Zvct Zvc GK cökvi kw³ hv e yi AšÍt kw³i ewntcökvk K i Zvc kw³ e yi mkj AYyi MwZ kw³i dj e yi AYyi MwZkw³ evo j Zvckw³ e w cvq Ges e yi AYyi MwZkw³ Kg j Zvckw³ K g hvq h kw³ Mig ev VvÛi Abyf~wZ Rb vq Zvn jv Zvc kw³ Zvc kw³ K Ab kw³ Z iæcvšíi Ki Z h š i cö qvrb nq Zvckw³ m ú K `ybwu gzev` cöpwjz Av Q K vjwik gzev` I MZxq gzev`t K vjwik gzev`: GB gzev` Abymv i Zvc K vjwik bvgk GK cökvi IRbnxb A` k KYv hv me e yi g a Abvq m cö ek Ki Z cv i Ges ci úi K wekl Y K i Kv bv e y Z K vjwik bvgk KYv cö ek Ki j e y DËß nq Ges e y n Z wbm Z n j e y VvÛv nq GKwU e h cwigvy K vjwik bvgk KYv nviv e Aci GKwU e m cwigvy KYv AR b Ki e GB gzev` Abymv i Zv ci GKK K vjwi K vjwi: GK MÖvg weï cvwbi ZvcgvÎv GK wwwmö mjwmqvm e w Ki Z cö qvrbxq Zvc K GK K vjwi e j MZxq gzev`: GB gzev` Abymv i Zvc n Q e yi AYyi MwZkw³i mgwó Kv bv e yi Dci hvwš K KvR m úvw`z n j h kw³ e wqz nq Zv GB Zvc kw³ Z cwiyz nq GB gzev` Abymv i Zvc kw³ e envi K i KvR Kiv m e Ges Zvc kw³ K Ab kw³ Z iycvšíwiz Kiv hvq GB gzev` Abymv i Zvc kw³i GKK Ryj MZxq gzev` `b weávbx KvD U ivg dv W ivg dv W j K ib Zzicy bi mvnv h bj wq `ªi mgq Zzicyb I bj DfqB Mig nq wzwb e jb e i Dci KvR Ki j kw³ e q Ki Z nq, GB e wqz kw³b Zvc kw³ iæ c cökvk cvq 4.2J hvwš K kw³ e q K i GK K vjwi Zvc Drcbœ Kiv hvq 4.2 Ryj = 1 K vjwi Zvc kw³i wnmve: Zvc kw³ wnmve Kiv hvq K qkwu Dcv q hgb: Kv Ri gva gq = mgh = ms θ = 1 2 mv2 ZvcgvÎv cwiez bi Kvi Y Q = ms θ e yi Ae vi cwiez bi Kvi Y Q = ml f GLv b Q = Zvckw³ J S = Av cw K Zvc Jk 1 g k 1 l f = myßzvc Jk 1 m = fi kg θ = ZvcgvÎvi cwiez b k ei di Av cwÿk Zvc S = 2100 Jk 1 g k 1 cvwbi Av cwÿk Zvc S = 4200 Jk 1 g k 1 eid Mj bi myß Zvc S = 336000 Jk 1 cvwbi ev úxfe bi myß Zvc S = 2268000 Jk 1 ZvcgvÎv: ZvcgvÎv n Q Kv bv e yi Zvcxq Ae v hv Ab e yi ms ú k Avm j Zvc MÖnY Ki e bv er b Ki e Zv wbavib K i `q A_ev m gvò cöwµqvq e yi h Zvcxq ag w i _v K Zv K ZvcgvÎv e j Zvc Ges ZvcgvÎv GK bq Kv bv e Z Zv ci cöevn wbf i K i ZvcgvÎvi Dci,Zv ci cwigv Yi Dci bq ZvcgvÎv cwigv c ji bvg _v g vwguvi _v g vwguvi Zwi nq c`v _ i ZvcgvÎvwÎK ev D òvzvwgwzk a g i Dci wbf i K i Zvc cwigvc Kiv nq K vjwiwguv ii mvnv h DòZvwgwZK ag : ZvcgvÎv cwiez bi mv _ c`v _ i h mkj a g i wbqwgz cwiez b nq Zv K DòZvwgwZK ag e j hgb `N, AvqZb,Pvc, iva,d¾ jzv,cvi` Í BZ vw` DòZvwgwZK c`v_ : h mkj c`v _ i ZvcgvÎv cwiez bi mv _ DòZvwgwZK a g i wbqwgz cwiez b nq Zv K DòZvwgwZK c`v_ e j hgb cvi`,a vj Kvnj,mKj avze c`v_,k ò e BZ vw` _v g vwguvi: h h š i mvnv h ZvcgvÎv cwigvc Kiv nq Zv K _v g vwguvi e j _v g vwguvi Zwi Kiv nq c`v _ i DòZvwgwZK ag e envi K i ZvcgvÎv cwigv ci wewfbœ j Av Q hgb: mjwmqvm j dv ibnvbu j Kjwfb j Av` k M vm j ZvcgvÎv AvšÍR vwzk j ivgvi j i vswkb j mjwmqvm j : myb W bi R vwzwe ` A vbwvm mjwmqvm GB j D veb K ib GB j `yb w i we `yy c wz Z ZvcgvÎv cwigvc Kiv nq GB j eid we `y 0 0 C Ges ev ú we `y100 0 C aiv nq dv ibnvbu j: Rvgv b weávbx wr.ww dv ibnvbu GB j D veb K ib GB j `yb w i we `y c wz Z ZvcgvÎv cwigvc Kiv nq GB j eid we `y 32 0 F Ges ev úwe `y 212 0 F aiv nq Kjwfb j : jw Kjwfb GB j D veb K ib GB j GK w i we `y I `yb w i we `y Dfq c wz Z ZvcgvÎv cwigvc Kiv nq GB j eid we `y n jv 273K Ges ev úwe `y n jv 373K aiv nq MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 1
ZvcgvÎv cwigv ci g~jbxwzt Kjwfb j GK w i we `y c wz: GB c wz Z cvwbi Îa we `y K (273.16) K w i we `y aiv nq Kjwfb j ZvcgvÎv T = x x tr 273.16 K GLv b x tr = Îa we `y Z c`v _ i ZvcwgwZK ag x = T ZvcgvÎvq c`v _ i ZvcwgwZK ag DòZvwgwZK ag `N n j x = l T = l l tr 273.16 K DòZvwgwZK ag Pvc n j x = P T = P P tr 273.16 K DòZvwgwZK ag iva n j x = R T = R R tr 273.16 K DòZvwgwZK ag AvqZb n j x = V T = V V tr 273.16 K Kjwfb j `yb w i we `y c wz: GB c wz Z eid we `y K 273K Ges ev ú we `y K 373K a i GB j Kiv n q Q X θ X ice GB j, θ = X steam X ice GLv b X θ = θ ZvcgvÎvq c`v _ i ZvcwgwZK ag Ges X ice = eid we `y Z c`v _ i ZvcwgwZK ag θ =ZvcgvÎv Ges n = g wjk e eavb `yb w i we `y c wz: ZvcgvÎvwgwZK ag wn m e c`v _ i mme ag K e envi Kiv nq hv ZvcgvÎvi mv _ mylgfv e cwiewz Z nq A_v r ZvcgvÎvi cwiez b c`v _ i ZvcgvÎvwgwZK a g i mgvbycvwzk θ 1 I θ 2 ZvcgvÎvq Kv bv GKwU c`v _ i ZvcgvÎvwgwZK ag h_vµ g x 1 I x 2 n j- θ 2 θ 1 x 2 x 1 ev, θ 2 θ 1 = a x 2 x 1 a GKwU mgvbycvwzk aªyek wb œ w i we `y ev eid we `y θ ice I DaŸ w i we `y ev ev ú we `y θ steam ZvcgvÎvq Kv bv GKwU c`v _ i ZvcgvÎvwgwZK ag h_vµ g X ice I X steam Ges h Kv bv θ ZvcgvÎvq x n j θ steam θ ice = a X steam x ice Ges θ θ ice = a x x ice θ θ ice θ steam θ ice = x x ice X steam x ice GLv b θ steam θ ice = n n Q g wjk e eavb g wjk e eavb K n msl K mgvb fv M wef³ Kiv n j θ θ ice n ev, θ = = x x ice X steam x ice x x ice X steam x ice n + θ ice GUvB `yb j we `y c wz Z ZvcgvÎv cwigv ci g~jbxwz mjwmqvm j n = 100 Ges θ ice = 0 0 C myzvivs, mjwmqvm j ZvcgvÎv- θ c = x x ice X steam x ice 100 0 C dv ibnvbu j n = 180 Ges θ ice = 32 0 F myzivs,dv ibnvbu j ZvcgvÎvx x ice θ F = 180 + 32 X steam x ice Kjwfb j n = 100 Ges θ ice = 273K myzvivs, Kjwfb j ZvcgvÎv- θ K = x x ice X steam x ice 100 + 273 K mjwmqvm,dv ibnvbu I Kjwfb ji g a m úk t ev ú we `y eid we `y 100 212 373 R n R C F K ZvcgvÎv cwigv ci g~jbxwz e envi K i 0 32 273 R n 0 = R 0 = C = F 32 = K 273 100 0 100 0 100 212 32 373 273 ev, C = F 32 = K 273 100 180 100 C = F 32 = K 273 5 9 5 C = F 32 = K 273 = R n 492 = R 5 9 5 9 4 MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 2
