Title 10. P1C10 (Ideal Gas and Kinetics of Gases) With Solve.pdf ✅

Av`k© M ̈vm I M ̈v‡mi MwZZË¡  Varsity Practice Sheet......................................................................................................... 1 weMZ mv‡j DU-G Avmv cÖkœvejx 1. `ywU GK-cigvYyK Av`k© M ̈vm ci ̄ú‡ii mv‡_ Zvcxq mvg ̈ve ̄’vq Av‡Q| A M ̈vm m f‡ii AYy Øviv MwVZ, Ges B M ̈vm 4 m f‡ii AYy Øviv MwVZ| A M ̈v‡mi AvqZb B M ̈v‡mi AvqZ‡bi wØ ̧Y| G‡`i Pv‡ci AbycvZ PA PB KZ? [DU 23-24] 1 4 1 2 1 2 DËi: 2 e ̈vL ̈v: PV = nRT  T = PV nR ∵ TA = TB  PAVA nA = PBVB nB  PA PB = VB VA  nA nB     n  1 M ; mgvb fi a‡i wb‡q  PA PB = 1 2  4 = 2 2. †Kv‡bv Av`k© M ̈v‡mi ZvcgvÎv †Kjwfb † ̄‹‡j 4 ̧Y e„w× †c‡j Zvi AYy ̧‡jvi g~j Mo eM©‡eM KZ ̧Y e„w× cvq? [DU 20-21, 15-16] 4 1 2 2 1 DËi: 2 e ̈vL ̈v: crms  T  T2 = 4T1 n‡j, c2 = 2c1 3. GKwU M ̈vm AYyi e ̈vm 2  10–10 m Ges cÖwZ Nb †mw›UwgUv‡i AYyi msL ̈v 3  1019 n‡j M ̈vm AYyi Mo gy3c_ n‡eÑ [DU 16-17] 3  10–3 cm 3  104 cm 3  10–5 cm 6  10–6 cm DËi: 3  10–5 cm e ̈vL ̈v: K¬wmqv‡mi m~Î Abyhvqx Mo gy3 c_,  = 1  2 n = 1 3.1416  (2  10–8 ) 2  3  1019 = 2.65  10–5 cm Option Abyhvqx KvQvKvwQ DËi 3  10–5 cm| 4. GKwU KYvi ̄^vaxbZvi gvÎvi msL ̈v 5 n‡j kw3i mgwefvRb bxwZ Abyhvqx KYvwUi †gvU kw3 KZ? [DU 15-16] kT 2 kT 3kT 2 5kT 2 DËi: 5kT 2 e ̈vL ̈v: †Kv‡bv KYvi ̄^vaxbZvi gvÎv cÖwZ kw3i cwigvY 1 2 kT| ̄^vaxbZvi gvÎv f n‡j †gvU kw3 f 2 kT  f = 5 n‡j †gvU kw3 n‡e E = 5 2 kT 5. GKwU wmwjÛv‡i ivLv GKwU Av`k© M ̈v‡mi AYy ̧‡jvi eM©g~j Mo eM©‡eM u| M ̈v‡m Zvc cÖ‡qv‡Mi d‡j Pvc 9 ̧Y e„w× †cj| wmwjÛv‡ii AvqZb AcwiewZ©Z _vK‡j M ̈v‡mi AYy ̧‡jvi cwiewZ©Z eM©g~j Mo eM©‡eM KZ? [DU 14-15] 9u 6u 3 u 2 3u DËi: 3u e ̈vL ̈v: †h‡nZz AvqZb AcwiewZ©Z _v‡K Ges fi aaæeK ZvB NbZ¡  aaæeK n‡e|  crms = 3P  Zvn‡j, crms  P  c rms crms = P P  c rms = 9 crms = 3u
