‡¼i GKK cvIqv hvq| GB

GKK nj K-1 ev cÖwZ †Kjwfb| jÿ¨ Kiæb †Kvb Zi‡ji cÖmviY ¸Yv‡¼i gvb AvqZ‡bi gv‡bi ev GK‡Ki Dci

wbf©i K‡i bv|

Zvrch© t cvi‡`i cÖK…Z cÖmviY ¸Yv¼ 1810-5 K-1 ej‡Z eySvq 1m3

AvqZ‡bi cvi‡`i ZvcgvÎv 1K evo‡j

Gi AvqZb cÖK…Zc‡ÿ 1810-5 m3 evo‡e|

†Kv‡bv Zi‡ji cÖK…Z cÖmviY ¸Yv¼ r Ges V0 AvqZ‡bi GB Zi‡ji ZvcgvÎv θ cwigvY evov‡j, Gi P‚ovšÍ

AvqZb n‡e, V = Vo + Vor θ = Vo(1+ r θ) ... ... .... ... ... ... ... ..... ... ... ... ... ... ... ... (6.18)

Zij c`v‡_©i AvcvZ cªmviY ¸Yv¼, a (Coefficient of apparent Expansion)

GKBfv‡e †`Lv †M‡Q †Kv‡bv wbw`©ó Zij c`v‡_©i AvcvZ cÖmviY H Zij c`v‡_©i Avw` AvqZb Ges ZvcgvÎv

e„w×i mgvbycvwZK| A_©vr, ZvcgvÎv θ e„w×i Rb¨ V0 GKK AvqZ‡bi †Kvb Zi‡ji AvcvZ cÖmviY Va n‡j,

Va V0 θ

ev, Va = a V0 θ ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (6.19)

GLv‡b a GKwU mgvbycvwZK aªæeK| Gi gvb Zi‡ji cÖK…wZ Ges cv‡Îi Dcv`v‡bi Dci wbf©i K‡i| G‡K cv‡Îi

Dcv`v‡bi mv‡c‡ÿ Zij c`v‡_©i AvcvZ cÖmviY ¸Yv¼ ev AvcvZ cÖmviY mnM e‡j|

Dc‡ii mgxKi‡Y AvqZb V0 =1m3, ZvcgvÎvi e„w× θ =1K ai‡j, mgvbycvwZK aªæeK

a = Va nq| G †_‡K AvqZb cÖmviY ¸Yv‡¼i wb‡¤œviƒc msÁv †`qv n‡q‡Q|

cÖK…Z cÖmviY


GmGmwm †cÖvMÖvg


†Kv‡bv cv‡Î ivLv 1m3 AvqZ‡bi †Kv‡bv Zij c`v‡_©i ZvcgvÎv 1K e„w× Ki‡j H cv‡Îi mv‡c‡ÿ Zij c`v‡_©i

AvqZ‡bi †h cÖmviY N‡U Zv‡K H Zij c`v‡_©i AvcvZ cÖmviY ¸Yv¼ e‡j| G‡K a Øviv cÖKvk Kiv nq|

AZGe, MvwYwZKfv‡e, Zi‡ji AvcvZ cÖmviY ¸Yv¼

a =

0

aVV

= ... ... .... ... ... ..... ... ... ... ... ... ... ... (6.20)

GKK : Zi‡ji AvcvZ cÖmviY ¸Yv‡¼i GKK nj K-1 ev cÖwZ †Kjwfb|

Zvrch© t Kuv‡Pi mv‡c‡ÿ cvi‡`i AvcvZ cÖmviY ¸Yv¼ 1510-5 K-1 ej‡Z eySvq Kv‡Pi cv‡Î ivLv 1m3

AvqZ‡bi cvi‡`i ZvcgvÎv 1K evo‡j Gi AvqZb AvcvZ `„wó‡Z 1510-5 m3 evo‡e|

†Kv‡bv Zi‡ji AvcvZ cÖmviY ¸Yv¼ a Ges V0 AvqZ‡bi GB Zi‡ji ZvcgvÎv θ cwigvY evov‡j, Gi P‚ovšÍ

AvqZb n‡e, V = Vo + Voa θ = Vo(1+ a θ) ... ... .... ... ... ...... ... ... ... ... ... ... ... (6.21)

wnmve K‡i †`Lv †M‡Q, †Kv‡bv Zi‡ji AvcvZ cÖmviY ¸Yv‡¼i mv‡_ cv‡Îi Dcv`v‡bi AvqZb cÖmviY ¸Yv¼ †hvM

Ki‡j Zi‡ji cÖK…Z cÖmviY ¸Yv¼ cvIqv hvq | A_©vr ,

cÖK…Z cÖmviY ¸Yv¼ = AvcvZ cÖmviY ¸Yv¼ + cv‡‡Îi Dcv`v‡bi AvqZb cÖmviY ¸Yv¼

ev, r = a + g [GLv‡b, g = cv‡Îi Dcv`v‡bi AvqZb cÖmviY ¸Yv¼] ... ... ... ... ... ... ... ... ... (6.22)

mvi-ms‡ÿc:

1. Zij c`v‡_©i cÖK…Z cÖmviY t Zij c`v_©‡K cv‡Î bv †i‡L DËß Kiv m¤¢e n‡j Zi‡ji †h cÖmviY cvIqv hv‡e

Zv‡K Zi‡ji cÖK…Z cÖmviY e‡j| cv‡Î †i‡L Zij c`v_© DËß Kiv nq e‡j cv‡Îi cÖmviY we‡qvM K‡i †h

cÖmiY cvIqv hvq ZvB Zi‡ji cÖK…Z cÖmviY|

cÖK…Z cÖmviY = AvcvZ cÖmviY + cv‡Îi cÖmviY|

2. AvcvZ cÖmviY t cv‡Îi cÖmviY we‡ePbv bv K‡i AvcvZ `„wó‡Z cvÎ ’ Zi‡ji †h cÖmviY `„ó nq A_©vr cv‡Îi

mv‡c‡ÿ Zi‡ji †h cÖmviY cvIqv hvq Zv‡K Zi‡ji AvcvZ cÖmviY e‡j|

3. Zij c`v‡_©i cÖK…Z cÖmviY ¸Yv¼, r t 1m3 AvqZ‡bi †Kv‡bv Zij c`v‡_©i ZvcgvÎv 1K e„w× Ki‡j H Zij

c`v‡_©i AvqZ‡bi †h cÖK…Z cÖmviY N‡U Zv‡K H Zij c`v‡_©i cÖK…Z cÖmviY ¸Yv¼ e‡j|

4. Zij c`v‡_©i AvcvZ cÖmviY ¸Yv¼, a t †Kv‡bv cv‡Î ivLv 1m3 AvqZ‡bi †Kv‡bv Zij c`v‡_©i ZvcgvÎv

1K e„w× Ki‡j H cv‡Îi mv‡c‡ÿ Zij c`v‡_©i AvqZ‡bi †h cÖmviY N‡U Zv‡K H Zij c`v‡_©i AvcvZ

cÖmviY ¸Yv¼ e‡j|

5. cÖK…Z cÖmviY ¸Yv¼ = AvcvZ cÖmviY ¸Yv¼ + cv‡Îi Dcv`v‡bi AvqZb cÖmviY ¸Yv¼

ev, r = a + g

6. Zij c`v‡_©i cÖmviY ¸Yv‡¼i GKK t K-1 cÖwZ †Kjwfb|

AvcvZ cÖmviY


c`v_©weÁvb




1| †Kvb ai‡Yi cÖmviY‡K Zij c`v‡_©i cÖmviY wnmv‡e weePbv Kiv nq?

(K) ˆ`N© cÖmviY (L) Zjxq cÖmviY

(M) †ÿÎ cÖmviY (N) AvqZb cÖmviY

2| cÖK…Z cÖmviY ¸Yv¼ = r, AvcvZ cÖmviY ¸Yv¼ = a Ges cv‡Îi c`v‡_©i cÖmviY ¸Yv¼ = g n‡j wb‡Pi †Kvb

mgxKiYwU mwVK?

