SUARY * Gas Laws:. yle's law: Fr a given mass f an ideal gas at cnstant temperature, the vlume f a gas is inversely prprtinal t its pressure, i.e. α r cnstant m ( i) cnstant cnstant r m Where density,, and m cnstant (ii) As number f mlecules per unit vlume (iii) n N N als N cnst. n N cnstant n cnstant r n n n (iv) Graphical representatin: (If m and are cnstant). harle's law: At cnstant pressure, the vlume f the given mass f a gas is directly prprtinal t its abslute temperature. i.e. (i) cnstant m m cnstant ρ r cnstant 89
(ii) Graphical representatin: (If m and are cnstant). Gay-Lussac`s Law r pressure law: Accrding t it fr a given mass f an ideal gas at cnstant vlume, pressure f a gas is directly prprtinal t its abslute temperature. i.e. r cnstant (i) Graphical representatin: (If m and are cnstant) * Avgadr's law: Equal lume f all the gases under similar cnditins f temperature and pressure cntain equal number f mlecules. i.e. N N Avgadr Number: he number f particles (atms r mlecules) in ne mle f substance (gas) is called Avgadr number (N A ) which has a magnitude N A 6.0 0 ml - 90
* Equatin f State OR Ideal Gas Equatin he equatin which relates the pressure (), vlame () and temperature () f the given state f an f an ideal gas is knwn as ideal gas equatin r equatin f state. Ideal gas equatin is µr where µ number f mle R universal gas cnstant 8.4 J.ml - K - * Different f f Ideal gas-state-equatin (i) N R µr R Nk k NA NA where k ltzmann`s cnstant.8 0 - JK - N (ii) k nk (iii) where N n number density f gas R µ number f mlecules per unit vlume where mlar mass f the gas R ρr m ( ρ density f the gas) * he wrk dne during the change in vlume f the gas: It can be btained frm the graph f 9 f W dν * Assumptin f Ideal gases (r kinetic thery f gases) Kinetic thery f gases relates the macrscpic prperties f gases (such as pressure, temperature etc.) t the micrscpic prperties f the gas mlecules (such as mmentum, speed, kinetic enengy f mlecule etc.) Assumptins:. Gas is made up f tiny particles, hese particles are called mlecules f the gas.. he mlecules f a gas are identical, spherical, rigid and perfectly elastic pint masses.. he mlecules f a gas perfrm incessant randm mtin. 4. he mlecules f a gas fllw Newtn's laws f mtin. 5. he number f mlecules in a gas is very large. 6. he vlume f mlecules is negligible in cmparisin with the vlume f gas. i
7. Inter mlecular frces act nly when tw mlecules cme clse t each ther r cllide. 8. he time spent in a cllisin between tw mleules is negligible in cmparisin t time between tw successive cllisins. he cllisins between the mlecules and between a mlecule and the wall f a cntainer are elastic. * ressure f an Ideal gas ρ ν ρ ν where density f the gas v < > mean squre velcity f mlecule * Relatin between pressure and kinetic energy ρ ν (i) K.E. per unit vlume is E ( ii) Frm equatin (i) and (ii) E * Rt mean square speed (v ) : It is defined as the square rt f mean f squares f the speed f the speed f different mlecules. i.e. ν ν ν... ν N N Frm the expressin f pressure ρ R k m where ρ density f the gas m mass f each mlecule N A - ν - with increase in mlecular weight speed f gas mlecule decreases as v 9
- speed f gas mlecules des nt depend n the pressure f gas (If temperature remains cnstant) - At 0 K, v 0, i.e. the speed f mlecules f a gas is zer at O K. his temperature is called abslute zer. * Kinetic interpretatin f temperature Kinetic energy f f mle ideal gas R E ν R - Fr mlecule E k, k ltzmann`s cnstant - Fr N mlecule E N k - Kinetic energy per nlecule f gas des nt depend upn the mass f the mlecule but nly depends n the temperature. * ean free path:- he distance travelled by a gas mlecule between tw successive cllisins is knwn as free path. he average f such free paths travelled by a mlecule is called mean free path. mean free path, - tal distance travelled by a gas mlecule between tw successive cllisins tal number f cllisins nd k nk n nπd π d k - - llisin frequency number f cllisins per secnd. ν * Degrees f Freedm : he term degrees f freedm f a mlecule r gas are the number f independent mtins that a mlecule r gas can have. he independent mtin f a system can be translatinal, rtatinal r vibratinal r any cmbinatin f these. Degress f freedm, f A - ; where A Number f independent particles, Number f independent restrictins - mnatmic gas degrees f freedm ( All translatinal) 9