GK cigvyyk M v mi Rb n gvj M v mi AšÍt kw³ Av` k M vm j : E = 3 Pvj m Gi m~î n Z cig k~b ZvcgvÎvi gvb cviqv hvq 2 wø cigvyyk M v mi Rb n gvj M v mi AšÍt kw³ 273 273 ZvcgvÎv K cig k~b a i Ges Av iv wkqy w i we `yi mgš^ q h j wbaviy Kiv nq E = 5 nr Zv K Av` k j ev cig j e j eû cigvyyk M v mi Rb n gvj M v mi AšÍt kw³ mjwmqvm ji AbyKi Y h cig j MVb Kivm nq Zv K cig mjwmqvm j ev Kjwfb j e j GB E = 6 nr j ZvcgvÎvi GKK kelvin K ZvB cig ZvcgvÎv gqv ii cökí: T = (C + 273)K Kv bv wbw` ó cwigvy M v mi Af šíixy kw³ ïaygvî Gi Avvevi dv ibnvbu ji AbyKi Y h cig j MVb ZvcgvÎvi Dci wbf i, Gi Pvc I AvqZ bi Dci wbf i Kiv nq Zv K cig dv ibnvbu j ev i vswkb j e j K i bv GB ZË K gqv ii cökí e j GB j ZvcgvÎvi GKK Rankin R. ZvcgvÎvq AvšÍR vwzk j: AvšÍRv wzk IRb I cwigvc KwgwU ZvcgvÎv cwigv ci Rb Kjwfb ji Abyiy c GKwU e envwik j `b GB j K ZvcgvÎvq AvšÍRv wzk j e j ZvcgvÎvq AvšÍR vwzk ji kzv byhvqx ZvcgvÎvq ji bvg n e kelvin ZvcgvÎvq GKK n e Kjwfb K 1000K ch ší ZvcgvÎv cwigv ci Rb cøvwubvg iva _v gv wguvi e envi n e 1000 1400K ch ší ZvcgvÎv cwigv ci Rb Zvc hymj _v gv wguvi e envi n e 1400K Gi D aÿ ZvcgvÎv cwigv ci Rb cvb ivwguvi e envi n e Af šíixy kw³ ev AšÍt kw³t cöwzwu wm gb AmsL AYy-cigvYyi mgš^ q MwVZ AvbweK MwZZË Abymv i G AYyMy jv mzz K úgvb ev MwZkxj Ges G `i ci ú ii g a AvKl YRwbZ ej wµqv K i myzvivs AYy jvi MwZkw³ I wefe kw³ Av Q G MwZkw³ I wefe kw³ AvYyex wyk G MwZkw³ I wefe kw³i mgwób H wm gi Af šíixy kw³ AYy jvi gvu MwZkw³i mgvb M v mi MwZZË _ K Avgiv Rvwb, E = 3 2 PV = 3 2 RT Kv bv wm g Zvc cö qvm Kiv n j Gi AYy jvi MwZkw³ e w cvq d j Gi Af šíixy kw³ii e w N U Kv bv wm gi Af šíixy kw³i gvb Gi Ae vi Ici wbf i K i bv wkš y Kv bv wm gi Af šíixy kw³i cig gvb Rvbv m e bq ïay Gi cwiez b cwigvc Kiv m e GK cigvyyk M v mi Rb GK gvj M v mi AšÍt kw³ E = 3 2 RT M vm I cömvi Y K ZKvRt GKwU wmwjûv ii g a wc b Øviv Ave wkqy cwigvc M vm Av Q cö_ g G M v mi Pvc I AvqZb h_vµ g P i I V i wqj cömvi Yi d j Gi kl Pvc P f I AvqZb V f n jv G cömvi Yi Rb K ZKv Ri cwigvy wby q Ki Z n e Kv bv GK Ae vq Gi Pvc P wqj wc bi cö Q `i Îdj A n j Gi Ici wµqvkxj gvu ej F = PA G e ji wµqvi wc bi miy dx n j K ZKvRdW = F dx = PAdx = PdV A B M v mi AvqZb V i _ K cömvwiz P n q V f niqvq gvu K ZKvR- W = dw = V i PdV M vm A(V i, P i ) Ae v _ K B(V f, P f D V C Ae vq h Z M vm KZ K gvu K ZKvR- MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 3 W = V f V i PdV V f n e cöwµqv c_ I AvqZb A Øviv mxgve ABCD Îi Îdj ZvcMwZwe` vi cö_g m~ît 1847 mv j weávbx Ryj Zvc I Kv Ri g a GKwU m úk vcb K ib Zvc kw³ e e v I cwi e ki g a kw³i cöevn NVvq hzlb e e v I cwi e ki g a ZvcgvÎvi cv_ K _vk e kw³i iƒcvšíi wewa Z Zvc kw³ K Ab kw³ K wksev Ab kw³ K Zvc kw³ K cwibz Kiv m e weávbx Ryj Zvc I Kv Rv g a m úk `LvbÑ hlb mg Í KvR Zvc kw³ K ev Zvc m ú~b iƒ c Kv R cwibz nq ZLb KvR I Zvc ci úi mgvbycvwzk nq Kv bv wm gi Ici W cwigvy KvR Kivq hw` Q cwigvy Zvc Drcbœ nq Z e Ry ji m~îvbymv i MvwYwZK fv e
W H ev,w = JH GLv b J GKwU aªye ivwk _v K Zvc I hvwš K mgzv ev hvwš K Zzj v ev Ry ji aªyek e j weávbx K wmqv mi g Z Kv bv e e vq mieivnk Z Zvc kw³ e e vi AšÍt kw³i cwiez b I evwn K Kv Ri hvmd ji mgvb n e MvwYwZKfv e Kv bv e e vi dq cwigvb Zvckw³ `Iqvq e e vq AšÍt kw³i cwiez b du Ges K ZKvR dw n j ZvcMwZwe` vi cö_g m~î n Z cvb dq = du + dw ev, dq = du + PdV Dc ii m~î n Z cvb, Kv bv e e vq Zvc kw³ `Iqv n j ev e e v KZ K Zvc kvwlz n j dq abvz K n e Kv bv e e v n Z Zvckw³ wbm Z n j ev e e v KZ K Zvc ewr Z n j dqfbvz K n e Kv bv e e v KvR m úbœ Ki j dw abvz K n e Kv bv e e vi Dci KvR m úbœ n j dw FbvZ K n e Kv bv e e vi AšÍt kw³ e w n j du abvz K n e Kv bv e e vi AšÍt kw³ K g M j du FbvZ K n e m gvò cöwµqvt h ZvcMZxq cöwµqvq e e vq ZvcgvÎv w i _v K Zv K m gvò cöwµqv e j m gvò cöwµqvq Av`k e e vi Rb du = 0 niqvq ZvcMwZwe` vi cö_g m~î n Z cvb, dq = du + dw ev, dq = 0 + dw ev, dq = dw Dc ii m~î n Z cvb, e e vq Zvc kw³ `Iqv n j ev e e v Zvc kw³ kvlb Ki j e e v KvR m úbœ Ki e e e v Zvc kw³ er b Ki j e e vi Dci KvR m úbœ n e mgavqzb cöwµqv t h ZvcMZxi cöwµqvq e e vq AvqZb cwiez b nq bv Zv K mgavqzb cöwµqv e j mgavqzb cöwµqvq dv = 0 niqvq ZvcMwZwe` vi cö_g m~î n Z cvb, dq = du + PdV ev, dq = du Dc ii m~î n Z cvb, Kv bv e e vq Zvc kw³ kvly n j e e vi AšÍt kw³ e w cv e Ges ZvcgvÎv e w cv e Kv bv e e v n Z Zvc kw³ wbm Z n j e e vi AšÍt kw³ n«vm cv e Ges ZvcgvÎv K g hv e cö_g m~ Îi e envi t iƒ Zvcxq cöwµqvt h ZvcMZxq cöwµqvq e e vi Zv ci Kv bv Av`vb-cÖ`vb nq bv Zv K iƒ Zvcxq cöwµqv e j iƒ Zvcxq cöwµqvq dq = 0 niqvq ZvcMwZwe` vi cö_g m~î n Z cvb, dq = du + dw ev, 0 = du + dw ev, du = dw ev, dw = du Dc ii m~î n Z cvb, e e vi Dci h cwigvb KvR m úbœ nq Zv e e vi mb cwigvy AšÍt kw³i e w K i e e v h cwigvb KvR m úbœ K i Zv e e vi mb cwigvb AšÍt kw³i n«vm cvq AšÍt kw³i e w n j e e vq ZvcgvÎv e w cv e AšÍt kw³i n«vm c j e e vq ZvcgvÎv K g hv e P~V jlwp Îi gva g ZvcMwZwe` vi cö_g m~ Îi e envit P c b a V acbc _ kvwlz Zvc Q acb = U b U a + W adbc _ kvwlz Zvc Q adb = U b U a + W ba c _ Q ba = U a U b + W ab c _ Q ab = U b U d + W ad c _ Q ad = U d U a + W d MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 4
Av`k M v mi Rb C p I C v Gi m úk t w i Pv c GK gvj M v mi ZvcgvÎv dt e w Ki Z cö qvrbxq Zvc dq p = C p dt w i AvqZ b GK gvj M v mi ZvcgvÎv dt e w Ki Z cö qvrbxq Zvc dq v = C v dt w i AvqZ b K ZKvR dw = PdV = 0 ZvcMwZwe` vi cö_g m~îvbymv i dq v = du + PdV ev, dq v = du + 0 ev, dq v = du ev, C v dt = du w i Pv c ZvcMwZwe` vi cö_g m~îvbymv iñ dq p = du + dw Avgiv Rvwb, M vm cömvi Y K ZKvR dw = PdV Avevi GK gvj M v mi Rb PV = RT P V + dv = R(T + dt) PdV = RdT w i Pv c ZvcMwZwe` vi cö_g m~îvbymv i C p dt = C v dt + PdV ev, C p C v = R h nzz R Gi gvb me `v abvz K, m nzz C p > C v w i Pv c M v mi gvjvi ZvcaviY gzv, w i AvqZ b M v mi gvjvi ZvcaviY gzv A c v eo C p I C v Gi AbycvZ: C p I C v Gi AbycvZ K γøviv cökvk Kiv nq C p = γ C v GK cvigvywek M v mi Î γ = 1.67 wøcvigvywek M v mi Î γ = 1.4 Ges eû cvigvywek M v mi Î γ = 1.33 iƒ Zvcxq cöwµqvq Av`k M v mi Pvc I AvqZ bi m úk t M v mi AvqZb dv cwigvy cwiez b n j Gi Ici K ZKvR dw = PdV Ges iƒ Zvcxq cöwµqvq dq = 0 niqvq ZvcMwZwe` vi cö_g m~îvbymv i 0 = du + dw ev, C v dt + PdV = 0 [C v dt = du ] Av`k M v mi mgxkiy n Z PV = RT G K e ekjb K i cvb PdV + VdP = RdT PdV +VdP ev,dt = R PdV +VdP dt Gi gvb ewm q cvb C v + PdV = 0 R mgvavb K i cvb PV γ =aªyek ev, P 1 V γ γ 1 = P 2 V 2 GUvB iƒ Zvcxq cöwµqvq Av`k M v mi Pvc I AvqZ bi m úk iƒ Zvcxq cöwµqvq Av`k M v mi AvqZb I ZvcgvÎvi m úk t GK gvj M v mi Rb Av`k M v mi mgxkiy _ K cvb P = RT V Avevi, iƒ Zvcxq cöwµqvi Î PV γ =aªyek Dc iv³ mgxkiy `ywu n Z cvb MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 5 RT V Vγ = aªyek TV γ 1 =aªyek V 1 γ 1 = V 2 γ 1 GUvB iƒ Zvcxq cöwµqvq Av`k M v mi AvqZb I ZvcgvÎvi m úk iƒ Zvcxq cöwµqvq Av`k M v mi Pvc I ZvcgvÎvi m úk t Av`k M v mi mgxkiy _ K cvb V = RT P Avevi, iƒ Zvcxq cöwµqvi Î PV γ =aª ek Dc iv³ mgxkiy `ywu n Z cvb P RT γ P =aªyek ev, R γ P 1 γ T γ =aªyek 1 γ ev, TP γ =aªyek 1 γ γ P 1 1 γ γ = P 2 GUvB iƒ Zvcxq cöwµqvq Av`k M v mi Pvc I ZvcgvÎvi m úk ZvcMwZwe` vi wøzxq m~ît cøv ¼i wee wz: Ggb GKwU BwÄ bi cwikíbv KL bvb m e bq, hvi c~y AveZ b KejgvÎ GKwU Zvcxq Drm n Z Zvc msm nxz n e Ges Ab Î Kv bv cwiez b e ZxZ msm nxz Zv ci meuzkz Kv R iƒcvšíwiz Kiv hv e Kjwfb wee wz: Kv bv e y ev Drm n Z Zvc msmön Kivi d j hlb Gi ZvcgvÎv cvwicvwk Ki e y jvi g a kxzjzg e yi ZvcgvÎv A c vi Kg nq ZLb Avi Kv bv hvwš K e e vq mvnv h B (BwÄb KZ K) Zv n Z Zvc msmön K i KvR Kiv m e bq K wmqv mi wee wz: Kv bv h š i c B evb ii RM Z cwiez b m wó e ZxZ Gi c~y AveZ b GKwU Zvcxq Drm n Z Zvc msmön K i H Zvc DòZi Ab Kv bv Dr m Pvjbv Kiv m e bq
