Title 32. Kinetic Theory of Gases Medium.pdf ✅

1. Molecular motion shows its self as (a) Temperature (b) Internal energy (c) Friction (d) Viscosity 2. An air bubble of volume 1.0 cm3 rises from the bottom of a lake 40 m deep at a temperature of 12°C. To what volume does it grow when it reaches the surface, which is of a temperature of 35°C? (a) 10.6 × 10–6 m3 (b) 5.3 × 10–6 m3 (c) 2.8 × 10–6 m3 (d) 15.6 × 10–6 m3 3. A real gas behaves like an ideal gas if its (a) Both pressure and temperature are high (b) Both pressure and temperature are low (c) Pressure is high and temperature is low (d) Pressure is low and temperature is high 4. The diameter of an oxygen molecule is 3. o A The ratio of molecular volume to the actual volume occupied by the oxygen gas at STP is (a) 2 × 10–4 (b) 1 × 10–4 (c) 1.5 × 10–4 (d) 4 × 10–4 5. One half mole each of nitrogen, oxygen and carbon dioxide are mixed in enclosure of volume 5 litres and temperature 27°C. The pressure exerted by mixture is (R = 8.31 J mol–1 K–1 ) (a) 7.8 × 105 N m–2 (b) 5 × 105 N m–2 (c) 6 × 105 N m–2 (d) 3 × 105 N m–2 6. A vessel contains two non-reactive gases neon (monoatomic) and oxygen (diatomic). The ratio of their partial pressures is 3 : 2. The ratio of number of molecules is (a) 2 3 (b) 3 2 (c) 3 1 (d) 2 1 7. From a certain apparatus, the diffusion rate of hydrogen has an average value of 28.7. The diffusion of another gas under the same conditions is measured to have an average rate of 7.2 cm3 s –1 . The gas is (a) Nitrogen (b) Helium (c) Argon (d) Oxygen 8. When the temperature of a gas filled in a closed vessel is increased by 1°C, its pressure increases by 0.4 percent. The initial temperature of gas was (a) 250°C (b) 25 °C (c) 250 K (d) 25 K 9. The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be (where R is the gas constant) (a) PV = (5/32) RT (b) PV = 5 RT (c) PV = (5/2) RT (d) PV = (5/16) RT 10. A balloon contains 1500 m3 of helium at 27°C and 4 atmospheric pressure. The volume of helium at –3°C temperature and 2 atmospheric pressure will be (a) 1500 m3 (b) 1700 m3 (c) 1900 m3 (d) 2700 m3 11. The volume of water molecule is (Take, density of water is 103 kg m–3 and Avogadro’s number = 6 × 1023 mole–1 ) (a) 3 × 10–28 m3 (b) 3 × 10–29 m3 (c) 1.5 × 10–28 m3 (d) 1.5 × 10–29 m3 12. If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature (a) Is doubled (b) Becomes one-fourth (c) Remains constant (d) Become four times 13. An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume (g = 1.4 and 2–1.4 = 0.38). The ratio of the final to initial pressure is (a) 0.76 : 1 (b) 1 : 1 (c) 0.66 : 1 (d) 0.86 : 1 14. If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature (a) Is doubled (b) Becomes one-fourth (c) Remains constant (d) Become four times 15. If three molecules have velocities 0.5 km s–1 , 1 km s–1 and 2 km s–1 , the ratio of the rms speed and average speed is (a) 2.15 (b) 1.14 (c) 0.53 (d) 3.96 16. The internal energy of one gram of helium at 100 K and one atmospheric pressure is (a) 100 J (b) 1200 J (c) 300 J (d) 500 J 17. The kinetic energy of 1 g molecule of a gas, at normal temperature and pressure, is (a) 0.56 × 104 J (b) 2.7 × 102 J (c) 1.3 × 102 J (d) 3.4 × 103 J 18. A gas is filled in a container at pressure P0 . If the mass of molecules is halved and their rms speed is doubled, then the resultant pressure would be (a) 2P0 (b) 4P0 (c) 4 P0 (d) 2 P0 19. Pressure of a gas at constant volume is proportional to (a) Total internal energy of the gas (b) Average kinetic energy of the molecules (c) Average potential energy of the molecules (d) Total energy of the gas 20. An insulated