Varsity Weekly-7 (Set-A) Solution.pdf

Nội dung text Varsity Weekly-7 (Set-A) Solution.pdf

1 Varsity (Second Timer) Weekly-07 [A (Solution)] wm‡jevm: Av`k© M ̈vm I M ̈v‡mi MwZZË¡ + cwi‡ek imvqb + †hvMRxKiY-1 + RxecÖhyw3 + evsjv-7 + Bs‡iwR-7 c~Y©gvb: 100 †b‡MwUf gvK©: 0.25 mgq: 1 NÈv c`v_©weÁvb (Physics) 1. 27C ZvcgvÎvq †Kv‡bv cv‡Î 2 mol Ar M ̈vm Ges Aci GKwU cv‡Î 56g N2 M ̈vm we` ̈gvb| D3 ZvcgvÎvq Ar Gi ˆiwLK MwZkw3 Ges N2 M ̈v‡mi N~Y©b MwZkw3i AbycvZ KZ? 3 : 5 3 : 2 1 : 1 2 : 3 DËi: 3 : 2 e ̈vL ̈v: Ek = f 2 nRT  Ek  f [T  same] Ar Gi f = 3 (ˆiwLK)   EAr = 3 2  2  R  T = 3RT N2 Gi f = 3 + 2 (ˆiwLK) 3 + 2 (N~Y©b) EN2 = 2  1 2  56 28 RT = 2  1 2  2 RT = 2RT  EAr EN2 = 3RT 2RT = 3 2 2. wb‡¤œi †Kvb ˆewkó ̈wU Av`k© M ̈v‡mi †ÿ‡Î cÖ‡hvR ̈? Av`k© M ̈v‡mi KYvmg~‡ni wbw`©ó AvqZb we` ̈gvb Av`k© M ̈v‡mi NbZ¡ cwieZ©bkxj bq M ̈vm AYymg~‡ni `ywU μwgK msN‡l©i ga ̈eZ©x mg‡qi Zzjbvq msNl©Kvj AwZ bMY ̈ Av`k© M ̈vmmg~n D‧PPv‡c wbR ̄^ AvPiY eRvq iv‡L DËi: M ̈vm AYymg~‡ni `ywU μwgK msN‡l©i ga ̈eZ©x mg‡qi Zzjbvq msNl©Kvj AwZ bMY ̈| e ̈vL ̈v: (K) Av`k© M ̈v‡mi KYvmg~n bMY ̈ AvqZbwewkó e‡j we‡ePbv Kiv nq| (L) Av`k© M ̈v‡mi mgxKiY PV = nRT n‡Z cÕgvY Kiv hvq, PM = dRT [d = NbZ¡|] A_©vr, d = PM RT  d  P T  NbZ¡  Pvc Ges †Kjwfb ZvcgvÎvi Dci wbf©ikxj ZvB Bnv cwieZ©bkxj| d = NbZ¡ P = Pvc T = ZvcgvÎv (†Kjwfb) R = †gvjvi M ̈vm aaæeK M = †gvjvi fi D‧PPv‡c Av`k© M ̈vm Av`k© AvPiY n‡Z wePz ̈wZ †`Lvq| 3. 1 wjUvi AvqZ‡bi GK cvigvYweK M ̈v‡mi MwZkw3 900 J n‡j, Pvc KZ? 2  105 Nm–2 105 Nm–2 2  106 Nm–2 6  105 Nm–2 DËi: 6  105 Nm–2 e ̈vL ̈v: E = 3 2 nRT = 3 2  PV  P = 2 3  E V V = 1 L = 10–3 m 3 = 2 3  900 10–3 = 600  103  P = 6  105 Nm–2 4. g~j Mo eM©‡eM c Ges Pvc P- Gi g‡a ̈ m¤úK© n‡jvÑ c = 3P  c = 3 P c = P 3 c =  3P DËi: c = 3P  e ̈vL ̈v: c = 3RT M GLb, RT M = PV M = P   c = 3P  5. Am¤ú„3 ev®ú Pv‡ci Rb ̈ wb‡Pi †KvbwU mwVK? ïaygvÎ Ave× ̄’v‡b ˆZwi Kiv hvq e‡qj I Pvj©‡mi m~Î gv‡b bv GB Pvc m¤ú...3 ev®úPv‡ci †P‡q †ewk nq †Kv‡bvwUB bq DËi: †Kv‡bvwUB bq e ̈vL ̈v: i) Am¤ú...3 ev®ú Pvc Ave× I †Lvjv Dfq ̄’v‡b ˆZwi Kiv hvq| ii) e‡qj I Pvj©‡mi m~Î gv‡b| iii) GB Pvc m¤ú...3 ev®úPv‡ci †P‡q Kg nq| 6. PV 2 = RT M ̈vm mgxKi‡Y V wb‡`©k K‡iÑ 1 2 †gvj M ̈v‡mi AvqZb 1 †gvj M ̈v‡mi AvqZb 2 †gvj M ̈v‡mi AvqZb cv‡Îi AvqZb DËi: 2 †gvj M ̈v‡mi AvqZb e ̈vL ̈v: PV 2 = RT  PV = 2RT  PV = nRT Abyhvqx n = 2