- Diatmic gas 5 degrees f freedm ( translatinal + rtatinal) - triatmic gas 6 degrees f freedm (at rm temperature) (Nn-linear) ( translatinal + rtatinal) 8 degrees f freedm (at very high temperature) ( translatinal + rtatinal + vibratinal) * Law f equipartitin f energy (ltzmann law) Accrding t this law, fr any system in equilibrium, the ttal energy is equally distributed amng its varius degrees f freedm and each degrees f freedm is assciated with energy k where k ltzmann`s cnstant. - At a given temperataue, all ideal gas mlecules n matter what their mass have the same average translatinal kinetic energy k - At same temperature gases with different degrees f freedm (i.e. H and He) will have different average energy f k ( f degress f freedm different fr different gases.) f - he ttal energy assciated with each mdlec k * Specific heat f a gas : - Specific heat at cnstant vlume ( v ) - he amunt f heat required t change the temperature f l mle f gas by K, keeping its vlume cnstant, is called specific heat f the gas at cnstant vlume. - Specific heat at cnstant vlume ( p ) he amunt f heat required t change the temperature f l mle f gas by K, keeping its pressure cnstant, is called specific heat f the gas at cnstant pressure. lar specific heat: - he quantity f heat required t change the temperature f mle f gas by K (r ) is called mlar specific heat f the gas. Rati f and is. f R f R, R R f f f 94
Q hse the crrect alternative frm given ptins.. lume, pressure and temperature f an ideal gas are, and respectively. If mass f mlecule is m, then its density is [ k ltzmann`s cnstant] (A) k () m k (). k (D) mk. he temperature f an ideal gas at atmspheric pressure is 00 K and vlume m. If temperature and vlume becme duble, then pressure will be (A) 4 0 5 Nm () 0 5 Nm () 0 5 Nm (D) 0.5 0 5 Nm. At 00 K and 0. atmspheric pressure, the vlume f helium gas is 0 litres. If vlume and pressure are dubled, its temperature will change t (A) 7 K () 400 K () 5 K (D) 00 K 4. What is the mass f litres f nitrgen at.4 atmspheric pressure and 7 K. (R 8.4 Jml k - ) (A) 4.4 g () 56 g () 8 g (D) Nne f these. 5. An electrn tube was sealed ff during manufacture at a pressure f. 0-7 mm f mercury at 7 0. Its vlume is 00 cm. he number f mlecules that remain in the tube is (density f mercury is.6 gcm ) (A).9 0 () 0 6 () 0 4 (D) 7 0 6. A vessel cntains mle f O gas (relative mlar mass ) at a temperature. he pressure f the gas is. An identical vessel cntaining mle f He gas (relative mlar mass 4) at a temperature has pressure f... (A) 8 () p 8 () (D) 7. he equatin f state fr 5 g f xygen at a pressure and temperature, when ccupying a vlume, will be (A) 5 5 5 R () R () R 6 95 (D) 5 R 8. A gas at atmsphere and having vlume 00 ml is mixed with anther gas f equal mles at 0.5 atm and having vlume 50 ml in flask f ne litre, what is the final pressure? (A) 0.5 atm () 0.75 atm () atm (D) 0.5 atm 9. he quantity k represents (A) mass f gas () number f mles f gas () number f mlecules in gas (D) K. E. f gas 0. Equatin f gas in te f pressure (), abslute temperature () and density () is (A) ρ ρ () () ρ ρ ρ ρ (D) ρ ρ