(K) r = a + g (L) r = a - g

(M) a = r + g (N) g = a + r

3| Vr = Zi‡ji cÖK…Z cÖmviY, Va = Zi‡ji AvcvZ cÖmviY Ges Vg = cv‡Îi cÖmviY n‡j †KvbwU mwVK

bq|

(K) Vr = Va + Vg (L) Va = Vr - Vg

(M) Vg = Vr - Va (N) Vr = Va - Vg

cvV-4 Zvc cwigv‡ci bxwZ (Principle of Calorimitry)

D‡Ïk¨


1. e ‘i ZvcaviY ÿgZv e¨vL¨v Ki‡Z cvi‡eb|

2. c`v‡_©i Av‡cwÿK Zvc e¨vL¨v Ki‡Z cvi‡eb|

3. Zvc aviY ÿgZv I Av‡cwÿK Zv‡ci g‡a¨ m¤úK© ’vcb Ki‡Z cvi‡eb|

4. Zvc cwigv‡ci g~jbxwZ e¨vL¨v Ki‡Z cvi‡eb|

6.4.1 Zvc aviY ÿgZv (Thermal Capacity) GKB mvB‡Ri `ywU nvwo wbb| GKwU nvwo‡Z Avav wjUvi Ges Ab¨ GKwU nvwo‡Z 5-6 wjUvi cwigvY

dzUšÍ cvwb wb‡q cvkvcvwk ewm‡q w`b| †`L‡eb 5-6 wgwb‡Ui g‡a¨ cÖ_g nvwoi (Avav wjUvi) cvwb VvÛv n‡q †M‡Q|

wKš‘ Ab¨ nvwoi cvwb †ek Mig i‡q‡Q| GwU VvÛv n‡Z 30-40 wgwbU mgq jvM‡e| KviY wK ? Avcwb Aek¨

ej‡eb Aí cvwbi cvÎwU †ewkÿY Zvc a‡i ivL‡Z cv‡i bvB| †ewk cvwbi cvÎwU †ewkÿY ev †ewk cwigvY Zvc

a‡i †i‡L‡Q| Avm‡j me cv‡Îi ev c`v‡_©i Zvc a‡i ivLvi ÿgZv mgvb bq| e¯‘i Zvc a‡i ivLvi ÿgZv‡K

Avgiv ewj Zvc aviY ÿgZv| GwU e¯‘i Dcv`vb Ges cwigvY Z_v f‡ii Dci wbf©i K‡i|

†Kvb e¯‘i ZvcvÎv 1K evov‡Z ev Kgv‡Z †h cwigvY Zv‡ci cÖ‡qvRb Zv‡K H e¯‘i ZvcaviY ÿgZv e‡j| †Kvb

e¯‘i Zvc aviY ÿgZv 56 JK-1 ej‡Z eySvq H e¯‘i ZvcgvÎv 1K evov‡Z 56 J Zv‡ci cÖ‡qvRb| aiv hvK

†Kvb e¯‘i ZvcgvÎv θ evov‡Z Q cwigvY Zvc jv‡M| Zvn‡j H e¯‘i ZvcgvÎv 1K evov‡Z Zv‡ci cÖ‡qvRb

n‡e,

Q

Ryj|

GmGmwm †cÖvMÖvg


AZGe H e¯‘wUi ZvcaviY ÿgZv,

QC

... .... .... .....(6.23)

ZvcaviY ÿgZvi GKK JK-1|

6.4.2 Av‡cwÿK Zvc (Specific Heat) GKB c`v‡_©i cwigvY ev fi wfbœ n‡j Zv‡`i ZvcaviY ÿgZvI wfbœ nq| †hgb Avav wjUvi (0.5 kg) cvwbi Zvc

aviY ÿgZv †_‡K cvuP wjUvi ev (5 kg) cvwbi ZvcaviY ÿgZv †ewk| mgvb f‡ii wfbœ wfbœ c`v‡_©i ZvcaviY

ÿgZvi Zzjbv Ki‡Z n‡j me †ÿ‡Î f‡ii cwigvY wbw`©ó Ki‡Z nq| ZvB G‡ÿ‡Î GKK fi ev 1 kg f‡ii e¯‘i

ZvcaviY ÿgZv we‡ePbv Kiv nq| ZvB 1 kg f‡ii †Kvb e¯‘i ZvcgvÎv 1K evov‡Z †h cwigvY Zv‡ci cÖ‡qvRb

nq Zv‡K H e ‘i Dcv`v‡bi Av‡cwÿK Zvc e‡j| Av‡cwÿK Zvc‡K Bs‡iwR s Aÿi Øviv cÖKvk Kiv nq|

AZGe m f‡ii e¯‘i ZvcaviY ÿgZv c n‡j,

H e¯‘i Av‡cwÿK Zvc, s = Cm =

Q ×

1m =

Qm [ ... QC

] .... .... (6.24)

Av‡cwÿK Zv‡ci GKK, Jkg-1K-1|

mxmvi Av‡cwÿK Zvc 130 Jkg-1K-1 ej‡Z eySvq 1kg mxmvi ZvcgvÎv 1K evov‡Z 130 J Zv‡ci cÖ‡qvRb|

wb‡Pi ZvwjKvq K‡qKwU c`v‡_©i Av‡cwÿK Zv‡ci D‡jøL Kiv n‡jv|

c`v_©

Av‡cwÿK Zvc (Jkg-1K-1) c`v_©

Av‡cwÿK Zvc (Jkg-1K-1) cvwb 4200

eid 2100

Rjxq ev®ú 2000

Zvgv 400

iƒcv 230

mxmv 130

gvwU 800 †_‡K1400 evqy 700†_‡K 1000

6.4.3 Av‡cwÿK Zvc I ZvcaviY ÿgZvi m¤úK© (Relation between Specific Heat and Thermal Capacity)

Avgiv Rvwb, †Kv‡bv e¯‘i ZvcvÎv 1K evov‡Z ev Kgv‡Z †h cwigvY Zv‡ci cÖ‡qvRb Zv‡K H e¯‘i ZvcaviY

ÿgZv (C) e‡j| Ges 1 kg f‡ii †Kv‡bv e¯‘i ZvcgvÎv 1K evov‡Z †h cwigvY Zv‡ci cÖ‡qvRb nq Zv‡K H

e¯‘i Dcv`v‡bi Av‡cwÿK Zvc e‡j (s)|

AZGe, s = Cm

ev, C = ms

A_©vr ZvcaviY ÿgZv = fiAv‡cwÿK Zvc

ev, Av‡cwÿK Zvc =

ZvcaviY ÿgZv

fi

c`v_©weÁvb


6.4.4 K¨vjwiwgwZi g~jbxwZ (Fundamental principle of calorimetry) Kÿ ZvcgvÎvi GKwU avZe cv‡Îi g‡a¨ LvwbKUv dzUšÍ cvwb †X‡j w`b| cvÎwU‡K nvZ w`‡q ¯úk© Ki‡j eyS‡Z

cvi‡eb cvÎwU ax‡i ax‡i Mig n‡”Q Ab¨w`‡K Mig cvwb µ‡gB VvÛv n‡”Q| A_ev GKwU avZz `‡Ûi GKcÖvšÍ †ek

Mig K‡i GK Møvm VvÛv cvwbi g‡a¨ Wzevb, †`L‡eb cvwb Mig n‡q DV‡Q| wKš‘ avZz `‡Ûi Mig cÖvšÍwU VvÛv n‡q

hv‡”Q| †Kb Ggb nq? wfbœ ZvcgvÎvi `ywU e¯‘‡K ci¯ú‡ii ms¯ú‡k© Avbv n‡j Zv‡ì g‡a¨ Zv‡ci Av`vb cÖ vb

N‡U| †h e¯‘wUi ZvcgvÎv †ewk †mwU Zvc †Q‡o †`q ev eR©b K‡i, Avi †h e¯‘wUi ZvcgvÎv Kg †mwU Zvc †bq ev

MÖnY K‡i| `ywU e ‘i ZvcgvÎv mgvb bv nIqv ch©šÍ Zv‡ci GB Av`vb cÖ vb ev MÖnY- eR©b Pj‡Z _v‡K|

hw` Zv‡ci GB Av`vb cÖ v‡bi mgq Ab¨ †Kv‡bv fv‡e Zvc bó bv nq, Z‡e †ewk ZvcgvÎvi e¯‘wU †h cwigvY Zvc

eR©b Ki‡e Kg ZvcgvÎvi e¯‘wU wVK †mB cwigvY Zvc MªnY Ki‡e| A_©vr †gvU ewR©Z Zvc = †gvU M„nxZ Zvc|