2 .......................................................................................................................................  Physics 1st Paper Chapter-10 6. GKwU Av`k© M ̈v‡mi bgybvi ZvcgvÎv 20C| hw` bgybvwUi Pvc Ges AvqZb wØ ̧Y Kiv nq, Z‡e cwiewZ©Z ZvcgvÎv KZ? [DU 13-14] 20C 80C 900C 1200C DËi: 900C e ̈vL ̈v: P1V1 T1 = P2V2 T2  T2 = P2V2 P1V1 T1 = 2P1  2V1 P1V1  293 K = 1172 K = 899C Option Abyhvqx KvQvKvwQ DËi 900C| 7. †KD hw` cvnv‡oi P‚ovq cvwb dzUv‡Z Pvq Z‡e Zv‡K KZ ZvcgvÎvq †duvUv‡Z n‡e? [DU 08-09] 100C Gi †ewk 100C Gi Kg 100C Awb‡Y©q DËi: 100C Gi Kg e ̈vL ̈v: †h‡nZz cvnv‡oi P‚ovq Pvc Kg ZvB Kg ZvcgvÎvq cvwb dzU‡Z _vK‡e| cvwbi ùzUbv1⁄4 100C wKš‘ cvnv‡oi P‚ovq cvwb 100C A‡cÿv Kg ZvcgvÎvq dzU‡Z _vK‡e| weMZ mv‡j GST-G Avmv cÖkœvejx 1. †Kvb GKwU n«‡`i Zj‡`k n‡Z GKwU evqy ey`ey` cvwbi Dcwic„‡ô Avm‡j Gi AvqZb wØ ̧Y nq| evqyi Pvc 1.01  105 Pa n‡j n«‡`i MfxiZv KZ? [GST 23-24] 10.0 m 10.1 m 10.2 m 10.3 m DËi: 10.3 m e ̈vL ̈v: MfxiZv, h = (n – 1) P g = 1.01 × 105 103 × 9.8  h = 10.1 98  102  0.103  102  h  10.3 m 2. KZ ZvcgvÎvq Aw·‡Rb AYyi g~j Mo eM©‡eM –100C ZvcgvÎvq nvB‡Wav‡Rb AYyi g~j Mo eM©‡e‡Mi mgvb n‡e? [GST 23-24] 27.68 K 227.8 K 276.8 K 2768 K DËi: 2768 K e ̈vL ̈v: Crms(O2 ) = Crms(H2 )  T1 M1 = T2 M2  T2 = – 100 + 273 2  32 = 173 + 16  T2 = 2768 K 3. M ̈v‡mi AYyi Mo gy3c_ () I NbZ¡ () Gi g‡a ̈ m¤úK©Ñ [GST 22-23; RU 21-22; JnU 16-17]      1    1  2    2 DËi:   1  e ̈vL ̈v: g ̈v·I‡q‡ji m~Î Abymv‡i M ̈v‡mi AYyi Mo gy3 c_,  = 1 2 2 n   = m 2 2 nm   = m 2 2     1  4. hw` 30C ZvcgvÎv I 6  105 Pa Pv‡ci GKwU M ̈vm‡K m‡gvò cÖwμqvq wZb ̧Y AvqZ‡b cÖmvwiZ Kiv nq, Z‡e M ̈vmwUi P‚ovšÍ Pvc KZ Pa? [GST 22-23] 2  105 2.5  105 3  105 4.5  105 DËi: 2  105 e ̈vL ̈v: P1V1 = P2V2  6  105  V1 = P2  3V1  P2 = 2  105 Pa 5. w ̄’i AvqZ‡b GKwU M ̈v‡mi ZvcgvÎv evov‡j H M ̈v‡miÑ [GST 21-22] Pvc I MwZkw3 evo‡e Pvc I MwZkw3 Kg‡e NbZ¡ evo‡e NbZ¡ Kg‡e DËi: Pvc I MwZkw3 evo‡e e ̈vL ̈v: †M-jymv‡Ki Pvcxq m~Î Abymv‡i, P  T Avevi MwZkw3, Ek = 3 2 nRT  Ek  T ZvB ZvcgvÎv evov‡j Pvc I MwZkw3 e„w× cv‡e|