. 0 gas is filled in a vessel. If pressure is dubled, temperature becmes fur times, hw many times its density will becme. (A) 4 () 4 () (D). At a given vlume and temperature the pressure f a gas (A) aries inversely as the square f its mass () is independent f its mass 96 () aries inversely as its mass (D) aries linearly as its mass. If pressure f a gas cntained in a clsed vessel is increased by 0.4% when heated by 0 the initial temperature must be. (A) 50 0 () 5 0 () 50 K (D) 500 K 4. decrease the vlume f a gas by 5% at cnstant temperature the pressure shuld be (A) Incseased by 5.6% () Decreased by 5.6% () Decreased by % (D) Increased by % 5. A gas at the temperature 50 K is cntained in a clsed vessel. If the gas is heated thrugh K, then the percentage increase in its pressurse will be (A) 0.4% () 0. % () 0.8% (D) 0.% 6. he prduct f the pressure and vlume f an ideal gas is (A) A cnstant () Directly prprtinal t its temperature. () Inversely prprtinal t its temperature. (D) Apprx. equal t the universal gas cnstant. 7. At O the density f a fixed mass f a gas divided by pressure is x. At 00, the rati will be 7 (A) x () x 7 () 7 x 7 (D) 00 x 7 8. Air is pumped int an autmbile tube upt a pressure f 00 ka in the mrning when the air temperature is. During the day, temperature rises t 4 and the tube expands by % he pressure f the air in the tube at this temperature will be apprximately. (A) 09 ka () 06 ka () 00 ka (D) ka 9. he vlume f a gas at 0 is 00 ml. If the temperature is reduced t 0 at cnstant pressure, its vlume will be. (A) 7.6 ml () 7.6 ml () 9.7 ml (D) 9.7 ml 0. g f O gas is taken at 7 and pressure 76 cm Hg. Find ut vlume f gas (ln litre) (A).08 () 44. ().5 (D).44. mle f gas ccupies a vlume f 00 ml at 50 mm pressure. What is the vlume ccupied by tw mles f gas at 00 mm pressure and at same temperature (A) 50 ml () 00 ml () 00 ml (D) 500 ml
. A partitin divides a cntainer, having insulated walls, int tw cmpartments, I and II. he same gas is filled the cmpartments. he rati f number f mlecules in cmpartments I and II is. (A) 6: () :6 () 4: (D) :4. A cylinder cntains 0 kg f gas at pressure f 0 7 N/m. he quantity f gas taken ut f the cylinder, if final pressure is 0 6.5 Nm, will be (temperature f gas is cnstant) (A) 5. kg ().7 kg () 7.5 kg (D) kg 4. he vlume f a gas at pressure 0 4 Nm and temperature 7 is 8 Litres. If R 8. J ml K. hen the quantity f gas in g-mle will be (A) 4 () 7 () 4 (D) 5 5. he pressure and temperature f an ideal gas in a clsed vessel are 70 ka and 40 respectively. If th 4 f the gas is released frm the vessel and the temperature f the remaning gas is raised t 5, final pressure f the gas is (A) 440 ka () 540 ka () 080 ka (D) 70 ka 6. Suppse ideal gas equatin fllws cnstant, Initial temperature and vlume f the gas are and respectively. If gas expand t 7, then temperature will becme (A) 9 () 7 () 9 (D) 7. he temperature f a gas at pressure and vlume is 7 0 Keeping its vlume cnstant if its temperature is raised t 97 0, then its pressure will be (A) () () 4 (D) 6 8. Air is filled in a bttle at atmspheric pressure and it is crked at 5, If the crk can cme ut at atmspheric pressure then upt what temperature shuld the bttle be heated in rder t remve the crk. (A) 5.5 () 65 () 85 (D)Nne f these 9. At what temperature vlume f an ideal gas becmes triple (A) 89 () 8 () 646 (D) 546 0. duble the vlume f a given mass at an ideal gas at 7 0 keeping the pressure cnstant ne must raise the temperature in degree centigrade (A) 54 () 600 () 7 (D) 70. At cnstant temperature n incerasing the pressure f a gas 5% its vlume will decrease by (A) 5% () 5.6% () 4.76% (D) 4.6%. At n 0 pressure measured by barmeter is 760 mm. what will be pressure at 00 (A) 780 mm () 760 mm () 70 mm (D) Nne f these.. Hydrgen gas is filled in a balln at 0 0. If temperature is made 40 0, pressure remaining the same what fractin f haydrgen will cme ut (A) 0.75 () 0.07 () 0.5 (D) 0.5 97,, I,, II
4. When the pressure n 00 ml f a gas is increased frm 70 cm t 0 cm f mercury at cnstant temperature, the new vlume f the gas will be (A) 400 ml () 600 ml () 700 ml (D) 500 ml 5. A gas at 7 0 temperature and 0 atmspheric pressure is allwed t expand t the atmspheric pressure if the vlume becmes tw times its initial vlume, then the final temperature becmes (A) 7 0 () -7 0 () 7 0 (D) 00 0 6. A gas at 7 0 has a vlume and pressure. On heating its pressure is dubled and vlume becmes three times. he resulting temperature f the gas will be (A) 57 0 () 600 0 () 6 0 (D) 800 0 7. A perfect gas at 7 0 is heated at cnstant pressure t 7 0. If