GB bxwZwU Kv‡R jvwM‡q mn‡RB Zvc kw³i cwigvY cwigvc Kiv hvq| G Rb¨ GwU‡K Zvc cwigv‡ci ev

K¨vjwiwgwZi g~j bxwZ e‡j AwfwnZ Kiv nq| e¯‘i ˆ`N©¨ ev fi gvcvi Rb¨ mivmwi †hgb cwigvcK hš¿ ev †¯‹j

Av‡Q, Zvc cwigv‡ci Rb¨ G ai‡Yi †Kvb eë¯’v †bB| ZvB Zv‡ci cwigvY cwigv‡ci Rb¨ GB bxwZwU Kv‡R

jv‡M| ciewZ© Aby‡”Q`¸wj‡Z wKfv‡e GB bxwZ eënvi K‡i Zvc cwigvc Kiv hvq Zv †`L‡bv n‡e|

s Av‡cwÿK Zv‡ci m f‡ii GKwU e ‘‡Z Q Zvc cÖ vb Kivq ZvcgvÎv 1 †_‡K e„w× †c‡q 2 n‡j, e ‘wU KZ„©K

M„nxZ Zvc, Q = ms(21) ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (6.25)

Avevi s Av‡cwÿK Zv‡ci mf‡ii †Kv‡bv e¯‘ †_‡K Q cwigvY Zvc AcmviY Ki‡j hw` ZvcgvÎv 2 †_‡K n«vm

†c‡q 1 nq Zvn‡j e ‘wU KZ©„K ewR©Z Zvc, Q = ms(12) ... ... .... ...... ... ... ... ... ... ... (6.26)

MvwYwZK D`vniY 6.6

500 g f‡ii GK UzK‡iv avZz LÛ‡K 100C ZvcgvÎvq DËß K‡i, GKwU KvP cv‡Î 15C ZvcgvÎvq iwÿZ

200 g cvwbi g‡a¨ Wywe‡q †`qv n‡jv| wKQzÿ‡Yi g‡a¨ cvwb Ges avZz L‡Ûi P~ovšÍ ZvcgvÎv n‡jv 21C| avZe

UzKivi Av‡cwÿK Zvc KZ n‡e? (G‡ÿ‡Î cvwbi Av‡cwÿK Zvc, s = 4200 Jkg-1K-1 Ges KvPcv‡Îi †kvwlZ

Zvc bMY¨)|

mgvavb t

Avgiv Rvwb ,

avZzi ewR©Z Zvc= m1 s1△ = m1 s1 (1- 2)

Ges cvwbi M„nxZ Zvc = m2 s△ = m2s (2- ) Avevi, †h‡nZz

ewR©Z Zvc = M„nxZ Zvc

∴ m1 s1 (1- 2) = m2s (2- )

GLv‡b

avZz L‡Ûi fi, m1 = 500 g = 0.5 kg avZzi cÖv_wgK ZvcgvÎv 1 = 100C

cvwbi fi, m2 = 200 g = 0.2 kg cvwbi cÖv_wgK ZvcgvÎv, = 15C

avZz I cvwbi P~ovšÍ ZvcgvÎv,2 = 21C cvwbi Av‡cwÿK Zvc, s = 4200 Jkg-1K-1

avZzi Av‡cwÿK Zvc, s1 = ?

ev, 0.5 kg s1(100C - 21C ) = 0.2 kg4200 Jkg-1K-1(21C-15C)

ev, 0.5 kg s1(79 K) = 0.2 kg4200 Jkg-1K-1(6K)

ev, s1

-1 -1-1 -1 -1 -10.2kg 4200 Jkg K 6K Jkg K Jkg K

0 5 kg 79 K5040 127 6 39 5

.. .

DËi t 128 Jkg-1K-1

GmGmwm †cÖvMÖvg


mvi-ms‡ÿc:

Zvc aviY ÿgZv t †Kv‡bv e ‘i ZvcgvÎv 1K evov‡Z ev Kgv‡Z †h cwigvY Zv‡ci cÖ‡qvRb Zv‡K H e ‘i Zvc

aviY ÿgZv e‡j| e¯‘i ZvcgvÎv θ evov‡Z Q cwigvY Zvc jvM‡j,

H e¯‘i ZvcaviY ÿgZv,

QC

ZvcaviY ÿgZvi GKK t JK-1|

Av‡cwÿK Zvc t 1 kg f‡ii †Kv‡bv e¯‘i ZvcgvÎv 1K evov‡Z ev Kgv‡Z †h cwigvY Zv‡ci cÖ‡qvRb nq Zv‡K

H e¯‘i Dcv`v‡bi Av‡cwÿK Zvc e‡j| e ‘i Av‡cwÿK Zvc s

Qm

|

Av‡cwÿK Zv‡ci GKK t Jkg-1K-1

m~Î t ZvcaviY ÿgZv = fiAv‡cwÿK Zvc, C = ms Zvc cwigv‡ci g~j bxwZ t ewR©Z Zvc = M„nxZ Zvc

ewR©Z ev M„nxZ Zvc, Q=ms



1| ZvcaviY ÿgZvi GKK Kx ?

(K) Ryj (L) †Kjwfb cÖwZ Ryj

(M) †Kjwfb (N) Ryj cÖwZ †Kjwfb

2| GKB Dcv`v‡bi (c`v‡_©i) ZvcaviY Kg †ewk nq -

(K) e¯‘i f‡ii ZviZ‡g¨i Rb¨ (L) GKB Dcv`v‡bi ZvcaviY ÿgZv Kg †ewk nq bv

(M) e¯‘i c`v‡_©i ZviZ‡g¨i Rb¨ (N) †Kv‡bvwUB bq

3| 1 kg f‡ii †Kvb e¯‘i ZvcgvÎv 1K evov‡Z †h cwigvY Zv‡ci cÖ‡qvRb nq Zv H e ‘i Dcv`v‡bi

(K) Zvcxq GKK (L) ZvcaviY ÿgZv

(M) Zvc e„w×i cwigvY (N) Av‡cwÿK Zvc

4| wb‡Pi †KvbwU e¯‘i Av‡cwÿK Zvc ?

(K) fiAv‡cwÿK Zvc (L) fi ZvcaviY ÿgZv

(M) (N)

fi

ZvcaviY ÿgZv

ZvcaviY ÿgZv

fi

c`v_©weÁvb


cvV-5 Ae¯’vi cwieZ©b (Change of state)

D‡Ïk¨


1. c`v‡_©i Ae¯’vi cwieZ©‡b Zv‡ci cÖfve e¨vL¨v Ki‡Z cvi‡eb|

2. Mjb, ev®úxfeb I Nbxfeb e¨vL¨v Ki‡Z cvi‡eb|

3. Mjbv¼ I ùzUbv¼ e¨vL¨v Ki‡Z cvi‡eb|

4. Mjbv‡¼i Dci Pv‡ci cÖfve e¨vL¨v Ki‡Z cvi‡eb|

6.5.1 Zvc cÖ‡qv‡M e¯‘i Ae¯’vi cwieZ©b (Change of state of matters due to Heat) wPÎ 6.9 †`Lyb, GKwU weKv‡i K‡qK UzK‡iv eid wb‡q Zvi g‡a¨

GKwU _v‡g©vwgUvi Lvov K‡i emv‡bv n‡q‡Q Ges weKviwU‡Z Zvc

†`qv n‡”Q| jÿ¨ Ki‡j †`L‡eb cÖwZ †m‡K‡Û _v‡g©vwgUv‡ii cvV

A_©vr ZvcgvÎv evo‡Q|

Avcwb cÖwZ 1 wgwbU cici _v‡g©vwgUv‡ii cvV †iKW© Ki‡Z _vKzb|

†`L‡eb ZvcgvÎv evo‡Z _vK‡e| wKš‘ nVvr GKmgq †`L‡eb

ZvcgvÎvi e„w× †_‡g †M‡Q| weKv‡i Zvc cÖ‡qvM Ae¨vnZ _vK‡jI

ZvcgvÎv Avi evo‡e bv| wKš‘ †`L‡eb weKv‡ii g‡a¨i eid Mj‡Z

ïiæ Ki‡e|

wPÎ t 6.9 ei‡di Mjb I cvwbi ùzUb

hZÿY mg¯Í eid Mjv †kl bv n‡e ZZÿY ZvcgvÎv w¯’i _vK‡e| nVvr †`L‡eb eid Mjv †kl n‡jB ZvcgvÎv