2 7. GKwU Av`k© M ̈vm GKwU fvimvg ̈ Ae ̄’v (P1, V1, T1, N) †_‡K Ab ̈ fvimvg ̈ Ae ̄’vq (2P1, 2V1, T2, N) cwiewZ©Z nq| Zvn‡j wb‡Pi †KvbwU mwVK? T1 = T2 T1 = T2 4 T1 = 6T2 T1 = 3T2 DËi: T1 = T2 4 e ̈vL ̈v: P1V1 T1 = P2V2 T2  T2 T1 = P2V2 P1V1 = 2P1  2V1 P1V1 = 4  T1 = T2 4 8. AvqZvKvi iæ‡gi gv‡S 3 mole Aw•‡Rb M ̈vm 27 C ZvcgvÎvq Ae ̄’vb Ki‡Q| iæ‡gi gvÎv 5  3  2 [m GK‡K]| AvqZvKvi iægwU‡Z Aw•‡Rb M ̈v‡mi Pvc KZ? 250 Pa 350 Pa 450 Pa 150 Pa DËi: 250 Pa e ̈vL ̈v: P = nRT V = 3  8.314  300 5  3  2 = 249.42 Pa  250 Pa 9. 25C ZvcgvÎvq †Kv‡bv n«‡`i Zj‡`‡k M ̈v‡mi ey`ey` m„wó n‡q Zv μgk c„‡ô P‡j Av‡m| n«‡`i MfxiZv 10 m, evZv‡mi Pvc 1  105 Nm–2 Ges cvwbi NbZ¡ 1200 kgm–3 | hw` n«‡`i Zj‡`k †_‡K c„‡ô †cuŠQvi ci ey`ey`wU bó n‡q hvq, Z‡e Zj‡`‡ki AvqZ‡bi Zzjbvq AvqZb KZ ̧Y n‡qwQj? 2 ̧Y 3 ̧Y 4 ̧Y 5 ̧Y DËi: 2 ̧Y e ̈vL ̈v: n«‡`i concept Gi Rb ̈, Shortcut: h = (n –1) Patm g  hg Patm = n – 1  n = 1 + hg Patm = 1 + 10  1200  9.8 1  105 = 1 + 12000  9.8 1  105 = 1 + 1.176 = 2.176  2 ̧Y (cÖvq) 10. 2 †gvj O2 M ̈v‡mi †ÿ‡Î R Gi gvb n‡eÑ 33.24 JK–1 mol–1 16.628 JK–1 mol–1 8.31 JK–1 mol–1 1.06  103 JK–1 mol–1 DËi: 8.31 JK–1 mol–1 e ̈vL ̈v: mve©Rbxb M ̈vm aaæeK, R Aw•‡Rbmn mKj M ̈v‡mi Rb ̈ GKB _v‡K| †gvjmsL ̈v 1 ev GKvwaK Gi Rb ̈ R Gi gv‡bi †Kv‡bv cwieZ©b bv NU‡jI kw3 ev Ab ̈vb ̈ ivwk wbY©‡q †gvj msL ̈v e ̈eüZ n‡e| 11. w ̄’i ZvcgvÎvq M ̈v‡mi †ÿ‡Î wb‡Pi †Kvb †jLwPÎwU mwVK bq? X Y  P V  O X Y  P 1 V  O X Y  V 1 P  O X Y  P PV O DËi: X Y  P 1 V  O e ̈vL ̈v: e‡q‡ji m~Îvbymv‡i, Avgiv Rvwb, V  1 P [hLb ZvcgvÎv I fi w ̄’i _v‡K] A_©vr, AvqZb Pv‡ci e ̈ ̄ÍvbycvwZK| d‡j AvqZb evo‡j Pvc Kg‡e| Avevi, PV = k  V = k  1 P [V †K y Ges 1 p †K x a‡i]  y = kx; hv g~jwe›`yMvgx mij‡iLvi mgxKiY| 12. GKwU wmwjÛv‡i 2 atm Pv‡c 27C ZvcgvÎvq 5 L evZvm ivLv Av‡Q| Lye ax‡i ax‡i evZv‡mi Pvc wØ ̧Y Kiv n‡j evZv‡mi ZvcgvÎv Ges AvqZb n‡eÑ 3 L, 95C 3.5 L, 25C 1.5 L, 28C 2.5 L, 27C DËi: 2.5 L, 27C e ̈vL ̈v: †h‡nZz ax‡i ax‡i Pvc wØ ̧Y Kiv nq ZvB GwU m‡gvò cÕwμqv| myZivs T2 = T1 = 27C e‡q‡ji m~Î Abymv‡i, V  1 P  P2V2 = P1V1 V2 = P1V1 P2  V2 = P1  5 2P1  V2 = 5 2 L  V2 = 2.5 L 13. Mo gy3c‡_i †ÿ‡Î †KvbwU mwVK? Mo gy3c_ ZvcgvÎvi e ̈ ̄ÍvbycvwZK Mo gy3c_ Pv‡ci e ̈ ̄ÍvbycvwZK Mo gy3c_ Nb‡Z¡i mgvbycvwZK Mo gy3c_ AYyi msL ̈vi mgvbycvwZK DËi: Mo gy3c_ Pv‡ci e ̈ ̄ÍvbycvwZK