Zvc BwÄ bi ` Zvt Zvc BwÄ b h cwigvy Zvc kw³ mieivn Kiv nq ev Zvc Pvc A(P 1, V 1 ) BwÄb h cwigvy Zvc kw³ MÖnY K i Zvi m ú~y Uv Kv R iƒcvšíwiz Ki Z cv i bv, Gi GKwU Ask Kv R iƒcvšíwiz K i Ges evwk Zvckw³ AcwiewZ Z AvKv i BwÄb n Z wbm Z nq Kv bv BwÄ bi Kv R cwiyz kw³ Ges gvu D(P 4, V 4 B(P 2, V 2 ) kw³i AbycvZ K Kg ` Zv e j Kg ` Zv K η Øviv m~wpz Kiv nq cwigvy Zvc MÖnY K i Kv bv BwÄb hw` WcwigvY C(P 3, V 3 ) KvR m úyœ K i Z e G BwÄ bi ` Zv η = W Avevi BwÄb Zvc MÖnY K i KvR m úv` bi ci hw` Q 2 Zvc er b K i Z e BwÄb KZ K m úvw`z KvR W = Q 2 myzvivs, BwÄ bi ` ZvÑ η = Q 2 = 1 Q 2 Q 2 = 0 m Î BwÄ bi ` Zv n e η = = 1 ev, 100% wkš y ev Í e hme BwÄb Avwe Z n q Q Zv `i Kv bvwuib ` Zv 100% bq ev ú BwÄ bi ` Zv gvî 20% _ K 25% Kv bv i cöz vezx BwÄbt Kv bv GKwU Av`k cöz vezx BwÄ bi cwikíbv K ib, hw`i Gi ev e i~c `qv m e nqwb, hv Kv bv i BwÄb bv g cwiwpz Kv bv i BwÄ bi AveZ bi cöwzwu ch v q Kvh Ki c`v _ i cwiez b cöz vezx cöwµqvq AbywôZ nq ZvB G K cöz vezx BwÄbI ejv nq Kv bv i BwÄ b Av`k Zvc Acwievnx c`v _ i Zwi wmwjûvi-wc b e e vq Kvh Ki c`v_ Ave _v K wkš y wmwjû ii Zjv Av`k Zvc cwievnx c`v_ w` q Zwi Ges Amxg Zvc avikz m úbœ `ywu wfbœ ZvcgvÎvi Zvcvavi I GKwU Av`k Zvc Acwievnx cvuvzb Øviv MwVZ K bv BwÄb PviwU av c GKwU Pµ m úbœ K i G K Kv bv i Pµ e j Kv bv i Pµ `ywu cöz vezx m gvò I `ywu cöz vezx iƒ Zvcxq cöwµqv mgš^ q MwVZ wmwjûvi Drm Zvc wb ivak MÖvnK e f AvqZb g h cö_g avc: cö_ g wmwjûviwu K ZvcgvÎvi Zvc Dr mi Dci ivlv nq mvg ve vq M v mi Pvc, AvqZb I ZvcgvÎv h_vµ g P 1, V 1 I wb ` kk wp Î A we `y M v mi cöv_wgk Ae v wb ` k Ki Q Gevi M vm K ZvcgvÎvq m gvò cöwµqvq ax i ax i cömvwiz K i B(P 2, V 2 ) Ae vq wb q hviqv nq G cöwµqvq M vm Drm n Z Zvc kw³ kvwlz nq Ges Gi meuzkz Kv R iƒcvšíwiz K i myzvivs K ZKvR W 1 = = R log ( V 2 V 1 ) = ABge Îi Îdj wøzxq avc: G av c wmwjûiwu K Acwievnx cvuvz bi Dci i L cömvwiz K i, P 3, V 3, Ae vq wb q hviqv nq G cömviy iƒ Zvcxq cöwµqvq msnwuz nq, KviY wm g Zvc MÖnY ev er b Ki Z cv i bv G chv q M vm Zvi Af š ixy kw³i wewbg q KvR K i d j ZvcgvÎv n«vm c q nq G Î K ZKvR W 2 = C v = BChg Îi Îdj Z Zxq avc: G av c wmwjûviwu K ZvcgvÎvi Zvc MÖvn Ki Dci i L m gvò cöwµqvq ax i ax i mskzwpz K i P 4, V 4 Ae vq wb q hviqv nq G chv q M v mi Ici evb i _ K KvR Kiv nq G Z M vm Zvc MÖvn K Q 2 cwigvy Zvc er b K i G Î K ZKvR W 3 = Q 2 = R log V 3 V 4 = CDfh Îi Îdj PZz_ avc: G av c wmwjûviwu K Acwievnx cvuvz bi Dci i L iƒ Zvcxq cöwµqvq mskzwpz K i P 1, V 1 I Ae vq wb q hviqv nq G chv q M v mi Ici evb i _ K KvR Kiv nq d j Gi Af š ixy kw³ e w cvq Ges ZvcgvÎv e o nq G Î K ZKvR W 4 = C v = ADfe Îi Îdj MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 6
myzvivs, GKwU c~y P µ Kv bv BwÄ bi Kvh wbev nx c`v_ KZ K m úvw`z KvR m~pk wp Î `ywu m gvò ilv I `ywu iƒ Zvcxq ilv Øviv Ave Îi Îd ji mgvb gvu KvR ABCD Ave Îi Îd ji mgvb myzvivs, Kv bv BwÄ bi ` ZvÑ η = W = Q 2 = 1 Q 2 Avevi,Kv Y v BwÄ bi Î Q 2 = ZvB Kv bv BwÄ bi ` Zv η = 1 cöz vezx cöwµqvt h cöwµqv wecixzgylx n q cöz vez b K i Ges m ylezx I wecixzgylx cöwµqvi cöwz i Zvc I Kv Ri djvdj mgvb I wecixz nq mb cöwµqv K cöz vmvgx ev cöz vezx cöwµqv e j GB cöwµqvi Aw wz vckzv, mv `ªZv, Nl Y, e`ÿ wzk iva, Pz ^Kxq wnm&uwiwmm cöf wzi b vq Ae qx djvdj jv _vk e bv gvu K_v GwU g~jz wzk Ges Abe qx AcÖZ ezx cöwµqvt h cöwµqv m ylmvgx niqvi ci wecixzgylx n q cöz vez b Ki Z cv i bv, Zv K AcÖZ vezx cöwµqv e j G K Abc bi cöwµqvi ejv nq h cöwµqvq m ve me cövk wzk Dcvq m Ë I mgmö ms v K cy ivcywi cövzwgk Ae vq wdwi q Avbv hvq bv ev h cöwµqv wecixzgylx n q cöz vez b Ki Z cv i bv Zv K AcÖZ vezx cöwµqv e j GKRb gvby li g Zz K AcÖZ vezx cöwµqv wn m e we epbv Kiv hvq GbUªwc I wek Ljvt iƒ Zvc cöwµqvq e yi h Zvcxq ag w i _v K, Zv K GbUªwc e j Ab fv e ejv nq GbUªwc n jv e yi Ggb GKwU f Z ag hv iƒ Zvc cöwµqvq w i _v K Kv bv GKwU ms v ev P µi ZvcgvÎv mv c M nxz ev ewr Z Zv ci cwiez b nvi Øviv GUwci cwigvc Kiv nq Kv bv GKwU e e v ev wm g T cig ZvcgvÎv dqcwigvy Zvc MÖnY ev er b K i AZGe G Uªwc ds = dq T myß Zv ci Rb GbUªwci cwiez b ds = dq T Av cw K Zv ci Rb GbUªwci cwiez b ds = dq T T = 2 msdt T = ms dt T = ms ln ( ) = ml f T iy Zvcxq cöz vezx cöwµqvq GbUªwc cwiez b k~b niqvi KviY cöz ezx cöwµqvq `ywu iƒ Zvc I `ywu m gvò cöwµqv _v K iƒ Zvc cöwµqv `ywui mgq Kv bv Zvc kvwlz ev ewr Z nq bv e j GbUªwciI Kv bv ciwez b nq bv GbUªwci Zvrch t GbUªwc GKwU cövk wzk iyz Acwimxg Gi wbæwjwlz Zvrch i q Q GwU e yi GKwU Zvcxq ag hv Zvc mâvj bi w`k wb ` k K i GwU e yi ZvcMZxq Ae v wba vi Y mnvqzv K i GwU ZvcgvÎv, Pvc,AvqZb, AšÍwb wnz kw³, Pz ^Kxq Ae vi b vq Kv bv e yi Ae v cökvk K i cök wzi mkj f Z A_ev ivmvqwbk wµqv Ggbfv e msnwuz nq h, hvi d j mvwe K e e vi GbUªwc e w cvq cöz vmvgx cöwµqvi GbUªwc w i _v Kt Kv bv Pµ _ K `Lv hvq h, AB I CD `ywu m gvò m cömviy I ms KvPb ilv Ab w` K BC I DA `ywu iƒ Zvcxq m cömviy I ms KvPb ilv e j Zv ci Kv bv cwiez b nq bv AB m gvò ilv eivei GbUªwci cwiez b = CD m gvò ilv eivei GbUªwci cwiez b= Q 2 Kvh wbev nk e yi gvu GbUªwci cwiez b = Q 2 wkš y Kv bv P µ = Q 2, P gvu GUªwci cwiez b ZvB cöz ezx P µ G Uªwc D B w i _v K ds = Q 2 = 0 AcÖZ vezx cöwµqvq GbUªwc n«vmt g b Kwi, Zvc Dr mi ZvcgvÎv K Ges Zvc Mvgjvi K GKwU AcÖZ vez K BwÄb ZvcgvÎvq cwigvy Zvc kvly K i Ges ZvcgvÎvq Q 2 cwigvy Zvc er b K i ZLb H BwÄ bi Kg gzv η = Q 2 MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 7 A V C