Avevi evo‡Z ïiæ K‡i‡Q| ZLb cv‡Î †Kej Zij cvwbB Av‡Q| Gevi †`L‡eb ZvcgvÎv †e‡oB Pj‡e| wKš‘ bv

nVvr GKmgq †`Lv hv‡e _v‡g©vwgUv‡ii cvV wbw`ó we›`y‡Z G‡m Avevi w¯’i n‡q †M‡Q| Avi ZLbB cvwb dzU‡Z ïiæ

Ki‡e| cvwb dzUv †kl bv nIqv ch©šÍ A_©vr cv‡Îi mg¯Í Zij c`v_© ev®úxf~Z bv nIqv ch©šÍ Zi‡ji ZvcgvÎv Avi

evo‡e bv| hLb cv‡Î cvwb Aewkó _vK‡e bv †Kej ev®ú _vK‡e ZLbB ZvcgvÎv evo‡Z ïiæ Ki‡e| (Zÿywb Zvc

†`qv eÜ Ki‡Z n‡e| bv n‡j yN©Ubvi NU‡Z cv‡i|)

Gfv‡eB †`Lv hvq Zvc cÖ‡qv‡Mi mv‡_ e¯‘i Ae¯’v cwieZ©b N‡U| Avevi wecixZ fv‡e cvwbi ev®ú‡K VvÛv Ki‡Z

_vK‡j A_©vr Zvc †ei K‡i wb‡j GK mgq Zij cvwb‡Z iƒcvšÍwiZ nq|Ges Zij cvwbi Zvc †ei K‡i wb‡Z

_vK‡j GK mgq Zv KwVb ei‡d iƒcvšÍwiZ nq|

6.5.2 Mjb, ev®úxfeb I Nbxfeb (Fusion, Vaporization and Condensation) Mjb I Mjbv¼ t †Kv‡bv e¯‘i KwVb Ae¯’v †_‡K Zij Ae¯’vq iƒcvšÍwiZ nIqvi cÖwµqv‡K Mjb e‡j| wbw`©ó Pv‡c

†h wbw`©ó ZvcgvÎvq KwVb c`v_© M‡j Zi‡j iƒcvšÍwiZ nq Zv‡K H c`v‡_©i Mjbv¼ e‡j| GK evqy gÛjxq Pv‡c

ei‡di MjbvsK 0C| mg¯Í c`v_© bv Mjv ch©šÍ ZvcgvÎ AcwiewZ©Z _v‡K|

ev¯úxfeb t †Kv‡bv e ‘i Zij Ae¯’v †_‡K M¨vmxq Ae¯’vq iƒcvšÍwiZ nIqvi cÖwµqv‡K ev®úxfeb e‡j| ev®úxfeb

`y fv‡e msNwUZ nq| (1) ¯Ztev®úxfeb ev ev®úvqb Ges (2) ùzUb|

¯Ztev®úxfeb ev ev®úvqb t jÿ¨ K‡i‡Qb wfRv Kvco †b‡o ivL‡j wKQzÿ‡Yi g‡a¨ kywK‡q hvq, cvKv †g‡Si

Dci LvwbKUv cvwb co‡j ZvI wKQzÿ‡Yi g‡a¨ ïwK‡q hvq|cvwb †Kv_vq hvq ? ev®ú n‡q D‡o hvq| †K‡ivwm‡bi

GmGmwm †cÖvMÖvg


†evZ‡ji gyL †Lvjv ivL‡j †Kiwmb ev®ú n‡q D‡o hvq| †Kv‡bv †ÿ‡Î Avgv‡ì AwZwi³ Zvc cÖ‡qvM Ki‡Z nq

bv| cwi‡ek †_‡KB cÖ‡qvRbxq Zvc msMÖn K‡i Zij DcwiZj †_‡K ax‡i ax‡i ev‡®ú cwiYZ nq| GB cÖwµqv‡K

¯Ztev®úxfeb ev ev®úvqb ejv nq|

ùzUb t Zvc cÖ‡qvM K‡i wbw`©ó Pv‡c †h wbw`©ó ZvcgvÎvq †Kv‡bv Zij c`v‡_©i `ªæZ ev®úxfeb NUv‡bvi cÖwµqv‡K

ùzzUb e‡j| †h wbw`©ó ZvcgvÎvq †Kv‡bv Zij c`v‡_©i ùzUb msNwUZ nq Zv‡K H c`v‡_©i ùzUbv¼ e‡j| GK evqy

gÛjxq Pv‡c cvwbi ùzUbv¼ 100C|

Nbxfeb t ZvcgvÎv Kwg‡q †Kv‡bv evqexq ev M¨vmxq c`v_©‡K Zvi Zij Ae¯’vq iƒcvšÍwiZ Kivi cÖwµqv‡K ejv nq

Nbxfeb| †Kv‡bv evqexq c`v‡_©i Zvc n«vm K‡i GKwU wbw`©ó ZvcgvÎvq G‡j H c`v‡_©i Nbxfeb ïiæ nq| H

wbw`©ó ZvcgvÎvwU g~jZ H c`v‡_©i ùzUbv¼| Zvc n«vm Kivi cÖwµqv Ae¨vnZ ivL‡j ZvcgvÎv ùzUbv‡¼ AcwiewZ©Z

†_‡K Nbxfeb Pj‡Z _v‡K| Nbxfeb †kl bv nIqv ch©šÍ Zi‡ji ev evqexq c`v‡_©i ZvcgvÎv ùzUbv‡¼ w ’i _v‡K|

6.5.3 Mjbv‡¼i Dci Pv‡ci cÖfve (Effect of pressure on Melting Point : Regelation) c`v‡_©i Dci Pvc Mjbv¼‡K cÖfvweZ K‡i| Pv‡ci Rb¨ Mjbv¼ yÕ fv‡e cÖfvweZ n‡Z cv‡i|

(K) wKQz wKQz c`v_© KwVb Ae¯’v †_‡K Zij Ae¯’vq iƒcvšÍ‡ii mgq AvqZb e„w× cvq †hgb †gvg, Zvgv BZ¨vw`|

Pvc evov‡j Hme c`v‡_©i Mjbv¼ †e‡o hvq| A_©vr †ewk ZvcgvÎvq M‡j| ewa©Z Pvc c`v‡_©i AvqZb Kwg‡q †`q

d‡j Mjbv¼ †e‡o hvq|

(L) wKQz wKQz c`v_© KwVb Ae¯’v †_‡K Zij Ae¯’vq iƒcvšÍ‡ii mgq AvqZb nªvm cvq †hgb †jvnv, eid, wemgv_

BZ¨vw`| Pvc evov‡j Hme c`v‡_©i Mjbv¼ K‡g hvq| A_©vr Giv Kg ZvcgvÎvq M‡j| ewa©Z Pvc c`v‡_©i AvqZb

ms‡KvP‡bi myweav K‡i †`q| d‡j Mjbv¼ K‡g hvq| cybtwkjxfeb Avcbvi cwiwPZ Mjbv‡¼i Dci Pv‡ci

cÖfv‡ei GKwU my›ì D`vniY|

cyb:wkjxfeb : ( Regelation)

K‡qKwU ei‡di †QvU †QvU UzK‡iv nv‡Zi

gy‡Vv‡Z wb‡q †Rv‡i †P‡c a‡i †Q‡o w`b|

†`L‡eb me¸‡jv UzK‡iv †Kgb †Rvov †j‡M

GK n‡q †M‡Q (wPÎ 6.10)| Gevi UzK‡iv¸‡jv

Avjv`v Kivi †Póv Kiæb| bv G‡ì Avi

Avjv`v Kiv hv‡e bv| Z‡e †f‡½ bZzb K‡i

wPÎ t 6.10

UzK‡iv Kiv hv‡e| wKš‘ †mB UzK‡iv¸‡jv Av‡Mi g‡Zv n‡e bv| UyK‡iv¸‡jv Gfv‡e †Rvov †j‡M GKwU UzK‡iv nIqvi

KviY KLbI †f‡e †`‡L‡Qb wK?