4 23. M ̈v‡mi GKwU AYyi ̄^vaxbZvi gvÎv 6 n‡j kw3i mgwefvRb bxwZ Abymv‡i cÖwZ AYyi Mo kw3 KZ? 6kT 3kT 2kT 3 2 kT DËi: 3kT e ̈vL ̈v: †Kv‡bv KYvi ̄^vaxbZvi gvÎv cÕwZ kw3i cwigvY 1 2 kT ̄^vaxbZvi gvÎv f n‡j cÕwZ AYyi Mokw3 = f 2 kT  f = 6 n‡j Mo kw3 n‡e, E = 6 2 kT  E = 3kT 24. GKwU Mvwoi PvKv 300 K ZvcgvÎvq Ges 3  105 Pa Pv‡c 0.02 m3 AvqZ‡bi evZvm aviY K‡i iv‡L| PvKvi Af ̈šÍi ̄’ evZv‡mi fi KZ? 2.41 g 28.8 g 67.36 g 239.3 g DËi: 67.36 g e ̈vL ̈v: PV = m M RT  m = PVM RT evqy‡Z bvB‡Uav‡R‡bi AvwaK ̈ _vKvi `iæY bvB‡Uav‡Rb‡K evZv‡mi AvYweK fi we‡ePbv Kiv n‡q‡Q = 3 × 105 × 0.02 × 28 8.314 × 300  m = 67.36 g 25. w ̄’i Pv‡c †Kv‡bv M ̈v‡mi ZvcgvÎv I AvqZb h_vμ‡g 30C I 10 L| ZvcgvÎv †mjwmqvm † ̄‹‡j wØ ̧Y Kiv n‡j Gi AvqZb KZ ̧Y n‡e? 1.5 2 0.5 1.1 DËi: 1.1 e ̈vL ̈v: cÖv_wgK, T1 = 30C = 303 K V1 = 10 L cieZ©x‡Z, T2 = 2  30C = 60C = 333 K V2 V1 = T2 T1  V2 = 333 303  V1  V2 = 1.1V1 imvqb (Chemistry) 1. w ̄’i Zv‡c GKwU M ̈v‡mi Pvc 1.5 ̧Y e„w× Kiv n‡j, cwiewZ©Z AvqZb I c~‡e©i AvqZ‡bi AbycvZ KZ n‡e? 3 : 5 5 : 3 2 : 5 5 : 2 DËi: 2 : 5 e ̈vL ̈v: T  constant P2 = P1 + 3 2 P1 = 5 2 P1 P1V1 = P2V2  V2 = P1V1 P2  V2 = 2 5 V1  V2 V1 = 2 5 2. 27C ZvcgvÎvq I 3 atm Pv‡c CH4 M ̈v‡mi NbZ¡ KZ? 3.84 g L–1 3.84 g mL–1 3 g cm–3 1.92 g L–1 DËi: 1.92 g L–1 e ̈vL ̈v: Avgiv Rvwb, PM = dRT  d = PM RT  d = 3  16 1 12  300  d = 1.92 g L–1 (Ans.) 3. GKwU ARvbv M ̈v‡mi NbZ¡ 2 gL–1 Ges 63C ZvcgvÎvq i‡q‡Q| Pvc 2 atm n‡j, ARvbv M ̈vmwUÑ O2 N2 CO2 None DËi: N2 e ̈vL ̈v: GLv‡b, PM = dRT  M = dRT P = 2  1 12  336 2  M = 28 ⸫ M ̈vmwU N2, hvi AvbweK fi 28 4. GKwU †ejy‡b 200 mL evqy Av‡Q, evqyi ZvcgvÎv 27C Ges H mg‡q Pvc 5 atm n‡j †ejy‡b KZwU M ̈vm AYy Av‡Q? 6.02  1023 6  1023 3  1023 2.4  DËi: 2.4  e ̈vL ̈v: PV = nRT  n = PV RT = x NA  x = PVNA RT = 5  2 10  6.023  1023 1 12  300  x = 0.24  1023  x = 2.4  1022 wU AYy 5. GKwU 500 cm3 Gi M ̈vmfwZ© †ejyb‡K 127C ZvcgvÎvq 10 atm Pv‡c ivLv Av‡Q| †ejybwU‡K 27C ZvcgvÎvq Ges 5 atm Pv‡c †bIqv n‡j Kx NU‡e? [†ejybwU m‡e©v”P 1000 cm3 AvqZb ch©šÍ AÿZ _v‡K] †ejybwU †d‡U hv‡e †ejybwU dvU‡e bv AvqZb aaæeK _vK‡e †Kv‡bvwUB bq DËi: †ejybwU dvU‡e bv

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