riginal vlume f gas at 7 is then vlume at 7 is (A) () () (D) 8. A vessel cntains mle f O gas (mlar mass ) at a temperature. he pressure f the gas is. An identical vessel cntaining ne mle f He gas (mlar mass 4) at temperature has a pressure f (A) () () 8 (D) 8 9. he pressure and temperature f tw different gases and having the vlumes fr each. hey are mixed keeping the same vlume and temperature, the pressure f the mixture will be, (A) () () 4 (D) 40. Air is filled at 60 0 in a vessel f pen muth. he vessel is heated t a temperature s that th part f air escapes. Assuming the vlume f the vessel remaining cnstant the value f is. 4 (A) 0 () 7 0 () 444 0 (D) 80 0 4. A gas is filled in a cylinder, its temperature is incresecd by 0% n kelvin scale and vlume is reduced by 0%. Hw much percentage f the gas will leak ut (A) 5% () 5% () 40% (D) 0% 4. he pressure is exerted by the gas n the walls f the cntainer because (A) It sticks with the walls () It is accelerated twards the walls () It lses kinetic energy (D) On cllisin with the walls there is a change in mmentum 4. he relatin between the gas pressure and average kinetic energy per unit vlume E is (A) E () E () E 98 (D) E 44. he rt mean square speed f hydrgen mlecules f an ideal hydrgen kept in a gas chamber at 0 0 is 80 ms. he pressure n the hydrgen gas is (Density f hydrgen gas is 8.99 0 kg m, atm.0 0 Nm 5 ) (A).0 atm ().0 atm ().0 atm (D).5 atm
45. Gas at a pressure is cntained in a vessel. If the masses f all the mlecules are halved and their speeds are dubled, the resulting pressure will be equal t (A) 0 () 4 0 () 0 (D) 0 46. A cylinder f capacity 0 litres is filled with H gas. he ttal average kinetic energy f translatry mtin f its mlecules is 5.5 0 J. he pressure f hydrgen in the cylinder is (A) 4 0 6 Nm () 0 6 Nm () 5 0 6 Nm (D) 0 6 Nm 47. he average kinetic energy per mlecule f a gas at - 0 4 and 75 cm pressure is 50 erg fr H. he mean kinetic energy per mlecule f the O at 7 and 50 cm pressure will be (A) () 4 4 80 0 erg () 00 erg 4 4 0 0 erg (D) 400 erg 48. he rati f mean kinetic energy f hydrgen and xygen at a given temperature is (A) :8 () :4 () :6 (D) : 49. he rati f mean kinetic energy f hydrgen and nitrgen at temperature 00 K and 450 K respectively is (A) : () : () 4:9 (D) : 50. ressure f an ideal gas is increased by keeping temperature cnstant what is the effect n kinetic energy f mlecules. (A) Decrease () Increase () N change (D) an`t be determined 5. A sealed cntainer with negligible c-efficient f vlumetric expansin cntains helium (a mnatmic gas) when it is heated frm 00 K t 600 K, the averagy K.E. f helium atm is (A) Halved () Dubled () Unchanged (D) Increased by factr 5. he mean kinetic energy f a gas at 00 K is 00J. mean energy f the gas at 450 K is equal t (A) 00 J () 50 J () 000 J (D) 450 J 5. At what temperature is the kinetic energy f a gas mlecule duble that f its value at 7 (A) 54 0 () 08 0 () 7 0 (D) 00 0 54. he average kinetic energy f a gas mlecule at 7 0 is 6. 0 J. Its average kinetic energy at 7 0 will be (A) 5. 0 J ().5 0 J () 5. 0 J (D).40 J 55. he average translatinal energy and speed f mlecules in sample f xygen gas at 00 K are 6. 0 J and 484 m s respectively. he crrespnding values at 600 K are nearly (assuming ideal gas behaviur) (A) 6. 0 J, 968 m s ().40 J, 684 m s ().4 0 J, 968 m s (D) 8.780 J, 684 m s 99
56. he average translatinal kinetic energy f O (mlar mass ) mlecules at a particular temperature is 0.068 e. he translatinal kinetic energy f N (mlar mass 8) mlecules in e at the same temperature is (A) 0.00 e () 0.068 e () 0.056 e (D) 0.678 e 57. At O K which f the fllwing prperties f a gas will be zer (A) Kinetic energy () Density () tential energy (D) ibratinal energy 58. he kinetic energy f ne mle gas at 00 K temperatue is E. At 400 K temperature kinetic enrgy is E'. he value f E' E is (A) () 6 9 (). 