Avgiv Rvwb ei‡di Mjbv¼ 0C| A_©vr cvwb 0C ZvcgvÎvq R‡g eid nq ev M‡j cvwb nq| hLb ei‡di

UzK‡iv¸‡jvi Dci Pvc †`qv nq ZLb UzK‡iv¸‡jvi ms‡hvM ¯’‡ji ZvcgvÎv 0C _v‡K wKš‘ Mjbv¼ 0C Gi wb‡P

†b‡g hvq, d‡j H GjvKvi eid M‡j hvq| AZtci GB Pvc AcmviY Ki‡j ms‡hvM ¯’‡ji Mjbv¼ Avevi 0C

†Z wd‡i Av‡m| d‡j ms‡hvM ¯’‡ji eid Mjv cvwb RgvU †eu‡a ei‡di UzK‡iv¸‡jv‡K Ry‡o †`q|

Gfv‡e Pvc cÖ‡qvM K‡i KwVb e¯‘‡K Zi‡j cwiYZ K‡i Avevi Pvc Zz‡j wb‡jB Giv cybivq wkjvq ev KwVb

Ae¯’vq wd‡i Av‡m (wPÎ t 6.10)|

Pvc cÖ‡qv‡Mi d‡j KwVb e¯‘i M‡j Zi‡j cwiYZ nIqv Ges Pvc cÖZ¨vnv‡i Avevi KwVb Ae¯’vq wd‡i Avmvi

cÖwµqv‡K cyb:wkjxfeb e‡j|

c`v_©weÁvb


¯vfvweK Pv‡c ei‡di Mjbv¼ 0C, wKš‘ evqyk~b¨ ¯’v‡b ei‡di Mjbv¼ 0.0078C| myZivs GK evqy gÛjxq Pv‡c

A_©vr 76 cm cvi` Pv‡ci cwieZ©‡bi Rb¨ ei‡di Mjbv¼ 0.0078C cwiewZ©Z nq|

mvi-ms‡ÿc:

Mjb I Mjbv¼ t †Kv‡bv e¯‘i KwVb Ae¯’v †_‡K Zij Ae¯’vq iƒcvšÍwiZ nIqv‡K Mjb e‡j| wbw`©ó Pv‡c ‡h wbw`©ó

ZvcgvÎvq KwVb c`v_© M‡j Zi‡j iƒcvšÍwiZ nq Zv‡K H c`v‡_©i Mjbv¼ e‡j| GK evqy gÛjxq Pv‡c ei‡di

MjbvsK 0C|

ùzUb I ùzUbv¼ t †Kv‡bv e ‘i Zij Ae¯’v †_‡K M¨vmxq Ae¯’vq iƒcvšÍwiZ nIqv‡K ùzUb e‡j| wbw`©ó Pv‡c †h

wbw`©ó ZvcgvÎvq †Kv‡bv Zij c`v‡_©i ùzUb msNwUZ nq Zv‡K H c`v‡_©i ùzUbv¼ e‡j| GK evqy gÛjxq Pv‡c

cvwbi ùzUbv¼ 100C|

ev®úvqb t cwi‡ek †_‡KB cÖ‡qvRbxq Zvc msMÖn K‡i DcwiZj †_‡K Zij c`v‡_©i ax‡i ax‡i ev‡®ú cwiYZ

nIqvi cÖwµqv‡K ¯Ztev®úxfeb ev ev®úvqb ejv nq|

Nbxfeb t ZvcgvÎv Kwg‡q †Kv‡bv evqexq ev M¨vmxq c`v_©‡K Zvi Zij Ae¯’vq iƒcvšÍwiZ Kivi cÖwµqv‡K ejv nq

Nbxfeb|

cybtwkjxfeb t Pvc cÖ‡qv‡Mi d‡j KwVb e¯‘i M‡j Zi‡j cwiYZ nIqv AZtci Pvc cÖZ¨vnv‡i Avevi KwVb

Ae¯’vq wd‡i Avmvi cÖwµqv‡K cyb:wkjxfeb e‡j|

cv‡VvËi g~j¨vqb - 6.5


1| KZ Pv‡c cvwbi ùzUbv¼ 100C n‡e ?

(K) †h †Kvb Pv‡c (L) GK evqygÛjxq Pv‡c

(M) 1 c¨vm‡Kj Pv‡c (N) 780 mm Pv‡c

2| ei‡di UzK‡ivi Dci Pvc cÖ‡qvM Ki‡j Gi Mjbv‡¼i Kx nq ?

(K) †e‡o hvq (L) me©wb¤œ 0C nq

(M) 0C Gi Kg nq (N) AcwiewZ©Z _v‡K

3| Kÿ ZvcgvÎvq cvwbi ev¯ú nIqvÑcÖwµqvwUi bvg Kx ?

(K) ev®úvqb (L) ùzUb

(M) Nbxfeb (N) Mjb

GmGmwm †cÖvMÖvg


cvV-6 myß Zvc (Latent Heat)

D‡Ïk¨


1. Mj‡bi myß Zvc e¨vL¨v Ki‡Z cvi‡eb|

2. ev®úxfe‡bi myßZvc e¨vL¨v Ki‡Z cvi‡eb|

3. ev®úvqb I kxZjxKi‡Yi KviY e¨vL¨v Ki‡Z cvi‡eb|

4. ev®úvq‡bi Dci wewfbœ wel‡qi cÖfve eY©bv Ki‡Z cvi‡eb|

6.6.1 c`v‡_©i Ae¯’v cwieZ©‡b myßZvc (Latent Heat for Change of state of matter) Avgiv †R‡bwQ Zvc cÖ‡qvM Ki‡j c`v‡_©i ZvcgvÎv ev‡o GK_v me mgq mZ¨ bq| Zvc cÖ‡qvM Ae¨vnZ

_vK‡jI eid Mjv ïiæ n‡q m¤ú~Y© eid cvwb bv nIqv ch©šÍ ZvcgvÎv ev‡o bv, Mjbv‡¼ (0C) w¯’i

_v‡K| G‡ÿ‡Î cÖhy³ Zvc ei‡di Ae¯’v iƒcvšÍ‡i e¨q nq ZvB ZvcgvÎv ev‡o bv|

Avevi GKBfv‡e cvwbi ZvcgvÎv ùzUbv‡¼ (100C) †cŠuQvi ci m¤ú~Y© cvwb ev‡®ú iƒcvšÍwiZ bv nIqv ch©šÍ

ZvcgvÎv ùzUbv‡¼ w ’i _v‡K| G‡ÿ‡Î cÖhy³ Zvc cvwbi Ae¯’v iƒcvšÍ‡i e¨q nq ZvB ZvcgvÎv ev‡o bv|

†h Zvc c`v‡_©i ZvcgvÎvi cwieZ©b bv NwU‡q †Kej Ae¯’vi cwieZ©b NUvq Zv‡K H c`v‡_©i Ae¯’v cwieZ©‡bi myß

Zvc e‡j| GB myß Zvc yB ch©v‡qi : Mj‡bi myß Zvc Ges ev®úxfe‡b myß Zvc|

GB Zvc kw³ c`v‡_©i ZvcgvÎv cwieZ©b K‡i bv, wKš‘ AvšÍtAvYweK eÜb wkw_j K‡i| G Kvi‡Y KwVb c`v‡_©i

AYyy¸‡jvi g‡a¨i AvšÍtAvYweK AvKl©Y ej ev eÜb wkw_j n‡q Zi‡j iƒcvšÍwiZ nq| Avevi Zij AYyy¸‡jvi

AvšÍtAvYweK eÜb wQbœ K‡i M¨vmxq Ae¯’vq iƒcvšÍwiZ nq| Avm‡j GB Zvc kw³ e¯‘i Ae¯’v iƒcvšÍ‡i e¨q nq|

GLv‡b KwVb †_‡K Zi‡j Ges Zij †_‡K evqexq Ae¯’vq iƒcvšÍi nq|

Mj‡bi myß Zvc (Latent Heat of Fussion) ZvcgvÎvi cwieZ©b bv NwU‡q †Kv‡bv KwVb c`v_©‡K m¤ú‚Y©iƒ‡c Zi‡j iƒcvšÍwiZ Ki‡Z †h cwigvY Zv‡ci cÖ‡qvRb