wkš y Ges ZvcgvÎvi g a Kvh Z cöz vez K BwÄ bi K i D P ZvcgvÎvq Zvc er b Ki Z evbi n Z e e vi Kg ` Zv,η = Dci W cwigvy KvR Ki Z n e Zvcxq m~î n Z W = Q Kv bv i Dccv` _ K Avgiv Rvwb, η > η 2 A_ v r > Q 2 iwd«rv iu ii Kvh K Z mnm n jv iwd«rv iui n Z ewr Z Zvc I K cömi KZ K Kv Ri AbycvZ ev, 1 > 1 Q 2 ev, < Q 2 ev, Q 2 > ev, Q 2 > 0 ev,s 2 S 1 > 0 ds > 0 A_v r AcÖZ vez K cöwµqvq GUªwc e w cvq m gvò cwiez bt h cwiez b Kv bv M v mi Pvc I AvqZ bi cwiez b nq wkš ZvcgvÎvi Kv bv cwiez i nq bv Zv K m gvò cwiez b e j m gvò cwiez b M vm K mycwievnx cv Î ivl Z n e cwicvk D P Zvc aviy gzv n Z n e ax i ax i cöwµqv n e GB cöwµqvq PV =aªyek n e ZvcgvÎv w i _v K iy Zvcxq cwiez bt h cöwµqvq M v mi Pvc I AvqZ bi cwiez bi mgq Zv ci cwigvy cwiez b nq bv, wkš ZvcgvÎvi cwiez b nq Ges GbUªwc w i _v K Zv K iy Zvcxq cöwµqv e j iy Zvcxq cwiez b M vm K Kycwievnx cv Î ivl Z n e cwicvk Kg Zvc aviy gzv n Z n e `ªƒZ cöwµqv n e GB cöwµqvqpv γ =aªyek n e GbUªwc w i _v K iwdªrv iuit iwd«rv iu i wb œ ZvcgvÎvi Zvc Drm n Z Zvc MÖnY K i Zv D P ZvcgvÎvq Zvc er b Kiv nq Gi Rb hvwš K KvR Ki Z nq iwd«rv iu i K cömi GB hvwš K KvR K i iwd«rvu i wb œ ZvcgvÎvi Zvc Drm n Z Q 2 Zvc MÖnY Kvh K Z mnm K = Q 2 PZz_ NvZ BwÄbt 1886 mv j A Uv me cö_g mdjzvi mv _ GB BwÄb Pvjy Ki b GB BwÄ b gvu PviwU NvZ Av Q cö_g NvZt cö_g Nv Z R vjvwb Kviey jui n Z `nb cö Kvó n q wmwjûv i cö ek K i GB NvZ K MÖnY NvZ e j wøzxq NvZt GB Nv Z `vn wgkªy AvqZb GK câgvs k ms KvwPZ nq wgkª Yi ZvcgvÎv cövq 600 0 C nq GB NvZ K ms KvPb NvZ e j Z Zxq NvZt GB Nv Z `vn wgkªy Gi ZvcgvÎv cövq 2000 0 C nq Ges Pvc 15 evqygûjx GB NvZ K Kvh Ki NvZ e j PZz_ NvZt GB Nv Z wbm gb kl K i c~ e i Ae vq wd i Av m GB NvZ K wbtmiy NvZ e j Zvcxq mgzvt GKvaxK e Zvcxqfv e mshy³ _ K hw` Zv `i g a Zv ci Avavb cö`vb bv nq Zvn j Zv `i K Zvcxq mgzv e j D ³ e e vt e e v I cwi e ki mv _ fi I kw³ Df qi wewbgq n j Zv K Db y³ e e v e j e e e vt h e e v I cwi e ki mv _ ïay kw³ wewbgq nq wkš fi wewbgq nq bv Zv K e e e v e j wew Qbœ e e vt h e e v I cwi e ki mv _ fi I kw³ KvbwUB wewbgq nq bv Zv K wew Qbœ e e v e j Af šíixy kw³t Kv bv e e vq h kw³ myß Ae vq _v K hv cwi ek cwiw wz Z cökvk K i Zv K AfšÍixY ev AšÍt kw³ e j m gvò cwiez bt h cwiez b Kv bv M v mi Pvc I AvqZ bi cwiez b nq wkš ZvcgvÎvi Kv bv cwiez i nq bv Zv K m gvò cwiez b e j m gvò cöwµqvq Av`k e e vi Rb du = 0 MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 8
iy Zvcxq cwiez bt h ZvcMZxq cöwµqvq e e vi Zv ci Kv bv Av`vb-cÖ`vb nq bv Zv K iƒ Zvcxq cöwµqv e j iƒ Zvcxq cöwµqvq dq = 0 cöz vez x cöwµqvt h cöwµqv wecixzgylx n q cöz vez b K i Ges m ylezx I wecixzgylx cöwµqvi cöwz Í i Zvc I Kv Ri djvdj mgvb I wecixz nq mb cöwµqv K cöz vmvgx ev cöz vezx cöwµqv e j AcÖZ vez x cöwµqvt h cöwµqv m ylmvgx niqvi ci wecixzgylx n q cöz vez b Ki Z cv i bv, Zv K AcÖZ vezx cöwµqv e j Kv b v Pµ t h P µ Kv bv GKwU Av`k M vm Kvh Kix c`v_ Ave K i GKwU m gvò cömviy I GKwU iy Zvcxq cömviy Ges GKwU m gvò ms KvPb I GKwU iy Zvcxq ms KvP bi ci c~e ve vq wd i Av m Zv K Kv b vi Pµ e j Zvc BwÄbt h BwÄb cwi ek _ K Zvc MÖnY K i KvR K i Zv K Zvc BwÄb e j ewn` n BwÄb t BwÄ b R vjwbi `nb wµqv BwÄ bi g~j As ki evb i N U Zv K ewn` n BwÄb e j hgb ev úxq BwÄb AšÍ` n BwÄbt h BwÄ b R vjwbi `nb wµqv BwÄ bi g~j As ki wfz i N U Zv K AšÍ` n BwÄb e j hgb c Uªvj I ww Rj BwÄb Kg ` Zvt Kv bv BwÄ bi Kv R cwiyz kw³ Ges gvu kw³i AbycvZ K Kg ` Zv e j Kg ` Zv K η Øviv m~wpz Kiv nq GbUªwct iƒ Zvc cöwµqvq e yi h Zvcxq ag w i _v K, Zv K GbUªwc e j Kvh K Z mnmt iwd«rv iu ii Kvh K Z mnm n jv iwd«rv iui n Z ewr Z Zvc I K cömi KZ K Kv Ri AbycvZ wngvqbt K wîg Dcv q Kv bv Ave vb K cwi ek n Z wbæ Ae vq ivlvi c wz K wngvqb e j wngvqk wb œ ùzubvs ¼i h Zij cwicvk n Z myß Zvc MÖnY K i cwicvk K kxzj K i Zv K wngvqk e j iwd«rv iuit h hš wb œ ZvcgvÎvi Zvc Drm n Z Zvc MÖnY K i Zv D P ZvcgvÎvq Zvc er b K i Zv K iwd«rv iui e j ZvcMwZwe` vi k~b Zg m~ît `ywu e hw` Z Zxq Kv bv e i mv _ Zvcxq mvg ve vq _v K Zvn j cö_ gv³ e `ywu ci úi Zvcxq mvg ve vq _vk e ZvcMwZwe` vi cö_g m~ît Kv bv e e vq mieivnk Z Zvc kw³ e e vi AšÍt kw³i cwiez b I evwn K Kv Ri hvmd ji mgvb n e ZvcMwZwe` vi wøzxq m~ît (cøv ¼i wee wz): GKwU BwÄ bi cwikíbv KL bvb m e bq, hvi c~y AveZ b KejgvÎ GKwU Zvcxq Drm n Z Zvc msm nxz n e Ges Ab Î Kv bv cwiez b e ZxZ msm nxz Zv ci meuzkz Kv R iƒcvšíwiz Kiv hv e Zvc I ZvcgvÎv 1 c`v _ i AvYweK MwZi mv _ m úwk Z GK cökvi kw³ hv VvÛv ev Mi gi Abyf~wZ R vq Zv K ejv nq-zvc 2 K vjwi e j ev Í e wkqz bb GUv cögvy K ibñ weávbx KvD U ivg dvw 3 GK MÖvg weï cvwbi ZvcgvÎv GK wwwmö mjwmqvm e w Ki Z cö qvrbxq Zv ci cwigvy n Q Ñ GK K vjwi 4 KvD U ivg dvw wq jb Ñ Av gwikvb weávbx 5 4.2 Ryj hvwš K kw³ e q K i K vjwi Zvc Drcbœ Kiv hvq, GUv cögvb K ibñ weávbx Ryj 6 Zv ci Gm. AvB. GKKÑ Ryj 7 GK Ki Gm. AvB. GKK Pvjyi c~ e Zv ci me P q cöpwjz GKK wqjñ K vjwi 8 Kv bv GKwU e wk cwigvy Mig ev VvÛv Zvi cwigvc K AvcvZfv e ejv nq H e i Ñ ZvcgvÎv 9 AvšÍR vwzk c wz Z ZvcgvÎvi GKK Ñ Kjwfb 10 Ô`ywU e Z Zxq Kv bv e i mv _ Zvcxq mgzvq _vk j cö_ gv³ e `ywui ci ú ii mv _ Zvcxq mgzvq _vk eõ GUv Ñ ZvcMwZwe` vi k~b Zg m~î ZvcgvÎv cwigv ci g~jbxwz 1 h hš Øviv e i ZvcgvÎv wbf ~jfv e cwigvc Kiv hvq Zv K _v g vwguvi e j 2 ZvcgvÎv cwigvb D cv hvmx c`v _ i h mkj ag Kv R jvmv bv nq, c`v _ i H ag jv K ejv nqñ D ZvwgwZK ag 3 cvwbi Îa we `yi ZvcgvÎvÑ 273.16K MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 9
4 `yb w i we `y c wz Z ZvcgvÎv wby vqk mgxkiy X o X ice X steam X ice n + θ ice 5 GK w i we `y c wz Z ZvcgvÎv cwigv ci g~jbxwzñ T = X tr 273.16K. X 6 ^vfvwek Pv c h ZvcgvÎvq weky cvwb dzu Z ïiæ K i Zv K ejv nq Ñ DaŸ w i we `y 7 dv ibnvbu j cvwbi Îa we `yi ZvcgvÎvÑ 32. 8 ^vfvwek Pv c h ZvcgvÎvq weky eid Mj Z ïiæ K i Zv K ejv nq Ñ wb œ w i we `y 9 wb œ w i we `y I DaŸ w i we `yi ga ezx e eavb K ejv nq Ñ g wjk e eavb 10 dv ibnvbu I Kjwfb j GKB cvv `q Ñ 574.25 K ZvcMwZwe` vi K qkwu AZ vek Kxq welq 1 c`v_ weáv bi h kvlv Zvc I hvwš K kw³i g a m úk wb q Av jvpbv K i Zv K ejv nq Ñ ZvcMwZwe` v 2 ZvcMZxq vbv ¼i mvnv h h me wm gi Ae vi ey bv `Iqv hvq Zv `i K e j Ñ ZvcMZxq wm g 3 GKwU wm g K vjwik nvwi q VvÛv nq Ges Aci wm g Zv MÖnb K i Mig nq GUv Ñ K vjwik gzev` 4 Kv bv wbw` ó e e vi mv _ kw³ wewbg q mÿg h Kv bv e e v K ejv nq H e e vi Ñ cwicvk 5 Kv bv wm ó gi g a h kw³ AšÍwbwnZ ev myß Ae vq _v K hv cwi ek cwiw wz Z ewntcökvk NUvq Zv K ejv nq Ñ Af šíixy kw³ 6 me cö_g KvR I Zv ci g a m úk vcb K ib Ñ weávbx Ryj 7 Kv bv wm g mvgwmökfv e h MwZkw³ I wefe kw³ _v K Zv K ejv nq H wm gi Ñ ewnt kw³ 8 MwZkw³ I wefe kw³ g a m úk n Q ÑAf šíixy kw³ 9 ïaygvî M v mi ZvcgvÎvi Dci wbf i K i, Pvc I AvqZ bi Dci wbf i K ibv 10 4.2 Ryj = 1 K vjwi ZvcMwZwe` vi cö_g m~î 1 weávbx Ryj Zvc I Kv Ri g a m úk vcb K ib Ñ 1847 mv j 2 hw` Zvc K m ú~b iæ c Kv R I KvR K m ú~b iæ c Zv c iæcvšíi Kiv hvq, Z e KvR Zv ci mgvbycvwzkñ ZvcMwZwe` vi cö_g m~î 3 kw³i wbz Zv m~ Îi