59. he average kinetic energy f hydrgen mlecules at 00 K is E. At the same temperature the average kinetic energy f xygen mlecules will be (D) 4 (A) E 6 () E () 4 E (D) E 4 60. he temperature at which the average translatinal kinetic energy f a mlecule is equal t the energy gained by an electrn accelerating frm rest thrugh a ptential differencc f vlt is (A) 4.6 0 K () 7.7 0 K ().6 0 K (D).0 K 6. At a given temperature the velcity f mlecules f the gas is (A) rprtinal t mlecular weight () Inversely prprtinal t mlecular weight () Inversely prprtinal t square rt f mlecular weight (D) rprtinal t square f mlecular weight 6. Accrding t the kinetic thery f gases the r.m.s velcity f gas mlecules is directly prprtinal t (A) () () (D) 6. he speeds f 5 mlecules f a gas (in arbitrary units) are as fllws:,, 4, 5, 6, he rt mean squre speed fr these mlecules is (A) 4.4 ().9 () 4.0 (D).5 64. what temperature shuld the hydrgen at rm temperature (7 ) be heated at cnstant pressuse s that the velcity f its mlecule becmes duble f its previus value (A) 97 () 600 () 08 (D) 00 65. Rt mean square velcity f a mlecule is at pressure. If pressure is increased tw times, then the velcity becmes (A) () () 0.5 (D) 66. he speed f gas mlecules is given by (A).5 R () R.5 () R.7 (D).7 R 00
67. A sample f gas is at O. what temperature it must be raised in rder t duble the speed f mlecule. (A) 70 () 89 () 00 (D) 090 68. If the rati f vapur density fr hydrgen and xygen is, then under cnstant pressure the 6 rati f their velcities will be (A) 4: () :6 () 6: (D) :4 69. he mlecules f a given mass f a gas have a velcity f 00 m s at 7 and 5.0 0 Nm pressure when the temperature is 7 and pressure is 0.5 0 5 Nm velcity in m s will be, the (A) 00 () 00 () 400 (D) Nne f these 70. If the mlecular weight f tw gases are and, then at a given temperature the rati f rt mean square velcity and will be (A) () () (D) 7. what temperature shuld the hydrgen at 7 cled at cnstant pressure, s that the rt mean square velcity f its mlcules becme half f its previus value (A) 00 () () 0 (D) 7. At what temperature is the rt mean square velcity f gaseus hydrgen mlecules equal t that f xygen mlecules at 47? (A) -7 K () 80 K () 0 K (D) K 5 7. he rt mean square velcity f the mlecules in a sample f helium is th 7 that f the mlecules in a sample f hydrgen. If the temperature f hydrgen sample is 0 0, then the temperature f the helium sample is abut (A) 7 () 0 () O K (D) 00 74. At rm temperature ( 7 ), the speed f the mlecules f certain diatmic gas is fund t be 90 m/s. he gas is (A) O () () H (D) F 75. If three mlecules have velcities 0.5, and the rati f speed and average speed is (he velcities are in km/s) (A) 0.4 ().4 ().4 (D).4 0
76. At what temperature pressure remaining cnstant will the speed f a gas mlecules increase by 0% f the speed at N? (A) 57. K () 57. 0 () 557. K (D) -57. 0 77. When temperature f an ideal gas is increased frm 7 t 7, its speed changed frm 400 ms t s. he s is (A) 56 ms () 746 ms () 0 ms (D) 450 ms 78. At what temperature the mlecules f nitrgen will have the same. velcity as the mlecules f Oxygen at 7. (A) 7 0 () 50 0 () 77 0 (D) 457 0 79. he temperature f an ideal gas is increased frm 7 0 t 7 0, then percentage increase in is (A) % () % () 5.5% (D) 7% 80. Let A and the tw gases and given : A A. Where is the temperature and is A mlecular mass. If A and are the r.m.s speed, then the rati will be equal t (A) () 4 () 0.5 (D) 8. he. speed f the mlecules f a gas in a vessel is 400 ms -. If half f the gas leaks ut, at cnstant temperature, the r.m.s speed f the remaining mlecules will be (A) 800 ms - () 00 ms - () 400 ms - (D) 400 ms - 8. At which temperature the velcity f 0 mlecules will be equal t the velcity f N mlecules at 0 0 (A) 9 0 () 40 0 () 9 0 (D) can nt be calculated. 8. he speed f the mlecules f a gas at a pressure 0 5 a and temperature 0 0 is 0.5 km/s. If the pressure is kept cnstant but temperature is raised t 89 0, the speed becmes (A).5 kms - () kms - () kms - (D) 5 kms - 84. he rt mean square velcity f a gas mlecule f mass m at a given temperature is prprtinal t (A) m 0 () m -/ () m / (D) m 85. he rati f the vapur densities f tw gases at a given temperature is 9:8, he rati f the velcities f their mlecule is (A) : () : () 9:8 (D) 8:9 86. At what temperature, pressure remaining unchanged, will the velcity f a gas be half its value at O? (A) 04.75 K () 04.75 0 () -04.75 K (D) -04.75 0 87. he velcity f gas mlecules is 00 ms -. he velcity f mlecules f gas with twice the mlecular weight and half the abslute temperature is (A) 00 ms - () 50 ms - () 600 ms - (D) 75 ms - 0 4