Zv‡K H e ‘i Mj‡bi myß Zvc e‡j|

ev®úxfe‡bi myß Zvc (Latent Heat of Vaporisation) ZvcgvÎvi cwieZ©b bv NwU‡q †Kv‡bv Zij c`v_©‡K

m¤ú‚Y©iƒ‡c M¨vmxq Ae¯’vq iƒcvšÍwiZ Ki‡Z †h cwigvY Zv‡ci cÖ‡qvRb Zv‡K H e ‘i ev®úxfe‡bi myß Zvc e‡j|

6.6.2 ev®úvqb I kxZjxKiY (Evaporation and cooling) nv‡Zi ZvjywU wPr K‡i a‡i Zvi Dci K‡qK †dvuUv w¯úwiU †djyb| Kx Abyfe Ki‡Qb ? nv‡Zi ZvjywU †ek VvÛv

jvM‡Q| jÿ¨ Kiæb Zvjyi Dc‡ii w¯úwi‡Ui †duvUv¸‡jv evZv‡m wgwj‡q †M‡Q? †f‡e †`‡L‡Qb G‡ÿ‡Î Kx N‡U?

w¯úwiU ev®úvqb ev ¯Ztev®úxfeb cÖwµqvq ev®ú n‡q hvq| Avgiv Rvwb Zij †_‡K ev®ú nIqvi Rb¨ Zi‡ji

Aby¸‡jvi g‡a¨ AvšÍtAvYweK eÜb gyw³i cÖ‡qvRbxq kw³ `iKvi| evB‡ii †_‡K Zvc cÖ‡qvM Ki‡j Zij GB kw³

cvq| Ae¯’v cwieZ©‡bi GB kw³‡K Avgiv ev®úxfe‡bi myß Zvc bv‡g AwfwnZ K‡iwQ| †f‡e †`Lyb nv‡Zi Zvjyi

Dc‡ii w¯úwiU ev®úxfe‡bi myß Zvc †Kv_vq cvq? Avcbvi nv‡Zi Zvjy †_‡K| GRb¨B nv‡Zi Zvjyi Zvc †ewi‡q

hvq| nv‡Zi Zvjyi Zvc †ewi‡q hvIqvq d‡j VvÛv Abyf~Z nq|

c`v_©weÁvb


ïay w¯úwiU bq †cUªj, †K‡ivwmb wb‡q cixÿv Ki‡jI GKB NUbv ch©‡eÿY Ki‡eb| GgbwK cvwb w`‡qI cixÿv

Ki‡Z cv‡ib| GKwU wfRv MvgQv wPc‡o wb‡q Zv w`‡q Mv gy‡Q ê`y¨wZK d¨v‡bi evZv‡m `vuovb| Avcbvi Mv‡q

†j‡M _vKv m~² RjKYv¸‡jvi ev®úvqb NU‡e| Avcwb kix‡i VvÛv Abyfe Ki‡eb| Ng©v³ kix‡i d¨v‡bi evZv‡m

ùvov‡jI GKB NUbv NU‡e| Gfv‡e ev®úvqb †_‡K kxZjxKiY msNwUZ nq|

ev®úvqb †_‡K kxZjxKi‡Yi bxwZ‡K Kv‡R jvwM‡q wiwd«Rv‡iUi ˆZwi Kiv nq| Mi‡gi w`‡b gvwUi Kjmx‡Z cvwb

†i‡L cvwb VvÛv Kiv nq| gvwUi Kjmxi Mv‡q AmsL¨ m~² wQ`ª c‡_ me© v cvwb PzuB‡q evB‡i Av‡m| d‡j Kjmxi

evB‡ii MvwU memgqB †fRv _v‡K| GB cvwbi KYv Kjmxi Mv Ges msjMœ evZvm †_‡K cÖ‡qvRbxq my&ß Zvc msMÖn

K‡i ev®ú n‡q D‡o hvq| Kjmxi Mv µgk VvÛv n‡Z _v‡K, d‡j Kjmxi †fZ‡ii cvwbI VvÛv nq| ev®úvqb †_‡K

kxZjxKiY cÖwµqvwU Avgv‡ì eënvwiK Rxe‡b AZ¨šÍ ¸iæZ¡c~Y©|

6.6.3 ev®úvq‡bi Dci wewfbœ wel‡qi cÖfve (Effects of various factors on evaporation) cwi‡ek †_‡K myß Zvc msMÖn K‡i †Kv‡bv Zij c`v‡_©i ev‡®ú cwiYZ nIqvi cÖwµqvwU n‡jv ev®úvqb| G †ÿ‡Î

Zij c`v_©wU‡K ùzUbv‡¼ DËß Kiv nq bv| GwU GKwU ¯ZtùzZ© NUbv| GRb¨ cÖwµqvwU‡K ¯Ztev®úfebI ejv

nq| wKš‘ Zi‡ji ev®úvqb mvaviYZ †ek K‡qKwU NUbv ev welq Øviv cÖfvweZ nq †m¸‡jv n‡jv:

Zi‡ji cÖK…wZ t wewfbœœ Zij c`v‡_©i ev®úvq‡bi nvi wewfbœ| mvaviYZ Zi‡ji ùzUbv¼ Kg n‡j ev®úvqb nvi †ewk

nq| DØvqx c`v‡_©i ev®úvqb nvi AZ¨šÍ †ewk|

evqy cÖevn t Zi‡ji Dci evqy cÖevn †ewk n‡j ev®úvqb ªæZ nq|

Zi‡ji Dci Pvc t Zi‡ji Dci evqy gÛ‡ji Pvc evo‡j ev®úvqb nvi K‡g hvq| Pvc Kg‡j ev®úvqb e„w× cvq|

k~b¨ ¯’v‡b ev®úvq‡bi nvi me©vwaK|

Zi‡ji Dcwi Z‡ji †ÿÎdj t ev®úvqb †Kej DcwiZ‡j msNwVZ nq| Zi‡ji DcwiZ‡ji †ÿÎdj hZ †ewk

we¯Í…Z n‡e ev®úvqb ZZ †ewk n‡e|

Zij Zj msjMœ evqy ev ev‡®úi ZvcgvÎv t ZvcgvÎv †ewk n‡j ev®úvqb `ªæZ nq|

Zij Zj msjMœ evqyi Av`ª©Zv t evqyi Av`©ªZv hZ Kg nq Zi‡ji ev®úvqb ZZ ªæZ nq|

mvi-ms‡ÿc:

Mj‡bi myß Zvc t ZvcgvÎvi cwieZ©b bv NwU‡q †Kv‡bv KwVb c`v_©‡K m¤ú‚Y©iƒ‡c Zi‡j iƒcvšÍwiZ Ki‡Z †h

cwigvY Zv‡ci cÖ‡qvRb Zv‡K H e¯‘i Mj‡bi myß Zvc e‡j|

ev®úxfe‡bi myß Zvc t ZvcgvÎvi cwieZ©b bv NwU‡q †Kv‡bv Zij c`v_©‡K m¤ú‚Y©iƒ‡c M¨vmxq Ae¯’vq iƒcvšÍwiZ

Ki‡Z †h cwigvY Zv‡ci cÖ‡qvRb Zv‡K H e ‘i ev®úxfe‡bi myß Zvc e‡j|

ev®úvqb †h me wel‡qi Dci wbf©i K‡i t Zi‡ji cÖK…wZ, evqy cÖevn, Zi‡ji Dci Pvc, Zi‡ji Dcwi Z‡ji

†ÿÎdj, Zij Zj msjMœ evqy ev ev‡®úi ZvcgvÎv, Zij Zj msjMœ evqyi Av`ª©Zv|



1| A‡b‡K Mig Pv †cø‡U †X‡j VvÛv K‡ib| G‡ÿ‡Z †Kvb NUbvwU N‡U?

(K) kxZjxKiY ªæZ nq (L) ev®úvqb nvi Kg nq

(M) Pv cv‡b Z…wß †ewk nq (N) †`L‡Z fvj jv‡M

GmGmwm †cÖvMÖvg


2| ev®úvqb †Kvb welqwUi Dci wbf©i K‡i bv ?