container containing monoatomic gas of molar mass m moving with a velocity v0 . If the container is suddenly stopped. The change in temperature is (a) 2R m 2 0 (b) 3R m 2 0 (c) 2 m 0 R  (d) 2R 3m 2 0 21. Two moles of a gas A at 27°C mixed with a 3 moles of gas at 37°C. If both are monoatomic ideal gases, what will be the temperature of the mixture ? (a) 66°C (b) 11°C (c) 22°C (d) 33°C 22. The average translational kinetic energy of O2 at a particular temperatures 0.768 eV. The average translational kinetic energy of N2 molecules in eV at the same temperature is (a) 0.0015 (b) 0.0030 (c) 0.048 (d) 0.768
23. At what temperature is the rms velocity of hydrogen molecule equal to that of an oxygen molecule at 47°C ? (a)10 K (b) 20 K (c) 30 K (d) 40 K 24. The root mean square speed of smoke particles each of mass 5 × 10–17 kg in their Brownian motion in air at N.T.P is (a) 3 × 10–2 m s–1 (b) 1.5 × 10–2 m s–1 (c) 3 × 10–3 m s–1 (d) 1.5 × 10–3 m s–1 25. When an ideal gas is compressed adiabatically, its temperature rises the molecules on the average have more kinetic energy than before. The kinetic energy increases (a) Because of collisions with moving parts of the wall only. (b) Because of collisions with the entire wall. (c) Because the molecules gets accelerated in their motion inside the volume. (d) Because the redistribution of energy amongst the molecules. 26. The molecules of a given mass of gas have root mean square speeds of 100 m s–1 at 27 °C and 1 atmospheric pressure. The root mean square speeds of the molecues of the gas at 127 °c and 2 atmosperic pressure is (a) 3 200 (b) 3 100 (c) 3 400 (d) 3 200 27. Which one of the following is not an assumption of kinetic theory of gases? (a) The volume occupied by the molecules of the gas is negligible. (b) The force of attraction between the molecules is negligible. (c) The collision between the molecules are elastic. (d) All molecules have same speed. 28. The temperature of an ideal gas is increased from 27°C to 127 °C, then percentage increase in vrms is (a) 37% (b) 11% (c) 33% (d) 15.5% 29. The temperature of 2 mole of an ideal monoatomic gas is raised to 15 K at constant volume. The work done by the gas is (a) Zero (b) 30 J (c) 420 J (d) 50 J 30. The ratio of the molar heat capacities of a diatomic gas at constant pressure to that at constant volume is (a) 5 7 (b) 2 3 (c) 5 3 (d) 2 5 31. The heat capacity per mole of water (R is universal gas constant) (a) 9R (b) 2 9 R (c) 6R (d) 5R 32. Three moles of oxygen are mixed with two moles helium. What will be the ratio of specific heats at constant pressure and constant volume for the mixture ? (a) 2.5 (b) 3.5 (c) 1.5 (d) 1 33. A cylinder of fixed capacity 44.8 litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by 15°C ? (R = 8.31 K mol–1 K–1 ) (a) 265 J (b) 310.10 J (c) 373.95 J (d) 387.97 J 34. At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of helium gas atom at –20°C ? (Atomic mass of Ar = 39 u and He = 400 u) (a) 2.52 × 103 K (b) 2.52 × 102 K (c) 4.03 × 103 K (d) 4.03 × 102 K 35. 1/2 mole of helium is contained in a container at STP. How much heat energy is needed to double the pressure of the gas, (volume is constant) heat capacity of gas is 3 J g–1 K–1 . (a) 1436 J (b) 736 J (c) 1638 J (d) 5698 J 36. One mole of an ideal monoatomic gas at temperature T0 expands slowly according to the law V P = constant. If the final temperature is 2T0 , heat supplied to the gas is (a) 2RT0 (b) RT0 (c) 2 3 RT0 (d) 2 1 RT0 37. If a gas has n degrees of freedom ratio of specific heats of gas is (a) 2 1+ n (b) n 1 1+ (c) 2 n 1+ (d) n 2 1+ 38. If for a gas CV R = 0.67, this gas is made up molecules which are (a) Monoatomic (b) Diatomic (c) Polyatomic (d) Mixture of diatomic and polyatomic molecules 39. The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K, the rms velocity of the gas molecules is vrms , then at 480 K, it becomes (a) 4 vrms (b) 2 vrms (c) 2 rms (d) 4 rms 40. 