GKwU we kl iæc n Q Ñ ZvcMwZwe` vi cö_g m~î 4 ZvcMwZwe` vi cö_g m~ Îi MvwbwZK iæc dq = du + dw 5 Zvc kw³ Ab Kv bv kw³ Z iæcvšíwiz n j wksev Ab Kv bv kw³ Zvckw³ Z iæcvšíwiz n j wm gi gvu kw³i cwigvy GKB _v KÑ weávbx K vwmqv qi g Z 6 KvR I Zvc G K Ac iiñmgzzj 7 Ggb hš D veb m e bq hv R vjvwb ev kw³ e wz i KÑ KvR Ki Z mÿg 8 Ry ji m~îvbymv i ZvcMwZwe` vi 1g m~ Îi mgxkiy W = JQ 9 KvR K Ryj Ges Zvc K K vjwi GK K cwigvc Ki j Ryj Zzj v¼ñj = 4.2 Ryj/K vjwi 10 Kv bv wm gi ZvcMZxq Ívbv¼mg~ ni h Kv bv cwiez b KB ejv nqñ ZvcMZxq cöwµqv ZvcMwZwe` vi cö_g m~ Îi K qkwu cö qvm 1 cixÿv-wbixÿvi mgq Avgiv Ro RM Zi h wbw`ó Zvcxq Ask wee Pbv Kwi Zv K ejv nqñzvcxq wm g 2 Kv bv M vm K cv Î Ave K i Zvc cö qvm Ki j Gi ZvcgvÎv I Pvc e w cvq wkš y AvqZb cwiewz Z n Z cv i bv G K ejv nqñmg-avqzb cöwµqv 3 m gvá cöwµqvq M v mi Pvc I AvqZ bi m úk g b P jñe q ji m~î 4 h cöwµqvq wm g Zvc MÖnY K i bv wksev Zvc er b K i bv Zv K ejv nq Ñiƒ Zvcxq cöwµqv 5 wøcvigvywek M v mi ÿ Î γgi gvbñ1.4 6 eûcvigvywek M v mi ÿ Î γgi gvbñ1.33 7 gvu Zv ci cwigvy w i i L Kv bv M v mi Pvc I AvqZ bi cwiez b K ejv nqñiƒ Zvcxq cwiez b 8 iƒ Zvcxq cöwµqvq Av` k M v mi AvqZb I ZvcgvÎvi m úk wbyv qk mgxkiyñtv γ 1 =aªæek 9 h cöwµqvq Kv bv wm gi ZvcgvÎv w i _v K wkš y Pvc I AvqZb cwiez Z nq ZvK ejv nqñm gvò cöwµqv 10 GK gvj Kv bv c`v _ i ZvcgvÎv 1K e w Ki Z cö qvrbxq Zvc K ejv nq H c`v _ iñ gvjvi Zvcavib ÿgzv ZvcMwZwe` vi wøzxq m~î 1 ÔÔevB ii Kv bv kw³i mvnv h e wz i K Kv bv ^qswµq h š i c ÿ wb œ ZvcgvÎvi Kv bv e y n Z D P ZvcgvÎvi Kv bv e Z Zv ci vbvšíi m e bqõõ GwUÑÑK wmqv mi wee wz 2 AveZ cöwµqvq e yi Af šíixy kw³i cwiez bñk~b MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 10
3 Kv bv wbw`ó cwigvb Zvc gw³ m ú~y ev cy ivcywifv e hvwš K kw³ Z iƒcvšíi Kivi g Zv Zwi m e bqñ Kv bv i wee wz 4 Kv bv e y K Zvi cwicv k i kxzjzg Ask n Z AwaKZi kxzj K i kw³i Aweivg mieivn cviqv m e bq Ñ Kjwf bi wee wz 5 Kv bv Zvc Drm n Z AbeiZ Zvc kvly Ki e Ges Zv m úy iƒ c Kv R iƒcvšíwiz n e Giƒc GKwU Zvc BwÄb Zwi Kiv m e bqñcø vk Gi wee wz 6 GKK Zvc Drcbœ Ki Z h cwigvy KvR Ki Z nq ev GKK Zvc Øviv h cwigvy KvR Kiv hvq Zv K ejv nqñhvwš K Zzj v¼ 7 wngvq Ki ` wó KvY _ K ZvcMwZwe` vi wøzxq m~î K cökvk K ibñk wmhvm 8 ÔÔBwÄb Qvov Zv ci iƒcvšíi m e bqõõ GwU me cö_g cögvy K ib ÑweÁvbx mv`x Kv bv 9 BwÄ bi ` wó KvY _ K ZvcMwZwe` vi 2q m~ Î K cökvk K ibñcøv¼ 10 `ywu e yi Zvc cö qvm I w`k wbav wiz nqñe yi ZvcgvÎv Øviv Zvc BwÄ bi `ÿzv 1 h BwÄb cwi ek _ K Zvckw³ MÖnY K i KvR m úbœ K i Zv K ejv nqñ Zvc BwÄb 2 mv`x Kv bv wq jb GKRbÑdivmx cö K kjx 3 Zvc BwÄb wb q e vck M elyv K i GKwU Av`k BwÄ bi cwikíbv K ibñmv`x Kv bv 4 Zvc K Kv R iƒcvší ii Rb cö qvrbñh š i 5 Zvc K hvwš K kw³ Z iƒcvšíwiz K iñzvc BwÄb 6 mvw` Kv bv GKwU Av`k BwÄb cwikíbv K ib hvñcwiwpz Kv ba I cöz vezx BwÄb bv g 7 Zvcxq BwÄb ev Kv bv BwÄ bi `ÿzvi mgxkiy n jvñη = 8 Kv bv Zvc BwÄb Øviv Kv Ri iƒcvšíwiz Zvckw³i cwigvy BwÄb Øviv kvwlz Zvckw³i cwigv Yi AbycvZ K ejv nqñkg `ÿzv 9 ev ú BwÄ bi `ÿzvñ20% 25% 10 c Uªvj BwÄ bi `ÿzv m ev PÑ50% cöz vez x I AcÖZ vez x cöwµqv 1 h cöwµqv wecixzgylx n q cöz vez b K i Ges m ylez x I wecixzgylx cöwµqvi cöwz Í i Zvc I Kv Ri djvdi mgvb I wecixz nq mb cöwµqv K ejv nq Ñ cöz vez x cöwkªqv 2 Kv bv wm g GK Ae v n Z Ab Ae vq cwiewz Z nq - `yb cöwkqvq 3 h cöwµqv m ylmvgx niqvi ci wecixzgylx n q cöz vez b Ki Z cv ibv, Zv K ejv nqñ AcÖZ vez x cöwkªqv 4 mkj AcÖZ vmvgx cöwkªqv Ñ GKgyLx 5 Av`k M v mi iæ Zvcxq cwiez b GKwU Ñ cöz vez x cöwkªqv 6 mkj ^Z:ùzZ cwiez b Ñ AcÖZ vez x cöwkªqv 7 `ywu e yi g a msn l i d j Zvc m wó nqñ AcÖZ vez x cöwkªqv 8 wm gi ZvcMZxq mvg ve v ervq _v KÑ cöz vez x cöwkªqv 9 e `yk n Z wj Qzo j eviæ `i weõiy Ñ AcÖZ vez x cöwkªqv 10 Av`k M v mi m gvò cwiez b GKwU - cöz vez x cöwkªqv Kv b vi cöz vez x BwÄb 1 divwm weávbx mvw` Kv bv 100% Kg `ÿzv m úbœ Av`k BwÄb Kíbv K ibñ1832 mv j 2 h hš Zvc kw³ K hvwš K kw³ Z iæcvšíwiz Kiv nq Zv K ejv nqñ Zvc BwÄb 3 Zvc kw³ K hvwš K kw³ Z iæcvšíwiz Kivi Rb mv`x Kv bv mkj `vl ÎæwU gy³ h Av`k h š i cwikíbv K ib Zv K ejv nqñ Kv bv BwÄb 4 Kv bv i BwÄ bi Ab bvg Ñ cöz vez x BwÄb 5 Kv bv i BwÄ bi e eüz wmwjûv ii `Iqvj Zix nq Ñ Zvc Acwievnx Øviv 6 Kv bv P µ Kvh wbev nk e Drm n Z Zvc MÖnb K i Ñ m gv cöwµqvq 7 Kv bv BwÄ bi ÿ Î, Kv h iæcvšíwiz Zvc I Drm n Z M wnz Zv ci AbycvZ K ejv nq Ñ `ÿzv 8 Kv bv i P µ PviwU chv qi ga w` q AwZµg Kiv bv nq Ñ Kvh wbev nk e 9 Zvc kw³ K KvR Kiv bvi Rb cö qvrb Ñ hvwš K e e vi 10 Kv bv P µi g~jbxwz e vl v Kiv hvq Ñ Pvi av c G Uªwc 1 iæ Zvc cöwµqvq e i h Zvcxq ag w i _v K Zv K ejv nq Ñ Gb&Uªwc 2 Gb&Uªwc bv gi cöez K Ñ weávbx K wmqvm 3 Gb&Uªwc m e v P niqv K we k i Zvcxq g Z y e j AwfnZ K i Qb Kjwfb 4 Gb&Uªwc I wek sljv m úwk Z evjrg v bi m~î Ñ s = KlnW 5 Gb&Uªwci gvîv Ñ ML 2 K 1 6 Gb&Uªwci cwiez b wby q mwvk m~î Ñ ds = dq T 7 ZvcMwZwe` vi wøzxq m~î h ZvcMZxq Pj Ki mv _ m úk hy³ Zvi bvg - Gb&Uªwc 8 iæ Zvcxq cwiez b wm gi iæ Zv Gb&Uªwc _v K Ñ aªæe 9 Gb&Uªwci Gm.AvB.GKK Ñ Ryj / Kjwfb 10 Kv bv GKwU P µi ZvcgvÎv mv c ÿ M wnz ev ewr Z Zv ci cwiez bi nvi Øviv cwigvc Kiv nqñ Gb&Uªwc MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 11
cö qvrbxq m~îvejx m~î Zvc,Q = ms θ = 1 2 mv2 = mg ZvcgvÎv T = x x tr 273.16 K mjwmqvm j ZvcgvÎv θ c = dv ibnvbu j ZvcgvÎv θ F = 32 F wewfbœ j C = F 32 5 9 θ = R R ice = K 273 5 100 R steam R ice θ = P P ice 100 P steam P ice θ = V V ice V steam V 100 θ = l l ice l l ice 100 E = 3 2 nrt x x ice X steam x ice 100 C x x ice X steam x ice 180 + MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. WWW.rashidedu.wordpress.com V f dw = PdV = PdV V i dq = du + PdV W = JH C p C v = R P 1 V γ γ 1 = P 2 V 2 V 1 γ 1 = V 2 γ 1 1 γ γ P 1 1 γ γ = P 2 η = = Q 2 E-mail:rashidmcsk@yahoo.com, Mobile:01721336740 = Q 2 ds = ml T = dq T K = Q 2 P in = Q in Ges η = P out Ges η = 1 Q out t P in Q in mgpvc cöwµqvq W = PdV m gvò cöwµqvq W = RT ln ( V 2 V 1 ) iy Zvcxq cöwµqvq W = R 1 γ ( ) MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 12