(K) Zi‡ji cÖK…wZ (L) Zi‡ji Dci evZv‡mi Pvc

(M) c`v‡_©i NbZ¡ (N) Zij Z‡ji †ÿÎdj

3| wb‡Pi †Kvb †kÖwYi e¯‘i ev®úvqb nvi †ewk ?

(K) KwVb (L) Zij

(M) DØvqx (N) wgkÖY

cvV 7 t e¨envwiK Ñ9 ei‡di Mjbv¼ wbY©q (Determining the Melting-Point of Ice)

D‡Ïk¨

GB cv‡Vi †k‡l AvcwbÑ

1. ei‡di Mjbv¼ wbY©q Ki‡Z cvi‡eb|

2. ZvcgvÎv ebvg mgq †jL wPÎ A¼b K‡i ei‡di Mjbv¼ wPwýZ Ki‡Z cvi‡eb|

hš¿cvwZ t weKvi, evb©vi ev w¯úwiU j¨v¤ú, _vgv Nwo, K¬v¤ú hy³ ÷¨vÛ, wÎc`x ÷¨vÛ, Zvi Rvwj,

†mjwmqvm _v‡g©vwgUvi Ges K‡qK UzK‡iv eid|

Kvh© cÖYvjx t

1. weKviwU cwi®‹vi K‡i Gi g‡a¨ K‡qK UzK‡iv eid wbb|

eid UzK‡ivi mvBR eo n‡j UzK‡iv¸‡jv P~Y© K‡i wbb|

2. wÎc`x ÷¨vÛwUi Dci Zvi RvwjwU ewm‡q Zvi Dci eid c~Y©

weKviwU emvb|

3. weKv‡ii eid P~‡Y©i g‡a¨ _v‡g©vwgUv‡ii cvi` KzÛwU Wzwe‡q

_v‡g©vwgUviwU‡K K¬ v‡¤úi mvnv‡h¨ Ggbfv‡e Lvov K‡i

÷¨v‡Ûi mvnv‡h¨ Szwj‡q w`b †hb KzÛwU ei‡di g‡a¨ Wz‡e

_v‡K, wKš‘ weKv‡ii Mv‡q ¯úk© bv K‡i|

wPÎ t 6.11

4. ei‡di ZvcgvÎv †iKW© Kiæb Ges Zvc cÖ‡qvM ïiæ Kiæb| eid Mj‡Z ïiæ Ki‡e| m¤ú~Y© eid M‡j cvwb

nevi ciI ZvcgvÎvi 20C bv nIqv ch©šÍ Zvc w`‡Z _vKzb|

5. ZvcgvÎv 20C ev Zvi Dc‡i n‡j Zvc †`qv eÜ Kiæb Ges weKvi I cvwb VvÛv n‡Z w`b|

6. GKwU †jL wP‡Îi myweavg‡Zv †¯‹j wb‡q X -Aÿ eivei mgq (wgwbU) Ges Y-Aÿ eivei ZvcgvÎv

(C) wb‡q cÖvß †iK‡W©i †jL wPÎwU A¼b Kiæb|

7. cixÿY †WUv Ges †jL wPÎ †_‡K MjbvsK gvb wbY©q Kiæb|

cixÿY ch©‡eÿY †WUvi QK

mgq 0 wgt 1g wgt 2q wgt 3q wgt 4_© wgt 5g wgt 6ô wgt 7g wgt ......

ZvcgvÎv

c`v_©weÁvb


djvdj I wm×všÍ

ch©‡eÿY †WUv †_‡K cÖvß

ei‡di Mjbv¼ t ...... C

†jL wPÎ †_‡K cÖvß

ei‡di Mjbv¼i t ... .... C

†jL wP‡Îi bgybv

mgq (wgwbU)

wPÎ t 6.12 ZvcgvÎv ebvg mgq †jL

cvV 8t e¨envwiK-10 cvwbi ùzUbv¼ wbY©q (To Determine the Boiling point of water) D‡Ïk¨ t GB cv‡Vi †k‡l Avcwb

1. cvwbi ùzUbv¼ wbY©q Ki‡Z cvi‡eb|

2. ZvcgvÎv ebvg mgq †jL wPÎ A¼b K‡i cvwbi ùzUbv¼ wPwýZ Ki‡Z cvi‡eb|

hš¿cvwZ t weKvi, evb©vi ev w¯úwiU j¨v¤ú, ÷c IqvP, K¬¨v¤ú hy³ ÷¨vÛ, wÎc`x ÷¨vÛ I Zvi Rvwj,

†mjwmqvm _v‡g©vwgUvi Ges cvwb|

Kvh© cÖYvjx t

1. weKviwU cwi®‹vi K‡i Gi g‡a¨ A‡a©K cwigvY cvwb wbb|

2. wÎc`x ÷¨vÛwUi Dci Zvi RvwjwU ewm‡q Zvi Dci cvwb c~Y©

weKviwU emvb|

3. weKv‡ii cvwbi g‡a¨ _v‡g©vwgUv‡ii cvi` KzÛwU Wzwe‡q

_v‡g©wgUviwU‡K K¬ v‡¤úi mvnv‡h¨ Ggbfv‡e Lvov K‡i

÷¨v‡Ûi mvnv‡h¨ Szwj‡q w`b †hb KzÛwU cvwbi g‡a¨ Wz‡e,

wKš‘ weKv‡ii Mv‡q ¯úk© bv K‡i|

4. cvwbi ZvcgvÎv †iKW© Kiæb Ges weKviwU‡Z Zvc w`b|

5. cvwb Mig n‡Z ïiæ Ki‡e| cÖwZ wgwb‡U cvwbi ZvcgvÎv

†iKW© Kiæb|

wPÎ 6.13

6. cvwb dzU‡Z ïiæ Ki‡e, cvwb dzUv ïiæ nIqvi c‡iI 7/8 wgwbU a‡i Zvc w`‡Z _vKzb Ges cÖwZ wgwb‡U

ZvcgvÎv †iKW© Kiæb| Gici Zvc cÖ‡qvM eÜ K‡i cvwb VvÛv n‡Z w`b|

mZK©Zv t

weKv‡ii eid P~‡Y©i g‡a¨ _v‡g©vwgUv‡ii cvi` KzÛwU

†hb m¤ú~Y©fv‡e Wz‡e _v‡K

Zvi Rvwji Dci bv ewm‡q mivmwi weKv‡i Zvc

†`‡eb bv|

Z

vc

gvÎ C

GmGmwm †cÖvMÖvg


7. GKwU †jL wP‡Îi myweavg‡Zv †¯‹j wb‡q X -Aÿ eivei mgq (wgwbU) Ges Y-Aÿ eivei ZvcgvÎv

(C) wb‡q cÖvß †iK‡W©i †jL wPÎwU A¼b Kiæb|

8. cixÿY †WUv Ges †jL wPÎ †_‡K ùzUbv¼ gvb wbY©q Kiæb|

cixÿY ch©‡eÿY †WUvi QK

mgq 0 wgt 1g wgt 2q wgt 3q wgt 4_© wgt 5g wgt 6ô wgt 7g wgt ......

ZvcgvÎv

djvdj I wm×všÍ

ch©‡eÿY †WUv †_‡K cÖvß

cvwbi ùzUbv¼ t ......... C

†jL wPÎ †_‡K cÖvß

cvwbi ùzUbv¼ t ... ........C

†jL wP‡Îi bgybv

mgq (wgwbU)

wPÎ t 6.14 ZvcgvÎv ebvg mgq †jL

P‚ovšÍ g~j¨vqb- 6

K. mvaviY eûwbe©vPbx cÖkœ t


1| _v‡g©vwgUv‡ii Ea© w¯’iv¼ KZ ?

(K) wngv¼ ev ev¯ú we› y (L) cvwb †h ZvcgvÎvq dzU‡Z _v‡K

(M) õzUbv¼ ev eid we› y (N) cvwb †h ZvcgvÎvq ev®ú nq

2| Zvc cwigv‡ci AvšÍR©vwZK GKK †KvbwU ?

(K) †mjwmqvm (L) †Kjwfb

(M) K¨vjwiwgUvi (N) dv‡ibnvBU

3| •`N© cÖmviY ¸Yv¼ , †ÿÎ cÖmviY ¸Yv¼ Ges AvqZb cÖmviY ¸Yv¼ n‡j wb‡Pi †Kvb m¤úK©wU mwVK?