88. alculate the temperature at which velcity f S0 mlecules is the same as that f O mlecules at 7 0. lecular weights f Oxygen and SO are g and 64 g respectively (A) 7 0 () 7 K () 7 0 (D) 7 0 89. Fr a gas, the speed at 800 K is (A) Fur times the value at 00 K () wice the value at 00 K () Half the value at 00 K (D) same as at 00 K 90. A mixture f mles f helium gas (atmic mass 4 amu), and mle f argn gas (atmic mass v(helium) 40 amu) is kept at 00 K in a cntainer. he rati f the speeds is v (argn) (A) 0.45 ().4 ().6 (D) 0. 9. he temperature f an ideal gas is increased frm 7 0 t 97 0. he rt mean square speed f its mlecules becmes (A) Fur times () One-furth () Half (D) wice 9. At a given temperature the rt mean square velcities f Oxygen and hydrgen mlecules are in the rati (A) :4 () :6 () 6: (D) 4: 9. If mass f He atm is 4 times that f hydrgen atm, then speed f the is (A) w times f H speed. () Fur times f H speed. () Same as f H speed. (D) half f H speed. 94. At temperature, the speed f helium mlecules is the same as speed f hydrgen mdecules at nrmal temperature and pressure. he value f is (A) 546 0 () 0 0 () 7 0 (D) 6.5 0 95. he rt mean square speed f hydrgen mlecules at 00 K is 90 m/s. hen the rt mean square speed f Oxygen mlecules at 900 K will be (A) 86 m/s () 64 m/s () 90 m/s (D) 90 m/s 96. If speed f a gas is 840 m/s and its density 8.99 0 - kg/m, the pressure f the gas will be (A).0 0 Nm ().0 0 5 Nm ().0 0 7 Nm (D).0 Nm 97. When the temperature f a gas is raised frm 7 0 t 90 0, the percentage increase in the velcity f the mlecules will be (A) 5% () 7.5% () 0% (D) 0% 98. he speed f a gas at a certain temperature is times than that f the Oxygen mlecule at that temperature, the gas is (A) SO () H 4 () H (D) He 0
99. he temperature at which the speed f hydrgen mlecules is equal t escape velcity n earth surface will be (A) 500 K () 006 K () 060 K (D) 870 K 00. What is the meanfree path and cllisin frequency f a nitrgen mlecule in a cylinder cntaining nitrgen at atm and temperature 7? ake the radius f nitrgen mlecule t be A. lecular mass f nitrgen 8, k.8 0 JK, atm.0 0 5 Nm 7 9 (A).0 7 8 m,.580 ().0 m, 4.580 7 9 ().0 7 9 m, 4.580 (D).0 m,.580 0. he radius f a mlecule f Argn gas is.78 0 A. Find the mean free path f mlecules f Argn at 0 0 temperature and atm pressure. k.80 JK (A) 8 7 7 8 6.65 0 m ().65 0 m () 6.65 0 m (D).650 m 0. A mnatmic gas mlecule has (A) hree degrees f freedm () Five degrees f freedm () Six degrees f freedm (D) Fur degrees f freedm 0. A diatmic mlecule has hw many degrees f freedm (Fr rigid rtatr) (A) 4 () () 6 (D) 5 04. he degrees f freedm fr triatmic gas is (At rm temperature) (A) 8 () 6 () 4 (D) 05. If the degrees f freedm f a gas are f, then the rati f tw specific heats p v is given by (A) () () f f f (D) f 06. A diatmic gas mlecule has translatinal, rtatinal and vibratinal degrees f freedm. he p v is (A).9 (). ().4 (D).67 07. he value f v fr ne mle f nen gas is (A) R () 7 R () R 08. he relatin between tw specific heats f a gas is (A) R J () J () R J (D) J (D) 5 R 04