1 mole of a gas with 5 7  = is mixed with 1 mole of gas with 3 5  = , the value of  of the resulting mixture of (a) 5 7 (b) 5 2 (c) 2 3 (d) 7 12 41. An ideal gas at a pressure of 1 atmosphere and temperature of 27°C is compressed adiabatically until its pressure becomes 8 times the initial pressure. Then the final temperature is        = 2 3 Given
(a) 627°C (b) 527°C (c) 427°C (d) 327°C 42. A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500 m/s in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground (a) Remains the same because 500 m/s is very much smaller than nrms of the gas (b) Remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls (c) Will increase by a factor equal to [v2 rms + (500)2 ]/v2 rms , where vrms was the original mean square velocity of the gas (d) Will be different on the top wall and bottom wall of the vessel 43. 1 mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at 300 K as shown in figure. One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At any given time, (a) The pressure on EFGH would be zero (b) The pressure on all the faces will be equal (c) The pressure of EFGH would be double the pressure on ABCD (d) The pressure on EFGH would be half that on ABCD. 44. Boyle’s law is applicable for an (a) Adiabatic process (b) Isothermal process (c) Isobaric process (d) Isochoric process 45. A cylinder containing an ideal gas is vertical position and has a piston of mass M that is able to move up or down without friction. If the temperature is increased. (a) Both P and V of the gas will change (b) Only P will increase according to Charle’s law (c) V will change but not P (d) P will change but not V 46. Volume versus temperature graphs for a given mass of an ideal gas are shown in figure at two different values of constant pressure. What can be inferred about relation between P1 and P2 ? (a) P1 > P2 (b) P1 = P2 (c) P1 < P2 (d) Data is insufficient 47. 1 mole of H2 gas is contained in a box of volume V = 1.00 m3 at T = 300 K. The gas is heated to a temperature of T = 3000 K and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal) (a) Same as the pressure initially (b) 2 time the pressure initially (c) 10 times the pressure initially (d) 20 times the pressure initially 48. A vessel of volume V contains a mixture of 1 mole of hydrogen and 1 mole of oxygen (both considered as ideal). Let f 1 (v)dv denote the faction of molecules with speed between v and (v + dv) with f 2 (v)dv, similarly for oxygen. Then (a) f 1 (v) + f 2 (v) = f(v) obeys the Maxwell’s distribution law (b) f 1 (v), f 2 (v) will obeys the Maxwell’s distribution law separately (c) Neither f 1 (v) nor f 2 (v) will obeys the Maxwell’s distribution law (d) f 2 (v) and f 1 (v) will be the same 49. A gas at 300 K has pressure 4 × 10–10 N m–2 . If k B = 1.38 × 10– 23 J K–1 , the number of molecules per cm3 of the order of (a) 103 (b) 105 (c) 106 (d) 109 50. The volume of vessel A is twice the volume of another vessel B, and both of them are filed with the same gas. If the gas in A is at twice the temperature and twice the pressure in comparison to the gas in B, then the ratio of the gas molecules in A to that of B is (a) 2 1 (b) 1 2 (c) 2 3 (d) 3 2 51. A cylinder contains 10 kg of gas at a pressure of 107 N m–2 . The quantity of gas taken out of the cylinder, if final pressure is 2.5 × 106 N m–2 is (a) 9.5 kg (b) 7.5 kg (c) 14.2 kg (d) Zero 52. Which of the following graphs represent the behaviour of an ideal gas ? (a) (b)