MvwYwZK mgm vi mgvavbt mgm v-1 t GKwU Zvc BwÄb 3400J Zvc MÖnY K i I 2400J Zvc er b K i BwÄ bi ` Zv wby q Ki Avgiv Rvwb η = 1 Q 2 = 1 2400 3400 = 29.41% mgm v-6t Kvb e e v aªye AvqZ b 300J Zvc er b K i e e vi AšÍt kw³i cwiez b wby q Ki Avgiv Rvwb, AvqZb w i _vk j, ewnt KvR, dw = PdV = O ( dv = O) Avevi, dq = du + dw ev, dq = du du = dq = 300J mgm v-2t GKwU Kv b v BwÄb 327 0 c Ges 27 0 ZvcgvÎvq KvR Ki Q Gi ` Zv KZ? Avgiv Rvwb η = 1 = 1 300 600 = 50% mgm v-3t GKwU Kv b v BwÄb 127 0 C ZvcgvÎvq Zvc MÖvn K KvR Ki Q Gi ` Zv 80% n j Dr mi ZvcgvÎv KZ? Avgiv Rvwb η = 1 ev, = 2000K mgm v-4 t GKwU wmwjû ii g a ivlv wkqy cwigvy MÖ vm cwi e ki Dci 200J KvR m úv` bi mgq cwi ek _ K 500J Zvckw³ kvly K i MÖ v mi AšÍt kw³i cwiez b KZ n e? wm gi AšÍt kw³ n«vm cv e, bv e w cv e? Avgiv Rvwb, ΔQ = ΔU + ΔW ev, ΔU = ΔQ ΔW ev, ΔU = 500 200 J = 300J ΔU ev AšÍt kw³i cwiez b abvz K; ZvB wm gi AšÍt kw³ e w cv e mgm v-5t Kvb e e v 1500J Zvc kvly K i Ges 82J KvR m úv`b K i e e vi AšÍt kw³i cwiez b wby q Ki Avgiv Rvwb, Zvc MwZwe` vi cö_g m~î _ K cvb, dq = du + dw ev, du = dq dw du = 1500 82 = 1418J mgm v-7t wc bhy³ GKwU wmwjû i wkqy M vm Ave Av Q M v mi Pvc 400Pa-G w i i L wm g ax i ax i 800J Zvckw³ mieivn Kivq 1200J KvR m úvw`z nq M v mi AvqZb Ges AšÍt kw³i cwiez b wby q Ki Avgiv Rvwb, K Z KvR, ΔW = P V V = W = 1200 = P 400 3m3 Avevi, Q = U + W U = Q W = 800J 1200J = 400J mgm v-8t AwK& ª R bi aªye AvqZ b gvjvi Av cw K Zvc C v I aªye Pv c gvjvi Av cw K Zvc C p wby q Ki R = 8.31J mole 1 K 1 ; Avgiv Rvwb, AwK& ª Rb GKwU wø- cigvyyk M vm γ = C p C v = 1.4 C p = 1.4C v Av`k M v mi Î, C p C v = R ev, C p C v = 8.31 ev, 1.4C v C v = 8.31 C v = 8.31 0.40 = 20.8J mole 1 K 1 Avevi, C p = 20.8 + 8.31 = 29.11J mole 1 K 1 mgm v-9t GK cvigvywek Av`k M v mi Rb C p I C v Gi gvb wby q Ki R = 8.31 J mole 1 K 1 ; Avgiv Rvwb, GK cigvyyk M v mi Î, γ = C p C v = 1.66 C p = 1.66C v Av`k M v mi Î, C p C v = R ev, 1.66C v C p = R ev, C v = 8.31 0.66 = 12.60 J mole 1 K 1 Avevi, C p = R + C v = 8.31 + 12.60 = 20.92 J mole 1 K 1 MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 13
θ = 5.6k mgm v-10t ^vfvwek ZvcgvÎv I Pv c wkqy ï evqy K m gvò cöwµqvq wø Y AvqZ b cömvwiz Kiv nj P~ovš Pvc wby q Ki Avgiv Rvwb, P 1 V 1 = P 2 V 2 [ P 1 = 1.01 10 5 Nm 2 V 2 = 2V 1 ] ev 1.01 10 5 V 1 = P 2 2V 1 ev, 1.01 10 5 V 1 = 2P 2 P 2 = 1.01 105 2 = 505 10 2 Nm 2 mgm v-11t evqy K iy Zv c cömvwiz K i Gi AvqZb wø Y Kiv nj hw` cöv_wgk Pvc 1evqygÛjxq Pvc nq, Zvn j P~ovš Pvc KZ n e? Avgiv Rvwb, P 1 V 1 γ = P 2 V 2 γ ev, P 1 P 2 = ( V 2 V 1 ) γ 1 4 ev 1 = 2V 1 P 2 V 1 ev, 1 = 2 1 4 P 2 ev,p 2 = 1 2 1 4 ev, P 2 = 0.3789 evqygûjxq Pvc mgm v-12t 27 ZvcgvÎvq Kvb wbw` ó cwigvy M vm nvvr cömvwiz n q wø Y AvqZb jvf K i P~ovšÍ ZvcgvÎv KZ? γ = 1 4 M vm K nvvr cömvwiz Kiv n q Q wm g Zvc MÖnY ev er bi my hvm cvqwb Avgiv Rvwbv, V 1 γ 1 = V 2 γ 1 ev, = V 1 = V 2V V 2 γ 1 T1 γ 1 300K = 1 = 227.36K = (227.36 273) = 45.65 2 0.4 300K mgm v: 13 GKwU wgvbv ii D PZv 90m wgbv ii P~ov n Z GK LÛ mxmv d j `Iqv n jv cz bi d j mg Í kw³ Zvc kw³ Z cwibz n jv 80% Zvc mxmv Øviv kvwlz n j mxmv L Ûi ZvcgvÎv KZ e w cv e? S = 126Jkg 1 k 1 mgvavb: awi, mxmvi fi = mkg D PZv h = 90m Avgiv Rvwb, mgh = ms θ ev, gh = s θ ev, θ = gh S ev, θ = 9.8 90 126 mgm v: 14 GKwU mxmvi ey ju Kv_vI evavcövß n q ZvcgvÎv 150K e w cj hw` Ab Kv bvfv e Zvc bó bv nq, Zvn j ey juwui em KZ wqj? S = 126Jkg 1 k 1 mgvavbt awi, ey juwui fi = mkg 1 Avgiv Rvwb, 2 mv2 = ms θ ev, v 2 = 2s θ ev, v = 2 126 150 v = 194.42ms 1 mgm v 15t GKwU w i Pvc M vm _v g vwguv ii M v mi AvqZb cvwbi Îa we `y Z 4 10 4 m 3 Ges mvjdv ii ùzubv ¼ 1.02 10 3 m 3 n j mvjdv ii ùyubv¼ wby q Ki GLv b, Îa we `y Z AvqZb, V tr = 4 10 4 m 3 wb Y q ZvcgvÎvq AvqZb V = 1.02 10 3 m 3 Avgiv Rvwb, T = V V tr 273.16K T = 1.02 10 3 m 3 4 10 4 m 3 273.16K = 696.6K mgm v 16t GKwU iva _v gv Uv ii iva 0 ZvcgvÎvq 8Ω Ges 100 ZvcgvÎvq 20Ω _v gv wguviwu K GKwU Pzwjø Z vcb Ki j iva 32Ω nq Pzwjøi ZvcgvÎv wby q Ki GLv b,mjwmqvm j n = 100 Ges θ ice = 0 myzvivs eid we `y Z iva, R ice = 8Ω w g we `y Z iva, R steam = 20Ω wb Y q ZvcgvÎvq iva, R = 32Ω Avgiv Rvwb,ZvcgvÎv θ = R R ice R steam R ice n + θ ice ev,θ = 32Ω 8Ω 20Ω 8Ω 100 + 0 = 200 mgm v-17t 10 0 C ZvcgvÎvi 5kg cvwb K 100 0 C ZvcgvÎvq DËxY Ki Z GbUªwci cwiez b wby q Ki Avgiv Rvwb, ds = dq T = ms dt T = 5 4200 (log 373 log 283) = 5.799 10 3 JK 1 MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 14
mgm v-18t 100 0 C ZvcgvÎvi 4kg cvwb K 100 0 C ZvcgvÎvq ev ú Ki Z GbUªwci cwiez b wby q Ki Avgiv Rvwb, ds = dq = ml = 4 2260000 = 2.42 10 3 JK 1 T T 373 mgm v-19t Kv bv Kv b v Pµ cöv_wgk 327 0 C ZvcgvÎvq KvR m úbœ K i cöwzwu av c ms KvPb ev cömvi Yi AbycvZ 1t6 n j P µi me wbæ ZvcgvÎv KZ n e? [γ = 1.4] Avgiv Rvwb, V 1 γ 1 = V 2 γ 1 ev, = 393K mgm v-20t Kvb ZvcgvÎvq mw U MÖW I dv ibnvbu j GKB cvv `q?? DËit awi x ZvcgvÎvq mw U MÖW I dv ibnvbu j GKB cvv w` e AZGe, C = F = x ZvB, C 5 = F 32 9 ev, x 5 = x 32 9 x = 40 mgm v-21 GKwU iva _v gvwg Uv ii iva 0 C ZvcgvÎvq 8Ω Ges 100 C ZvcgvÎvq 20Ω _v gv wguviwu K GKwU Pzwjø Z vcb Ki j iva 32Ω nq Pzwjøi ZvcgvÎv wby q Ki Avgiv Rvwb, ZvcgvÎv θ = R R ice n + θ R steam R ice ice GLv b, mjwmqvm j n = 100 Ges θ ice = 0 C myzvivs eid we `y Z iva, R ice = 8Ω θ = 32Ω 8Ω 100 + 0 C = 200 C 20Ω 8Ω mgm v-22 GKwU w i Pvc M vm _v g vwguv ii M v mi AvqZb cvwbi Îa we `y Z 4 10 4 m 3 Ges mvjdv ii ùzubv ¼ 1.02 10 3 m 3 n j mvjdv ii ùubv¼ wby q Ki Avgiv Rvwb, T = V V tr 273.16K T = 1.02 10 3 m 3 4 10 4 m 3 273.16K = 696.6K mgm v23 GKwU wmwjû ii g a ivlv wkqy cwigvy MÖ vm cwi e ki Dci 200J KvR m úv` bi mgq cwi ek _ K 500J Zvckw³ kvly K i MÖ v mi AšÍt kw³i cwiez b KZ n e? wm gi AšÍt kw³ n«vm cv e, bv e w cv e? Avgiv Rvwb, ΔQ = ΔU + ΔW ev, ΔU = ΔQ ΔW = 500 200 J = 300J ΔU ev AšÍt kw³i cwiez b abvz K; ZvB wm gi AšÍt kw³ e w cv e mgm v-24t evqy K iy Zv c cömvwiz K i Gi AvqZb wø Y Kiv nj hw` cöv_wgk Pvc 1evqygÛjxq Pvc nq, Zvn j P~ovš Pvc KZ n e? Avgiv Rvwb, P 1 V 1 γ = P 2 V 2 γ ev, P 1 = ( V 2 ) γ P 2 V 1 ev 1 = 2V 1 4 1 P 2 V = 2 1 4 1 ev, P 2 = 1 ev, P 2 1 4 2 = 0.3789 evqygûjxq Pvc mgm v-25t 27 C ZvcgvÎvq Kvb wbw` ó cwigvy M vm nvvr cömvwiz n q wø Y AvqZb jvf K i P~ovšÍ ZvcgvÎv KZ? γ = 1 4 M vm K nvvr cömvwiz Kiv n q Q wm g Zvc MÖnY ev er bi my hvm cvqwb Avgiv Rvwbv, V 1 γ 1 = V 2 γ 1 ev, = V 1 = 1 2 V 2 γ 1 T1 = V 2V 0.4 300K = 227.36K γ 1 300K = (227.36 273) C = 45.65 C mgm v-25t 27 C ZvcgvÎvq 0.02Kg nvb Wªv Rb M vm K m gvò cöwµqvq msbwgz K i cöv_wgk AvqZ bi GK PZz_ Ask Kiv n ja K Z Kv I cwigvb KZ n e Avgiv Rvwb, W = n RT ln V 2 = m RT ln V 2 V 1 M 0.02 8.314 300 0.002 ln 1 4 V 1 = = 34576.95J MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 15