Av`k© M ̈vm I M ̈v‡mi MwZZË¡  Varsity Practice Sheet........................................................................................................ 3 6. 27C ZvcgvÎvq evqyi Av‡cwÿK Av`a©Zv 70% Ges wkwkiv‡1⁄4 m¤ú„3 Rjxqev®ú Pvc 14  10–3 mHg n‡j, H ZvcgvÎvq m¤ú„3 Rjxqev®ú Pvc KZ mHg? [GST 21-22] 12  10–3 16  10–3 20  10–3 22  10–3 DËi: 20  10–3 e ̈vL ̈v: Av‡cwÿK Av`a©Zv R n‡j, R = wkwkiv‡1⁄4 m¤ú„3 ev®úPvc evqyi ZvcgvÎvq m¤ú„3 ev®úPvc  100%  R = f F  100%  70% = 14  10–3 F  100%  70  F = 14  10–3  100  F = 14  10–3  10 7  F = 20  10–3 mHg 7. 10 wjUvi AvqZ‡bi e× cv‡Î 300 K ZvcgvÎvq 16 g Aw·‡Rb †h Pvc cÖ`k©b K‡i, GKB cv‡Î GKB ZvcgvÎvq KZ MÖvg bvB‡Uav‡Rb ivL‡j GKB Pvc cÖ`k©b Ki‡e? [GST 20-21] 14 16 18 32 DËi: 14 e ̈vL ̈v: kZ©g‡Z, VO2 = VN2 = 10 L TO2 = TN2 = 300 K; nO2 = 16 32 = 1 2 PO2 = PN2 GLv‡b, PV = nRT  nO2  TO2 = nN2  TN2  nN2 = nO2  nN2 = 1 2  mN2 = 28 2 = 14 weMZ mv‡j Agri-G Avmv cÖkœvejx 1. ̄^vfvweK ZvcgvÎv I Pv‡c R Gi gvb n‡”QÑ [Agri. Guccho 21-22] 8.32 JK–1mol–1 8.31 KJ–1mol–1 8.31 JK–1mol 8.13 J–1mol–1 DËi: 8.32 JK–1mol–1 e ̈vL ̈v: R Gi gvbmg~n: 8.32 JK–1mol–1 0.082 L atm mol–1K –1 8.32  107 erg mol–1K –1 2. 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? [Agri. Guccho 21-22] 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 3. w ̄’i Pv‡c †Kvb ZvcgvÎvq †Kv‡bv M ̈v‡mi g~j Mo eM©‡eM cÖgvY Pvc I ZvcgvÎvi g~j Mo eM©‡e‡Mi A‡a©K n‡e? [Agri. Guccho 21-22; JU 19-20] 68.25 K 273 K 1029 K 34.125 K DËi: 68.25 K e ̈vL ̈v: M ̈vm wbw`©ó n‡j, crms c rms = T T  1 2 = T T  T = T 4  T = 273 4 K = 68.25 K weMZ mv‡j JU-G Avmv cÖkœvejx 1. GKwU Av`k© M ̈vm GKwU fvimvg ̈ Ae ̄’v (P1, V1, T1, N) †_‡K Ab ̈ fvimvg ̈ Ae ̄’vq (2P1, 3V1, T2, N) cwiewZ©Z nq| Zv n‡j wb‡Pi †KvbwU mwVK? [JU 22-23] T1 = T2 T1 = T2 6 T1 = 6T2 T1 = 3T2 DËi: T1 = T2 6 e ̈vL ̈v: P1V1 T1 = P2V2 T2 T2 = P2 P1  V2 V1  T1  T2 = 2P1  3V1 P1  V1  T1  T2 = 6T1
4 .......................................................................................................................................  Physics 1st Paper Chapter-10 2. ZvcgvÎv e„w× †c‡j AYy ̧‡jvi Mo eM©‡eMÑ [JU 22-23] n«vm cvq e„w× cvq AcwiewZ©Z _v‡K KL‡bv ev‡o KLbI K‡g DËi: e„w× cvq e ̈vL ̈v: AYyi Mo eM©‡eM ZvcgvÎv e„w×i mv‡_ e„w× cvq| g~j Mo eM©‡eM, crms = 3RT M  Mo eM©‡eM, c 2 rms = 3RT M  Mo eM©‡eM, c –  T 3. 