(c) (d) 53. Given is the graph between T PV and P for 1 g of oxygen gas at two different temperatures T1 and T2 , as shown in figure. Given, density of oxygen = 1.427 kg m–3 . The value of PV/T at the point A and the relation between T1 and T2 are respectively. (a) 0.259 J K–1 and T1 < T2 (b) 8.314 g J mol–1 K–1 and T1 > T2 (c) 0.259 J K–1 and T1 > T2 (d) 4.28 g J K–1 and T1 < T2 54. A vessel has 6 g of oxygen at pressure P and temperature 400 K. A small hole is made in it so that oxygen leaks out. How much oxygen leaks out if the final pressure is 2 P and temperature 300 K ? (a) 5 g (b) 4 g (c) 2 g (d) 3 g 55. 0.014 kg of nitrogen is enclosed in a vessel at a temperature of 27°C. How much heat has to be transferred to the gas to double the rms velocity of its molecules? (a) 1200 K (b) 600 K (c) 300 K (d) 150 K 56. In a certain region of space there are only 5 gaseous molecules per cm3 on an average. The temperature there is 3 K. The pressure of this gas is (k B = 1.38 × 10–23 J mol–1 K–1 ) (a) 20.7 × 10–16 N m–1 (b) 20.7 × 10–17 N m–1 (c) 10.7 × 10–16 N m–1 (d) 10.7 × 10–17 N m–1 57. The kinetic theory of gases gives the formula PV = 3 1 Nmv–2 for the pressure P exerted by a gas enclosed in a volume V. The term Nm represents (a) The mass of a mole of the gas (b) The mass of the gas present in the volume V (c) The average mass of one molecule of the gas (d) The total number of molecules present in volume V 58. If CP and CV denoted the specific heats of unit mass of nitrogen at constant pressure and volume respectively, then (a) CP – CV = 28 R (b) CP – CV = 7 R (c) CP – CV = 14 R (d) CP – CV = R 59. The equation of state corresponding to 8g of O2 is (a) PV = 8RT (b) PV = RT / 4 (c) PV = RT (d) PV = RT / 2 60. A flask is filled with 13 gm of an ideal gas at 270C and its temperature is raised to 520C. The mass of the gas that has to be released to maintain the temperature of the gas in the flask at 520C and the pressure remaining the same is (a) 2.5 g (b) 2.0 g (c) 1.5 g (d) 1.0 g 61. Air is filled at 600C in a vessel of open mouth. The vessel is heated to a temperature T so that 1 / 4th part of air escapes. Assuming the volume of vessel remaining constant, the value of T is (a) 800C (b) 4440C (c) 3330C (d) 1710C 62. If the intermolecular forces vanish away, the volume occupied by the molecules contained in 4.5 kg water at standard temperature and pressure will be given by (a) 3 5.6 m (b) 3 4.5 m (c) 11.2 litre (d) 3 11.2 m 63. The pressure P, volume V and temperature T of a gas in the jar A and the other gas in the jar B at pressure 2P, volume V/4 and temperature 2T, then the ratio of the number of molecules in the jar A and B will be (a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) 4 : 1 64. The expansion of an ideal gas of mass m at a constant pressure P is given by the straight line D. Then the expansion of the same ideal gas of mass 2m at a pressure P/ 2 is given by the straight line (a) E (b) C (c) B (d) A 65. If the value of molar gas constant is 8.3 J/mole-K, the n specific gas constant for hydrogen in J/mole-K will be (a) 4.15 (b) 8.3 (c) 16.6 (d) None of these 66. When an ideal gas is compressed isothermally then its pressure increases because : (a) its potential energy decreases (b) its kinetic energy increases and molec move apart (c) its number of collisions per unit area with walls of container increases (d) molecular energy increases A B C D E 8 6 4 2 1 Volume Temperature