mgm v-26t Ggb GKwU ZvcgvÎv ei Ki hvi gvb mw Uª MÖW Ges dv ibnvbu j GKB nq mgvavbt Avgiv Rvwb, C 5 = F=32 x ev, = x 32 ev, 9x = 5x 160 5 9 ev, 9x 5x = 160 ev, 4x = 160 ev, x = 160 4 x = 40 40 Ges 40 (Ans) mgm v-27t 25 ZvcgvÎvq I evqygðjxq Pv c Ave ï evqy K nuvr ev iæ Zv c msbwgz K i AvqZb A a K Kiv n jv P~ovšÍ (K) ZvcgvÎv (L) Pvc wby q Ki mgvavbt Avgiv Rvwb V 1 γ 1 = V 2 γ 1.... (1) P 1 V 1 γ = P 2 V 2 γ........ (2) (K) i bs mgxkiy n Z cvb, = V 1 V 2 = 2 1.4 1 298K = 393.18K (393.18 273 = 120.18 (Ans) (L) ii bs mgxkiy n Z cvb, 9 γ 1 T1 γ P1 P 2 = V 1 V 2 = 2 1.4 1 evqygðjxq Pvc = 2.64 evqygðjxq Pvc (Ans) mgm v-29t GKwU ÎæwUc~Y _v gv wguv ii wb œ w ivs¼ 4 Ges DaŸ w ivs¼ 98 H _v gv wguv ii 51 cvv w` j dv ibnvbu Ges Kjwfb j cvv KZ n e? mgvavbt Avgiv Rvwb, η = = 433K 300K 433K = 133K 433K = 31% Ans mgm v-30t 27 ZvcgvÎvq Kv bv wbw` ó cwigvy M vm nuvr cömvwiz n q wø Y AvqZb jvf K i P~ovšÍ ZvcgvÎv KZ? (γ = 1.4) Avgiv Rvwb, V γ 1 γ 1 1 = V 2 γ 1 T1 ev, = V 1 V 2 = (3) 1.41 1 273K = 3 0.41 273K = 428.33K = 155.33 Ans mgm v-31t ^vfvwek Pv c 100 m 3 AvqZ bi GKwU M v m 5 10 3 J Zvc w` j M v mi AvqZb 100.2 m 3 nq H M v mi K ZKv Ri gvb wby q Ki mgvavbt Avgiv Rvwb, W = P V = 1.013 10 5 (100.2 100) = 20260 J (Ans) mgm v-28t 100 ZvcgvÎvi 2kg cvwb K 100 ZvcgvÎvi ev ú cwiyz Ki j, GbUªwci cwiez b KZ nq wby q Ki [cvwbi evw úfe bi Av cwÿk myßzvc = 2.26 10 6 J kg 1 ] g bkwi, Gb&Uªwci cwiez b ds `Iqv Av Q, cvwbi evw úfe bi Av cwÿk myßzvc, L = 2.26 10 6 J kg 1 fi, m = 2kg ZvcgvÎv, T = 100 = 100 + 273 373K ei Ki Z n e Gb&Uªwci cwiez b ds =? Avgiv Rvwb, dq = ml = 2kg 2.26 10 6 J kg 1 = 4.52 10 6 J Avgiv Rvwb, ds = dq T = 4.52 106 J = 1.21 10 4 JK 1 (Ans) 373K mgm v-32t 27 ZvccgvÎvq Kv bv wøcvigvywek M v mi Pvc nuvr wø Y Kiv n j, Pvc cwiez bi ci ZvcgvÎvi cwiez b KZ n e? mgvavbt 1 γ Avgiv Rvwb, P 1 γ ev, = P 1 1 γ T P 2 γ 1 = P 2 1 γ γ MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 16 = 1 2 1 1.4 1.4 300K = 365.70K ZvcgvÎvi cwiez b, T = = 365.70 300 K = 65.70K = 65.70 T = 65.70 (Ans)
mgm v-33t GK cvigvywek M v mi R b c p I c v Gi gvb wby q Ki [R8.13J mole 1 K 1 ] mgvavbt `Iqv Av Q, R = 8.31 J mol 1 K 1 GK cvigvywek M v mi R b, γ = C P.. (i) C V Avevi, C P C V = R ev, C P = C V R.. (ii) (i) I (ii) bs n Z cvb C P = γ C P R [ C P = C V γ] ev, C P = γc P γr ev, ev, C P 1 γ = γr C P = γr γ 1 = 1.67 8.31 n 1.67 1 C P = 20.71 J mol 1 K 1 (Ans) (ii) C P Gi gvb emvb C V = 20.71 8.31 J mol 1 K 1 mgm v-34t GKwU Zvc BwÄb Drm _ K 600 K ZvcgvÎvq 2.56 10 6 J Zvc kw³ MÖnb K i Zvc MÖvn K 5.12 10 5 J Zvc kw³ er b K i Zvc MÖvn Ki ZvcgvÎv I BwÄbwUi `ÿzv wby q Ki mgvavbt Avgiv Rvwb, = Q 2 = Q 2 = 5.12 105 J 600 K 2.56 10 6 J = 120 Avevi, η = = 600 K 120K 600K = 80% (Ans) mgm v-35t GKwU Kv bv BwÄ bi Dr mi D Zv 400 K, G D Zvi Drm _ K GwU 840J Zvc er b Ki Q wm ¼i DòZv KZ? BwÄbwUi `ÿzv KZ? mgvavbt Avgiv Rvwb, η = Q 2 840J 630J = = 210J 840J 840J η = 0.25 = 25% (Ans) Avevi, Avgiv Rvwb, η = ev, 25 = 1 ev, = 1 25 100 400 400 100 ev, = 300 K (Ans) mgm v-36t 100 ZvcgvÎvq 5 kg cvwb K ev ú cwiyz Ki j G Uªwci cwiez b wby q Ki (cvwbi Av cwÿk myßzvc wby q Ki 2.26 10 6 J. kg 1 ) mgvavbt Avgiv Rvwb, ds = dq T = ml = 5 2.26 106 = 30294.90 JK 1 (Ans) T 373 C V = 12.40 mol 1. K 1 (Ans) mgm v-37t GKwU wmwjûv ii Af ší i evqhi Pvc 3 atm. ZvcgvÎv 300K I AvqZb 10 Litre (i) Pvc nuvr wømyy Kiv n j Gi AvqZb I ZvcgvÎv KZ n e? (ii) Pvc wa i wa i wømyy Kiv n j Gi AvqZb I ZvcgvÎv KZ n e? mgvavbt Avgiv Rvwb, iæ Zvcxq cwiez bi ÿ Î P 1 V γ 1 = P 2 V γ 2 V 2 = P 1 P 2 = 3atm 6atm 1 1.4 V 1 1 1.4 10 Litre h nzz M v mi cwiez b nq bv Kv RB, P 1 V 1 = P 2V 2 = P 2V 2 P 1 V 1 6atm 6.1Litre 3atm 10Litre 300K = 366K (Ans) e q ji m~î Abyhvqx, P 1 V 1 = P 2 V 2 V 2 = P 1V 1 P 2 = 3atm 10Litre 6atm = 5Litre (Ans) Avevi, m gvò cwiez bi ÿ Î DòZvi cwiez bi ÿ Î ZvcgvÎvi cwiez b nqbv d j = = 300K Ans mgm v-38t 3 10 5 Pa Pv c I 280KZvcgvÎvq wbw` ó f ii nvb Wªv R bi AvqZb 10 3 m 3 iy Zvcxq cöwµqvq Gi Pvc nuvr wø Y Kiv n j Gi AšÍt kw³i Kx cwiez b n e? nvb Wªv R bi C V = 20.4J. mol 1 K 1 Ges R = 8.314J mol 1 K 1 mgvavbt Avgiv Rvwb, PV = nrt n = PV = 3 105 Pa 10 3 m 3 = 0.20 mol RT 8.314Jmo l 1 K 1 280K iy Zvcxq cwiez bi ÿ Î, AvqZb I Pv ci m úk _ K cvb, GLv b, ZvcgvÎv = 280K Pvc, P 2 = 2P 1 1 γ 1 γ P 1 1 = P 2 1 MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 17
1 γ 1 = P 1 280K P 2 = 0. 5 0.4 1.4 280K = 229.69K iy Zvcxq cwiez b M vm KZ K K ZKvR, W = nc V ( ) = 0.129 20.4 280 229.69 = 132J AšÍt kw³i cwiez b, U = Q W = 0 132J = 132J GLv b ayvz K wpý wb ` k K i AšÍt kw³ n«vm c q Q myzivs AšÍt kw³i n«vm 132J (Ans) mgm v-39t 27 ZvcgvÎv I 10 5 Pa Pv c wbw` ó f ii Aw R bi AvqZb 10 2 m 3 m gvò cöwµqvq G Z 500J Zvc mieivn Kiv n jv Gi kl AvqZb I Pvc wby q Ki Aw R bi AvYweK fi, = 32gm Ges R = 8.314J mol 1 K 1 Avgiv Rvwb, PV = nrt ev, n = PV RT = 105 10 2 8.314 300 = 0.40mol m gvò cöwµqvq K ZKvR, W = nrt en V 2 V 1 ev, en V 2 V 1 = W nrt = 500 0.40 8.314 300 = 0.501162 V 2 V 1 = 1.65063 V 2 = V 1 1.650 = 10 2 1.650 = 16.50 10 3 m 3 Ans Avevi, P 1 V 1 = P 2 V 2 P 2 = P 1V 1 V 2 = 105 10 2 16.50 10 3 = 60 103 Pa (Ans) mgm v-40t GKwU Kv b v BwÄb 327 I 27 DòZvq KvR Ki Q Gi Kg `ÿzv KZ? Avgiv Rvwb, η = 1 = 1 300K 600K = 50% Ans mgm v-41t GKwU BwÄ bi Kg `ÿzv 40% wb œ Zvcvav ii ZvcgvÎv 7 Gi D P Zvcvav ii ZvcgvÎv wby q Ki mgvavbt Avgiv Rvwb, η = ev, 4 ev, 4 = 10 2800K = 280K 10 ev, 6 = 2800Kev, = 2800K 6 = 466.7K = 193.67 Ans mgm v-42t GKwU Zvc BwÄb Zvc Drm _ K 4.5 10 6 J Zvc MÖnb K i Ges cwi e k 3 10 6 J Zvc er b K i BwÄb KZ K K ZKvR I Gi `ÿzv wby q Ki mgvavbt Avgiv Rvwb, W = Q 2 = (4.5 10 6 3 10 6 )J = 1.5 10 6 J Ans Avevi, η = W = 1.5 106 J 4.5 10 6 J η = 0.3333 η = 33.33% Ans mgm v-43t GKwU Kv b v BwÄb 227 ZvcgvÎvi Zvc Drm _ K Zvc MÖnb K i I 27 ZvcgvÎvi Zvc Mªvn K Zvc er b K i BwÄbwUi Kg `ÿzv wby q Ki mgvavbt Avgiv Rvwb, η = 1 = 1 300K 500K = 0.4 η = 40% Ans mgm v-44t GKwU cöz vmvwg BwÄ bi `ÿzv 35% Zvc Mªvn Ki ZvcgvÎv 50 Zvc Dr mi ZvcgvÎv wby q Ki mgvavbt Avgiv Rvwb, η = ev, 35 100 = 1 323K ev, 323K = 1 35 100 ev, 323K = 65 100 ev, = 100 65 323K ev, = 496.92K = (496.92 273) = 223.92 Ans mgm v-45t 40%`ÿZv wewkó GKwU Av`k BwÄ bi Zvc MÖvn Ki ZvcgvÎv 7 BwÄ bi `ÿzv 50%-G DbœwZ Ki Z Zvc Dr mi ZvcgvÎv KZ e w Ki Z n e? mgvavbt Avgiv Rvwb, η = ev, 40 100 = 1 280K ev, 280K = 1 40 100 ev, = 100 60 280K = 466.66K MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 18