09. he mlar specific heat at cnstant pressure fr a mnatmic gas is (A) R () 5 R 7 () 4 R (D) R R 0. Fr a gas 0. 67. his gas is made up f mlecules which are (A) Diatmic () mnatmic () plyatmic (D) mixture f diatmic and plyatmic mlecules. he specific heat f an ideal gas is (A) rprtinal t () rprtinal t () rprtinal t (D) Independent f. he specific heats at cnstant pressure is greater than that f the same gas at cnstant vlume because (A) At cnstant vlume wrk is dne in expanding the gas. () At cnstant pressure wrk is dne in expanding the gas. () he mlecular vibratin increases mre at cnstant pressure. (D) he mlecular attractin increases mre at cnstant pressure. 5 7. One mle f ideal mnatmic gas is mixed with ne mle f diatmic gas. What is fr the mixture? dentes the rati f specific heat at cnstant pressure t that at cnstant vlume. (A) 5 () 5 () (D) 4 4. Fr a gas if rati f specific heats at cnstant pressure and vlume is, then value f degrees f freedm is (A) 5 () () 9 (D) 7 5. he mlar specific heat at cnstant pressure f an ideal gas is R. he rati f specific heat at cnstant pressure t that rati at cnstant vlume is (A) 5 7 () 9 7 () 8 7 (D) 7 5 6. Fr a gas 7, the gas may prbably be 5 (A) Nen () Argn () Helium (D) Hydrgen 7. Frm the fllwing - graph, what inference can be drawn (A) < () () > (D) nne f these 05
8. he figure shws the vlume versus temperature graphs fr a certain mass f a perfect gas at tw cnstant pressure f and. What inference can yu draw frm the graphs. (A) < () > () (D) N inference can be drawn due t insufficient infrmatin. 9. Which ne the fllwing graphs represents the behaviur f an ideal gas (A) () () (D) 0. Under cnstant temperature, graph between p and is (A) Hyperbla () ircle () arabla (D) Straight line Directin:- (a) If bth Assertin and Reasn are true and the Reasn is crrect explanatin f the Assertin. (b) If bth Assertin and Reasn are true, but Reasn is nt crrect explanatin f the Assertin. (c) If Assertin is true; the Reasn is false. (d) If Assertin is false, but the reasn is true.. Assertin : 00 cc f a gas at 7 0 is cled at - 0 at cnstant pressure. he final vlume f the gas wuld be 70 cc Reasn : his is as per charle's law (A) a () b () c (D) d. Assertin : he time f cllisin f mlecules is f the rder f 0-8 s, which is very very small cmpared t the time between tw successive cllisins. Reasn : his is an experimental fact. (A) a () b () c (D) d. Assertin : ean free path f gas varies inversly as density f the gas. Reasn : ean free path varies inversely as pressure f the gas. (A) a () b () c (D) d 06
KEY NOE 6 A A5 5 76 0 76 A 0 A 7 5 5 77 A 0 77 A A 0 A 8 8 5 5 78 0 78 D 0 D 4 9 D 54 D 79 04 4 9 D 54 D 79 04 5 A 0 55 80 A 05 6 5 A 0 55 56 80 A 05 8 D D 06 7 6 A D56 57 8 DA 06 8 07 A 8 7 A A D 57 A 58 8 07 8 A 08 9 4 59 84 09 8 A 58 8 08 0 5 60 85 0 9 D 4 6 A 59 6 84 09 86 D D 0D 5 7 A60 6 85 0 87 D 6 8 A A6 6 86 DA 88 D A 4 A D 7 9 A D6 64 87 A 89 4 A 5 A 40 65 D 90 5 D 8 A 6 A 88 A 6 4 66 9 D 6 D 7 4 A 9 4 D D 64 A 67 89 4 9 A A 7 8 5A A 40 4 A65 D 68 90 A 5 9 D D 8 9 6A 4 44 66 69 9 D 6 94 D 9 0 7 4 45 D A67 70 9 A 7 95 A 0 D 46 7 D 96 A 8 A 4 A 68 A 9 D 8 D 47 7 97 A 9 A 44 48 D 69 7 94 9 98 4 0 45 49 A70 74 95 A 0 99 D 5 46 50 7 D 75 96 00 A D 47 D 7 97 A 48 A 7 98 4 49 A 74 99 5 50 75 00 07
Hint / Slutin. () µr R O R. () m N m m R R R k N A A R If and bth dubled, then pressure remains same. () μr α 4. () If and dubled, then becmes fur times, µr µ R ass f litre nitrgen µ 5. (A) Gas equatin fr N mlecules, Nk 6. () N k µr Fr same µr µ, R and, 7. (A) mlecular weight f xygen (g) number f mles in 5 g f xygen 5 Equatin f state is µr 5 R 8. (A) tal number f mles is cnserved, R R R 0 0 0.5 5 0 0 0 0 + ( L 00 m ) R R R 0.5 atm 08
9. () he ideal gas equatin is 0. (). µr µr R µ R kn A k N A N A k Avgadr's number. R R R R cnst.. (D) µr µr. (D) µr. (). µr R R (, nstant ) ( lsed vessel i.e. vlume is cnstant) 4. (A). µr nstant ( temp. is cnst.) 95 95% 00 09
.056 0.056 5.6% ressure 5.6% increases. 5. (A) lsed essel. i.e. vlume remains cnstant. Frm, µr α 6. () ( µ,r nstant) 7. () µr R R density R density At 0 R 7 x...(i) density At 00 R7...(ii) density At 00 7 x 7 8. (A) µr 9. (A) µr cnstant since is cnst. 0. () µr R R 0
. () µr µ µ ( cnst.). (D) Nk N k Nw, N' 4 4 N k k N N' 4. () µr R (, R, - nstant) 4. () 7 0 0 6.50.5 kg Hence mass f the gas taken ut f the cylinder 0.5 7.5 kg µr R 5. () µr R 6. (A) cnstant k k k µr µr k µr µr k Hence 7 9 9
7. () Using Gay-lussac's law 8. () At cnstant vlume 9. (D) At cnstant ressure 0. () 00 00. () 0.954 05 05 0.0476 0.0476 4.76%. (D). () 7 40 7 0 7 0 4. () At cnstant ressure cnstant 9 0.07 9 5. () 6. (A) l 7. (A)