30C ZvcgvÎvq Aw·‡R‡bi g~j Mo eM©‡eMÑ [JU 22-23] 485 ms–1 850 ms–1 380 ms–1 548 ms–1 DËi: 485 ms–1 e ̈vL ̈v: crms = 3RT M  crms = 3  8.314  303 32  10–3  crms = 485 ms–1 4. †Kv‡bv n«‡`i Zj‡`k †_‡K cvwbi DcwiZ‡j Avmvq GKwU evqy ey`ey‡`i AvqZb 10 ̧Y nq| evqygЇji Pvc 105 Nm–2 n‡j n«‡`i MfxiZv KZ? [JU 21-22] 91.84 m 40.81 m 100 m 50.81 m DËi: 91.84 m e ̈vL ̈v: V1 = 10V, P1 V2 = V, P1 + hg P1V1 = P2V2  105  10V = {105 + (h  1000  9.8)}  V  h = 91.84 m 5. 27C ZvcgvÎvq `ywU Aw·‡Rb cigvYyi MwZkw3 KZ?[JU 21-22] 12.42  10–21 J 6.21  10–21 J 1.242  10–21 J 0.621  10–21 J DËi: 12.42  10–21 J e ̈vL ̈v: `ywU Aw·‡Rb cigvYyi †ÿ‡Î, MwZkw3, E = 2  3 2 kT = 3  1.38  10–23  300 J = 1.242  10–20 J = 12.42  10–21 J 6. m¤ú„3 ev®ú †Kvb m~Î †g‡b P‡j? [JU 21-22] e‡qj Gi m~Î Pvj©m Gi m~Î DfqwUB †Kv‡bvwUB bq DËi: †Kv‡bvwUB bq e ̈vL ̈v: m¤ú„3 ev®ú Av`k© M ̈vm m~Î †g‡b P‡j bv| ZvB GwU e‡qj, Pvj©‡mi m~Î gv‡b bv| 7. 0C ZvcgvÎvq Rjxq m¤ú„3 ev®úPvc KZ? [JU 21-22] k~b ̈ 0.40 cm Hg 76 cm Hg Amxg DËi: Blank e ̈vL ̈v: 0C ZvcgvÎvq m¤ú„3 ev®úPvc 4.58 mm (Hg) 8. M ̈v‡mi MwZZË¡ Abymv‡i 0 K ZvcgvÎvq M ̈v‡mi MwZkw3 n‡eÑ [JU 20-21] me©vwaK k~b ̈ me©wb¤œ gvSvgvwS DËi: k~b ̈ e ̈vL ̈v: M ̈v‡mi MwZkw3, E = 3 2 nRT  E  T MwZkw3 cig ZvcgvÎvi mgvbycvwZK| ZvcgvÎv 0 K n‡j MwZkw3 k~b ̈ n‡e| 9. ﮋ I wm3 nvB‡MÖvwgUv‡i ev‡j¦i g‡a ̈ ZvcgvÎvi cv_©K ̈ AwaK wb‡`©k Ki‡jÑ [JU 19-20; RU 15-16] D”P Av‡cwÿK Av`a©Zv wb¤œ Av‡cwÿK Av`a©Zv D”P wkwkiv1⁄4 wb¤œ wkwkiv1⁄4 DËi: wb¤œ Av‡cwÿK Av`a©Zv e ̈vL ̈v: ﮋ I wm3 nvB‡MÖvwgUv‡ii ev‡j¦i g‡a ̈ ZvcgvÎvi cv_©K ̈ AwaK wb‡`©k Ki‡j Av‡cwÿK Av`aZv Kg nq| 10. 0C ZvcgvÎvq Aw·‡R‡bi g~j Mo eM©‡eM KZ? [JU 17-18] 560 ms–1 461 ms–1 861 ms–1 961 ms–1 DËi: 461 ms–1 e ̈vL ̈v: crms = 3RT M = 3  8.314  273 32  10–3 = 461.287 ms–1  crms  461 ms–1 11. ̄^vfvweK ZvcgvÎv I Pv‡c GKwU M ̈v‡mi NbZ¡ 0.09 kgm–3 n‡j M ̈v‡mi AYymg~‡ni g~j Mo eM©‡eM KZ n‡e? [JU 17-18, 11-12, 09-10] 1939.38 ms–1 1839.38 ms–1 18.3938 ms–1 19.3938 ms–1 DËi: 1839.38 ms–1 e ̈vL ̈v: crms = 3P  = 3  101325 0.09 = 1837.797 ms–1  crms  1839.38 ms–1