Avevi, Avgiv Rvwb, η = ev, 50 100 = 1 280K ev, 280K = 1 40K 100K ev, = 100 50 280K = 560K ZvcgvÎv e w, T = 560K 466.66K = 93.34K = 93.34 Ans mgm v-46t 167 I 57 ZvcgvÎvi g a Kvh iz GKwU cöz vmvgx BwÄ bi me vwak `ÿzv wby q Ki mgvavbt Avgiv Rvwb, η = 1 ev, η = 1 330K 440K ev, η = 0.25 η = 0.25% Ans mgm v-47t GKwU cöz vmvgx BwÄb cöwz P µ Zvc avivi _ K 200J Zvc MÖnb K i Ges Zvc MÖvn K 110J Zvc er b K i Zvc Mªvn Ki ZvcgvÎv 320K n j Avav ii ZvcgvÎv I BwÄ bi `ÿzv Ges 50 P µ BwÄb KZ K K ZKvR wby q Ki mgvavbt Avgiv Rvwb, ev, 200 J = 100 J 320K = = Q 2 200 J 110 J 320K = 581.81K η = 1 Q 2 = 1 110J 200J GLb GKwU P µi K ZKvR, W = Q 2 = 200J 110J 90J 50 wu P µi K ZKvR = 50 W = 50 90J = 4500J Ans = 0.45 = 45% mgm v-48t 100 ZvcgvÎvi 400gm cvwb K ev ú cwiyz Kiv n j GbUªwci cwiez b KZ n e? cvwbi ev úxfe bi Av cwÿk myßzvc 2260000j. kg 1 mgvavbt Avgiv Rvwb, ds = dq T Avevi, dq = ml = 0.4kg 2.26 10 6 jkg 1 ds = 0.4kg 2.26 106 jk g 1 373K = 2423.59JK 1 Ans mgm v-49t 0 ZvcgvÎvi 200gm eid K 60 ZvcgvÎvi cvwb Z cwiyz Kiv n j GbUªwci cwiez b KZ n e? eid Mj bi Av cwÿ myßzvc 336000JK 1 Ges cvwbi Av cwÿk Zvc J. kg 1 K 1 mgvavbt Avgiv Rvwb, 0 ZvcgvÎvi 200gm eid K 0 ZvcgvÎvi 200gm cvwb Z cwibz Ki Z GbUªwci cwiez b ds 1 = d T = ml T = 0.2kg 3.36 105 kg 1 273K = 246.15 JK 1 0 ZvcgvÎvi 60 cvwb Z cwibz Ki Z GbUªwci cwiez b, ds 2 = dq 2 T = 2 ms dt T T [ dq = msdt] = ms[in T] = ms[in In ] = 0.2kg 4200Jkg 1 K 1 [In333 In273] = 166.88 JK 1 GbUªwci cwiez b ds = ds 1 + ds 2 = 246.15 JK 1 + 166.88 JK 1 = 413.03 JK 1 Ans mgm v-50t GKwU Av`k M v mi aªæe AvqZ b I aªæe Pv c gvjvi ZvcaviY ÿgzv h_vµ g 20.5 Jmole 1 K 1 I 28.8 Jmole 1 K 1 ; w i Pv c 8gm nvb Wªv Rb 10 _ K 15 ZvcgvÎvq DbœxZ Ki Z cö qvrbxq Zv ci cwigvy, AšÍt kw³i cwiez b I ewnt Kv Ri cwigvy wby q Ki mgvavbt Avgiv Rvwb, Q = m C p T M = 8 10 3 kg 28.8 5 2 10 3 = 576J Ans Avevi, Q = du + PdV ev, U = Q = m C v T M = 8 10 3 20.5 5 2 10 3 = 410J cybivq, Q = U + W ev, W = Q U = 576 410 = 166J (Ans) MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 19
mgm v-51t 25 ZvcgvÎvq evqygðjxq Pv c Ave M vm K nuvr mskzwpz K i Gi AvqZb A a K Kiv n jv P~ovšÍ Pvc ei Ki (γ = 1.4) mgvavbt Avgiv Rvwb, P 1 V γ γ 1 = P 2 V 2 ev, P 2 = P 1 V 1 V 2 1.4 = P 1 2V V = 1 (2) 1.4 = 2.64 evqygðjxq Pvc γ mgm v-52t 27 ZvcgvÎvq 2.02kg nvb Wªv Rb M vm K m gvò cöwµqvq msbwgz K i cöv_wgk AvqZ bi GK PZz_ vsk Kiv nj K ZKv Ri gvb ei Ki mgvavbt Avgiv Rvwb, W = V 2 PdV V 1 V = 2 nrt V 1 V V 2 V 1 dv PV = nrt = m M R V dv n = m M = m M RT InV V 2 V 1 = m M RT [InV 2 InV 1 ] = m M RT In V 1 V 2 = 0.02kg 8.314 Jmol e 1 K 1 300K In 1 4 10 3 kg = 34576.95 J GLv b FYvZ K wpý evb ii G R U Øviv K Z KvR eysvq mgm v-53t 10kg f ii GKwU e i em 100ms 1 n Z 40 ms 1 Ki Z KZ KvR Ki Z n e? K Z Kv Ri mgzzj Zvc KZ n e? mgvavbt Avgiv Rvwb, K ZKvR = MwZkw³i cwiez b ev, W = 1 2 mv 1 2 1 2 mv 2 2 = 1 2 m (v 1 2 v 2 2 ) = 1 2 10kg {(100mv 1 ) 2 (40ms 1 ) 2 } = 4.2 10 4 J (Ans) Avevi, Avgiv Rvwb, W = JH H = W J = 10 4 cal Ans = 4.2 104 J 4.2 mgm v 54t Kv bv Kv bv GKwU wm g 6000J Zvc `Iqvi 400J wm gwu KvR m úbœ K i G cöwµqvi wm gi Af šíixy kw³ cwiez b wby q Ki mgvavbt Avgiv Rvwb, U = Q W = 6000J 400J = 5600J = 5.6kJ Ans mgm v-55t GKwU cöz vmvgx BwÄb Drm n Z M nxz Zv ci 1 Ask Kv R 6 cwiyz K i Gi Zvc MÖvn Ki ZvcgvÎv AviI 62 n«vm Ki j Gi `ÿzv wø Y nq Zvc Drm I Zvc MÖvn Ki ZvcgvÎv ei Ki mgvavbt Avgiv Rvwb, η 1 = 1 ev, 1 6 = 1 ev, = 1 1 6 = 6 5 Avevi, MÖvn Ki ZvcgvÎv 62 n«vm Ki j Gi `ÿzv wø Y nq η 2 = 2 1 = 1 6 3 η 2 = 1 62 ev, 1 = 1 62 3 ev, 1 = 1 + 62 3 ev, 1 = 1 5 + 62 3 6 ev, 1 = 1 + 62 3 6 ev, 62 = 1 1 = 1 3 6 6 ev, = 372K (Ans) = 5 6 = 5 372 6 = 310K (Ans) mgm v-56t GKwU BwÄb 400K I 350K ZvcgvÎvq Ges Aci GKwU BwÄb 350K I 300K ZvcgvÎvq KvR Ki Q Kvb BwÄ bi `ÿzv ewk? mgvavbt cö_g BwÄ bi ÿ Î, = 400K, = 350K wøzxq BwÄ bi ÿ Î, = 350K = 300K cö_g BwÄ bi `ÿzv, η 2 = 1 = 1 300 350 = 1 0.857 = 0.125 = 12.5% MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 20
wøzxq BwÄ bi `ÿzv, η 2 = 1 T 1 = 1 350 400 = 1 0.857 = 0.14257 = 14.257% wøzxq BwÄ bi `ÿzv cö_g BwÄb _ K 14.257 12.5 % ev 1.8% ewk mgm v-57t 0 ZvcgvÎvq 3kg eid K 0 ZvcgvÎvq cvwb Z cwiyz Ki j GbUªwci cwiez b KZ n e? [L f = 3.3 10 5 Jkg 1 ] mgvavbt Avgiv Rvwb, ds = dq = ml f T T = 3 3.36 105 273 = 3692.3 JK 1 Ans mgm v-58t 100 ZvcgvÎvq 1kg cvwb K 100 ZvcgvÎvi ev ú cwiyz Ki j GbUªwci cwiez b KZ n e wby q Ki cvwbi ev úxfe bi Av cwÿk myßzvc 10 6 Jkg 1 mgvavbt Avgiv Rvwb, ds = dq T = 1kg 2.26 106 Jk g 1 373K = 6058.98Jk 1 (Ans) = ml v T mgm v-59t Kv bv ms v cwi ek _ K 800J Zvckw³ kvly Kivq Gi AšÍt kw³ 500J e w c jv ms v KZ K cwi e ki Dci m úvw`z Kv Ri cwigvy wby q Ki mgvavbt Avgiv Rvwb, Q = U + W W = Q U ev, W = 800 500 = 300 J (Ans) mgm v-60t ^vfvwek Pv c 100m 3 AvqZ bi GKwU M vm 5 10 3 J Zvc w` j M v mi AvqZb 100.2m 3 nq H M v mi K ZKv Ri gvb ei Ki mgvavbt Avgiv Rvwb, W = P V = 1.013 10 5 100.2 100 = 20260J(Ans) mgm v-61t GKwU BwÄb 3400J MÖnb K i I 2400J Zvc er b K i BwÄb Øviv m úvw`z KvR I BwÄ bi `ÿzv wby q Ki mgvavbt Avgiv Rvwb, m úvw`z KvR, W = Q 2 = 3400J 2400J = 1000J Avevi,`ÿZv, η = 1 Q 2 = 1 2400J 3400J = 0.2941 =29.41% (Ans) mgm v-62 t GKRb eávwbk `vwe Ki jb h, Zvi D vwez BwÄb 700K Ges 400K ZvcgvÎvi g a Kvh iz Ges Gi hvwš K `ÿzv 48% Zvi `vwe wk mwvk? mgvavbt Avgiv Rvwb, η = 1 = 1 400K 700K = 0.42857 = 42.85% h š i `ÿzv 42.80% ZvB Zvi `vwe mwvk wq jv bv Ans mgm v-64t gvwn bi kix i ^vfvwek ZvcgvÎv 98.4 AvR Ly e Amȳ eva Kivq gv Zvi Mv q nvz w` q `L jb Zvi kixi ek Mig kix i cök Z ZvcgvÎv cwigv ci Rb wzwb wk wbk vj _v gv wguvi e envi K i `L jb _v gv wguv ii cvv 105. (i) gvwn bi AvR Ki ZvcgvÎv Kjwfb j KZ n e? (ii) gvwn bi kix i ZvcgvÎvi e eavb mjwmqvm ji gva g cökvk Kiv hv e wk-bv? MvwYwZK hyw³ `vi mgvavbt Avgiv Rvwb, F 2 32 = K 273.15 180 100 ev, 105 32 9 ev, 73 9 = K 273.15 5 5 = K 273.15 ev, K = 73 5 = K + 273.15 9 = 313.7K (ii) cö_gz C 1 = F 1 32 5 9 ev, C 1 ev, C 1 = 36.88 Avevi, = 98.4 32 5 9 C 2 = F 2 32 5 9 ev, C 2 = 105 32 5 9 C 2 = 40.55 myzivs, C 40.55 36.88 = 3.67 (Ans) MD.ABDUR RASHID M.Sc (R.U) LECTURER (PHYSICS), POLICE LINES SCHOOL AND COLLEGE, RANGPUR. c ôv - 21