8. (A) µr µ ( and R cnstant ) µ µ 9. (D) µr µ and µ R R ' µ µ R R R 40. () Fr pen muth vessel, pressure is cnstant. vlume is als given cnstant. Hence frm µr R 4 th part escapes, s remaining mass in the vessel is 7 60 4 0 444 K 7 4 4. () Let initial cnditins, final cnditins ', ' y harle's law, ( remains cnstant ) ' ' '. '. ut as per questin, vlume is reduced by 0% means ' 0.9 s percentage f vlume leaked ut. 0.9 % 00 5%. 4. (D) ressure F A A t ( change in mmentum) 4. (A) ( Energy per unit vlume ) E E 44. ()
45. (A) 46. () E E 47. () he average kinetic energy E E k E 48. (D) Kinetic energy is a functin f temperature. 49. (A) E E E 50. () Kinetic energy f ideal gas depends nly n its temperature. Hence, it remains cnstant whether pressure is increased r decreased. 5. () Kinetic energy is directly prprtinal t temperature. Hence if temperature is dubled, kinetic energy will als be dubled. 5. () Average kinetic energy emperature E E 5. () E E E E 54. (D) E E 55. () Average translatinal K.E. f a mlecule is k At 00 K, average K.E. 6. 0 J At 600 K average K.E. We knw that k m At 00 K, 484 ms 6.0.40 J At 600 K, 484 684 ms 56. () Average translatinal K.E. f a mlecules k (Where, k ltzmann's cnstant ) his is same, fr all gases at same temperature. 57. (A) At 0 K Kinetic energy is zer. 4
58. () 59. () E E R E E' ' E 60. () k e 9 e.6 0 k.8 0 7.7 0 K 6. () R 6. () 6. () 4 5 5 4.4 64. (A) 65. (D) velcity des nt depend n pressure. 66. () R R R.7 67. (), duble the speed temperature shuld be made fur times i.e. 4 68. (A) 6 v 69. () velcity desn't depend n pressure, it depends upn temperature nly. 4 : R 70. () R and 7. (D) R R 7. () (, R cnstant) 5
R 7. () 5 He He H 7 H He He 0 7 K 0 H 5 4 7 49 74. () R R 8.00 90 Gas is hydrgen. 0 kg g 75. () speed, average speed, 76. () As t O 0 and speed increases by 0% 7 t. r 7 t.. 7 7 0 t 7. 57. 77. (A) R 78. () (, R cnstant) N O N O O O 79. () R % increase in R R 0 7. 00% 00% 5.5% R 7. 6
80. (A) 4 A A A A RA R A A A 8. (D) Since temperature is cnstant. s v remains same. R 8. () (, R nst. ) O O N N 8. () 84. () k m - m 85. () At a given temperature 86. (D) and 0 7 t 7 0 7 t 7 t 7 68.5-7 -04.75 7 4 4 0 87. () R R ; R R 4 R 4 v 50 ms 7
88. (A) R - 8.4 90 R 508.4 ms 8 0 here O SO 00 SO s 600 K 64 O SO 0 7 89. () v v 90. () He Ar R He 40 R 4 0.6 Ar 9. (D) 9. (A) S O H H O 9. (D) m m He m H H He R 94. () He 0 He H H 95. (A) R O O H H H O 96. () r 8
97. () R 7+90. 7+7 % increase 00% 0. 00% 0% 98. () 6 Hence the gas is H4 99. () Escape velcity frm the earth's surface is. kms S, escape R escape R k 00. () πd -.8 0 90-5 -0.4.06 0 0-7. 0 m llisin Frequency n. f cllisin per secnd 508.4 9 4.58 0-7. 0 k 0. (A) πnd πd 8 6.650 m - 8 0 8.490 R 508.4 ms 0. (A) A mnatmic gas mlecule has nly three translatinal degrees f freedm. 0. (D) A diatmic mlecule has three translatinal and tw rtatinal degrees f freedm. Hence ttal degrees f freedm, f + 5 04. () Fr a triatmic gas f 6 ( translatin + rtatinal ) 05. () p v f 06. () Degrees f freedm ( translatry ) + ( rtatry ) + ( vibratry ) 6 p v f 6 4. 07. (A) Nen gas is mn atmic and fr mn atmic gases v R 08. () When p and v are given with calric and R with Jule then p v R J 9
R R R+ R f 09. () p v R p R v R 0. () v.5 R R 0.67 f 5 R his is the value fr mn atmic gases. Accrding t the equilibrium therem, the mlar heat capacities shuld be independent f temperature Hw ever, variatins in v and p are bserved as the temperature changes. At very high temperatures, vibratins are als inprtant and that affects the values f v and p fr diatmic and ply atmic gases. Here in the questin accrding t given infrmatin (D) may be crrect answer.. () 5 7 µ µ 5 5 7 5. () mix.5 µ µ 5 7 4. (A) 5 f f f f 5. (D) mlar specific heat at cnstant pressure, p 7 R 6. (D) Since p v R v p R 7 fr a diatmic gas. 5 7. () As tan > tan Als frm 7 R R µr, 5 R 8. () As tan < tan frm µr ; Hence 9. () Fr an ideal gas cnstant i.e desn't vary with 0. (D) At cnstant temperature, cnstant 0