(K) (L)

(M) (N) 23

4| Zvc cÖ‡qv‡M wb‡Pi †Kvb c`v‡_©i cÖmviY me †P‡q †ewk nq?

(K) KwVb (L) Zij

(M) evqexq (N) c`v‡_©i Dcv`v‡bi Dci wbf©i K‡i

5| cÖK…Z cÖmviY ¸Yv¼ = r, AvcvZ cÖmviY ¸Yv¼ = a Ges cv‡Îi c`v‡_©i cÖmviY ¸Yv¼ = g n‡j wb‡Pi †Kvb

mgxKiYwU mwVK bq ?

mZK©Zv t

weKv‡ii cvwbi g‡a¨ _v‡g©vwgUv‡ii cvi` KzÛwU

†hb m¤ú~Y©fv‡e Wz‡e _v‡K |

ZviRvwji Dci bv ewm‡q mivmwi weKv‡i Zvc

†`‡eb bv|

Zvc

gvÎ C

c`v_©weÁvb


(K) r =a + g (L) r = a - g

(M) a = r - g (N) g = r - a

L. eûc`x mgvwßm~PK eûwbe©vPbx cÖkœ t

1| †Kv‡bv e ‘i Zvc aviY ÿgZv wbf©i K‡i e¯‘wUi-

i. Av‡cwÿK Zv‡ci Dci|

ii. f‡ii Dci|

iii. ZvcgvÎvi Dci|

wb‡Pi †KvbwU mwVK?

K) i I ii L) ii I iii M) iii I i N) i, ii I iii

2| myß Zvc g~jZ ywU KvR K‡i, Zv n‡jvÑ

i. e¯‘i ZvcgvÎvi cwieZ©b NUvq|

ii. e¯‘i Ae¯’vi cwieZ©b NUvq|

iii. e¯‘i KYv¸‡jvi AvšÍtAvbweK eÜb wkw_j K‡i|

wb‡Pi †KvbwU mwVK?

K) i I ii L) ii I iii M) iii I i N) i, ii I iii

M. Awfbœ Z_¨ wfwËK eû wbe©vPbx cÖkœ t

wb‡Pi e‡·i Z_¨¸wj co–b Ges 1-4 b¤i cª‡kœi mwVK DËiwU‡Z wUK w`b|

myZcv ¯‹z‡j hvIqvi mgq `ya †L‡Z †h‡q †`Lj `ya fxlY Mig| gv‡K ejj ÑÔgv `ya A‡bK Mig, VvÛv n‡Z mgq

jvM‡e| Avgvi †`ix n‡q hv‡”Q|Õ `ya bv ‡L‡qB myZcv ¯‹z‡j iIbv nw”Qj| gv ZvovZvwo GKwU eo _vjvq `ya

†X‡j Zvi Dci nvZ cvLv w`‡q GK wgwbU evZvm Ki‡jb| Gi ci Avi GKwU VvÛv Møv‡m `yaUzKz †X‡j w`‡q

ej‡jb-ÔGevi LvI VvÛv n‡q †M‡QÕ| myZcv †`Lj mwZ¨ `ya †ek VvÛv n‡q †M‡Q| †m AevK n‡jv| `ya †L‡q ¯‹z‡j

Pjj|

1| ya ZvovZvwo VvÛv n‡jv †Kvb cÖwµqvq ?

(K) ùzUb (L) ev®úvqb

(M) Zvcb (N) wewKiY

2| _vjvq Xvjvi Rb¨ ya `ªæZ kxZj nIqvi KviY †KvbwU?

(K) _vjwU VvÛv wQj (L) nvZ cvLvi evZvm Lye VvÛv wQj

(M) `ya myßZvc eR©b K‡iwQj (N) ev®úvqb †_‡K kxZjxKiY N‡U‡Q

3| G †ÿ‡Î Mig `y‡ai Zvc †Kvb Dcv`vb Øviv †kvwlZ n‡q‡Q ?

(K) _vjvwUi wbg©vb c`v_© (L) `y‡ai †_‡K D‡o hvIqv Rjxq ev®ú

(M) nvZ cvLvi wbg©vY c`v_© (N) Dc‡ii me wKQz|

4| _vjvq bv †X‡j Møv‡m ivL‡j `ya †`wi‡Z VvÛv n‡Zv| †m‡ÿ‡Î †Kvb cÖwµqvq `ya VvÛv n‡Zv ?

(K) wewKiY (L) cwiPjb

(M) ev®úvqb (N) cwienb

GmGmwm †cÖvMÖvg


N. m„Rbkxj cÖkœ t

1. wb‡Pi e‡·i Z_¨¸wj co–b

Aqb ¯‹z‡j hvIqvi mgq `ya †L‡Z †h‡q †`Lj `ya fxlY Mig| gv‡K ejj ÑÔgv `ya A‡bK Mig, VvÛv n‡Z mgq

jvM‡e| Avgvi †`ix n‡q hv‡”Q|Õ `ya bv ‡L‡qB Aqb ¯‹z‡j iIbv nw”Qj| gv ZvovZvwo GKwU eo _vjvq `ya †X‡j

Zvi Dci nvZ cvLv w`‡q GK wgwbU evZvm Ki‡jb| Gi ci Avi GKwU VvÛv Møv‡m `yaUzKz †X‡j w`‡q ej‡jb-

ÔGevi LvI VvÛv n‡q †M‡QÕ| Aqb †`Lj mwZ¨ `ya †ek VvÛv n‡q †M‡Q| †m AevK n‡jv| ya †L‡q ¯‹z‡j Pjj|

K. ev®úvq‡bi msÁv w`b|

L. ev®úvqb I õzU‡b g‡a¨ cv_©K¨ Kx?

M. ev®úvqb †_‡K Kxfv‡e kxZjZvi D™¢e N‡U eY©bv Kiæb|

N. _vjvq bv †X‡j Avi Kx fv‡e ya VvÛv Kiv †hZ ? †m †ÿ‡Î myweav Amyweav¸‡jv e¨vL¨v Kiæb|

eûwbe©vPbx cÖkœmg~‡ni DËigvjv

cv‡VvËi g~j¨vqb 6.1 t 1| (M) 2| (L) 3| (N) 4| (M) 5| (M)

cv‡VvËi g~j¨vqb 6.2 t 1| (K) 2| (M) 3| (K) 4| (M)

cv‡VvËi g~j¨vqb 6.3 t 1| (N) 2| (K) 3| (N)

cv‡VvËi g~j¨vqb 6.4 t 1| (N) 2| (K) 3| (N) 4| (M)

cv‡VvËi g~j¨vqb 6.5 t 1| (L) 2| (M) 3| (K)

cv‡VvËi g~j¨vqb 6.6 t 1| (K) 2| (M) 3| (K)

P‚ovšÍ g~j¨vqb 6

K. mvaviY eûwbe©vPbx cÖkœ t 1| (L) 2| (M) 3| (N) 4| (M) 5| (L)

L. eûc`x mgvwßm~PK eûwbe©vPbx cÖkœ t 1| (K) 2| (L)

M. Awfbœ Z_¨ wfwËK eû wbe©vPbx cÖkœ t 1| (L) 2| (N) 3| (L) 4| (M)

N. m„Rbkxj cÖkœ t (K) cvV 6 Gi mvims‡ÿc †`Lyb (L) 6.5.2 cvV¨vs‡k †`Lyb

(M) 6.6.2 cvV¨vs‡ki mvnvh¨ wbb

(N) Møv‡m †i‡L `y‡ai g‡a¨ ei‡di w`‡q A_ev ei‡di g‡a¨ MøvmwU Wzwe‡q `ya‡K `ªæZ VvÛv

Kiv ‡hZ | A_ev MøvmwU †Uwe‡ji Dci ‡i‡L w`‡jI `ya ax‡i ax‡i VvÛv n‡Zv

cÖ‡Z¨K †ÿ‡Îi myweav Amyweav Av‡Q Zv hyw³ w`‡q wb‡R eY©bv I e¨vL¨v Kiæb|

wUD‡Uvwiqvj K¬v‡m wkÿK‡K †`Lvb|

c`v ©weÁvb bdwbu t 6 · c`v_© av‡cwÿk zvc (jkg-1k ) c`v_© av‡cwÿk zvc (jkg-1k ) cvwb 4200...

Documents