Tiêu đề 32. Kinetic Theory of Gases Hard.pdf ✅

1. The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at 00C is 3180 m/s. The pressure on the hydrogen gas is (Density of hydrogen gas is 2 3 8.99 10 kg / m −  , 1 atmosphere 5 2 = 1.01 10 N / m ) (a) 0.1 atm (b) 1.5 atm (c) 2.0 atm (d) 3.0 atm 2. The temperature of a gas is raised while its volume remains constant, the pressure exerted by a gas on the walls of the container increases because its molecules (a) Lose more kinetic energy to the wall (b) Are in contact with the wall for a shorter time (c) Strike the wall more often with higher velocities (d) Collide with each other less frequency 3. A cylinder of capacity 20 litres is filled with H2 gas. The total average kinetic energy of translatory motion of its molecules is J 5 1.5 10 . The pressure of hydrogen in the cylinder is (a) 6 2 2  10 N / m (b) 6 2 3 10 N / m (c) 6 2 4 10 N / m (d) 6 2 5  10 N / m 4. N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel at temperature T. The mean square of the velocity of molecules of gas B is v2 and the mean square of x component of the velocity of molecules of gas A is w2 . The ratio 2 2 v w is (a) 1 (b) 2 (c) 3 1 (d) 3 2 5. A flask contains 3 3 10 m − gas. At a temperature, the number of molecules of oxygen are 22 3.0 10 . The mass of an oxygen molecule is 26 5.3 10 −  kg and at that temperature the rms velocity of molecules is 400 m/s. The pressure in 2 N / m of the gas in the flask is (a) 4 8.48 10 (b) 4 2.87 10 (c) 4 25.44 10 (d) 4 12.72 10 6. A gas at a certain volume and temperature has pressure 75 cm. If the mass of the gas is doubled at the same volume and temperature, its new pressure is (a) 37.5 cm (b) 75 cm (c) 150 cm (d) 300 cm 7. A gas at 270C has a volume V and pressure P. On heating its pressure is doubled and volume becomes three times. The resulting temperature of the gas will be (a) 18000C (b) 1620C (c) 15270C (d) 6000C 8. A balloon contains 3 500 m of helium at 270C and 1 atmosphere pressure. The volume of the helium at – 3 0C temperature and 0.5 atmosphere pressure will be (a) 3 500 m (b) 3 700 m (c) 3 900 m (d) 3 1000 m 9. When volume of system is increased two times and temperature is decreased half of its initial temperature, then pressure becomes (a) 2 times (b) 4 times (c) 1 / 4 times (d) 1 / 2 times 10. Two identical glass bulbs are interconnected by a thin glass tube. A gas is filled in these bulbs at N.T.P. If one bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes 1.5 times. The temperature of hot bath will be (a) 1000C (b) 1820C (c) 2560C (d) 5460C 11. Two containers of equal volume contain the same gas at pressures P1 and P2 and absolute temperatures T1 and T2 respectively. On joining the vessels, the gas reaches a common pressure P and common temperature T. The ratio P/T is equal to (a) 2 2 1 1 T P T P + (b) 2 1 2 1 1 2 2 (T T ) P T P T + + (c) 2 1 2 1 2 2 1 (T T ) P T P T + + (d) 2 2 1 1 2 2T P T P + 12. An ideal monoatomic gas is confined in a cylinder by a spring- loaded piston if cross-section 3 2 8 10 m −  . Initially the gas is at 300K and occupies a volume of 3 3 2.4 10 m −  and the spring is in a relaxed state. The gas is heated by a small heater coil H. The force constant of the spring is 8000 N/m, and the atmospheric pressure is Pa 5 1.0 10 . The cylinder and piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and cylinder. There is no heat loss through heater coil wire leads and thermal capacity of the heater coil is negligible. With all the above assumptions, if the gas is heated by the heater until the piston moves out slowly by 0.1m, then the final temperature is (a) 400 K (b) 800 K (c) 1200 K (d) 300 K 13. At the top of a mountain a thermometer reads 70C and a barometer reads 70 cm of Hg. At the bottom of the mountain these read 270C and 76 cm of Hg respectively. Comparison of density of air at the top with that of bottom is Spring H Gas Ice Hot bath
(a) 75/76 (b) 70/76 (c) 76/75 (d) 76/70 14. Under which of the following conditions is the law PV = RT obeyed most closely by a real gas (a) High pressure and high temperature (b) Low pressure and low temperature (c) Low pressure and high temperature (d) High pressure and low temperature 15. The conversion of ideal gas into solids is (a) Possible only at low pressure (b) Possible only at low temperature (c) Possible only at low volume (d) Impossible 16. At room temperature, the rms speed of the molecules of certain diatomic gas is found to be 1930 m/s. The gas is (a) H2 (b) F2 (c) O2 (d) Cl2 17. Let A and B the two gases and given : B B A A M T M T = 4. ; where T is the temperature and M is the molecular mass. If CA and CB are the rms speed, then the ratio B A C C will be equal to (a) 2 (b) 4 (c) 1 (d) 0.5 18. The rms speed of the molecules of a gas in a vessel is 400 ms– 1 . If half of the gas leaks out at constant temperature, the rms speed of the remaining molecules will be (a) 800 ms–1 (b) 1 400 2 − ms (c) 400 ms–1 (d) 200 ms–1 19. The root mean square speed of hydrogen molecules at 300 K is 1930 m/s. Then the root mean square speed of oxygen molecules at 900 K will be (a) 1930 3 m / s (b) 836 m/s (c) 643 m/s (d) m / s 3 1930 20. At what temperature is the root mean square velocity of gaseous hydrogen molecules is equal to that of oxygen molecules at 470C (a) 20 K (b) 80 K (c) – 73 K (d) 3 K 21. Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will (a) Increase (b) Decrease (c) Remain same (d) Decrease for some, while increase for others 22. The speeds of 5 molecules of a gas (in arbitrary units) are as follows : 2, 3, 4, 5, 6. The root mean square speed for these molecules is (a) 2.91 (b) 3.52 (c) 4.00 (d) 4.24 23. Gas at a pressure P0 in contained as a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to (a) 0 4P (b) 0 2P (c) P0 (d) 2 P0 24. At which of the following temperature would the molecules of a gas have twice the average kinetic energy they have at 200C (a) 400C (b) 800C (c) 3130C (d) 5860C 25. A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per O2 molecule to that per N2 molecule is (a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) Depends on the moments of inertia of the two molecules 26. A gas mixture consists of molecules of type 1, 2 and 3 with molar masses m1  m2  m3 . rms v and K are the rms speed and average kinetic energy of the gases. Which of the following is true (a) 1 2 3 ( ) ( ) ( ) rms rms rms v  v  v and 1 2 3 (K) = (K) = (K) (b) 1 2 3 ( ) ( ) ( ) rms rms rms v = v = v and 1 2 3 (K) = (K)  (K) (c) 1 2 3 ( ) ( ) ( ) rms rms rms v  v  v and 1 2 3 (K)  (K)  (K) (d) 1 2 3 ( ) ( ) ( ) rms rms rms v  v  v and 1 2 3 (K)  (K)  (K) 27. The kinetic energy of one gram mole of a gas at normal temperature and pressure is (R = 8.31 J/mole-K) (a) J 4 0.56 10 (b) J 2 1.3 10 (c) J 2 2.7 10 (d) J 3 3.4 10 28. The average translational kinetic energy of O2 (molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of N 2 (molar mass 28) molecules in eV at the same temperature is (a) 0.0015 (b) 0.003 (c) 0.048 (d) 0.768 29. The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300 K are J 21 6.21 10 −  and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour) (a) 12.42 10 J, 968 m / s −21  (b) 8.78 10 J, 684 m / s −21  (c) 6.21 10 J, 968 m / s −21  (d)12.42 10 J, 684 m / s −21  7 oC, 70 cm of Hg 27oC, 76 cm of Hg
30. A box containing N molecules of a perfect gas at temperature T1 and pressure P1 . The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is P2 and temperature T2 , then (a) P2 = P1 , T2 = T1 (b) P2 = P1 , 2 1 2 T T = (c) P2 = 2P1 , T2 = T1 (d) P2 = 2P1 , 2 1 2 T T = 31. Three closed vessels A, B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities. Vessel A contains only O2 , B only N2 and C a mixture of equal quantities of O2 and N2 . If the average speed of the O2 molecules in vessel A is V1 , that of the N2 molecules in vessel B is V2 , the average speed of the O2 molecules in vessel C is (where M is the mass of an oxygen molecule) (a) (V1 + V2 )/ 2 (b) V1 (c) 1 / 2 1 2 (V V ) (d) 3kT / M 32. Hydrogen gas is filled in a balloon at 20°C. If temperature is made 40°C, pressure remaining same, what fraction of hydrogen will come out (a) 0.07 (b) 0.25 (c) 0.5 (d) 0.75 33. The expansion of unit mass of a perfect gas at constant pressure is shown in the diagram. Here (a) a = volume, b = 0C temperature (b) a = volume, b = K temperature (c) a = 0C temperature, b = volume (d) a = K temperature, b = volume 34. A gas is filled in the cylinder shown in the figure. The two pistons are joined by a string. If the gas is heated, the pistons will (a) Move towards left (b) Move towards right (c) Remain stationary (d) None of these 35. An ideal gas is initially at a temperature T and volume V. Its volume is increased by V due to an increase in temperature T, pressure remaining constant. The quantity V T V    = varies with temperature as (a) (b) (c) (d) 36. On 00C pressure measured by barometer is 760 mm. What will be pressure on 1000C (a) 760 mm (b) 730 mm (c) 780 mm (d) None of these 37. If pressure of a gas contained in a closed vessel is increased by 0.4% when heated by 10C, the initial temperature must be (a) 250 K (b) 2500C (c) 2500 K (d) 250C 38. Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes are plotted as shown in figure. Choose the correct alternative (a) 1 2 3 4 V = V , V = V and V2  V3 (b) 1 2 3 4 V = V , V = V and V2  V3 (c) V1 = V2 = V3 = V4 (d) V4  V3  V2  V1 39. The temperature of argon, kept in a vessel is raised by 10C at a constant volume. The total heat supplied to the gas is a combination of translational and rotational energies. Their respective shares are (a) 60% and 40% (b) 40% and 60% (c) 50% and 50% (d) 100% and 0% 40. ( ) CO2 O − C − O is a triatomic gas. Mean kinetic energy of one gram gas will be (If N-Avogadro's number, k-Boltzmann's constant and molecular weight of CO 2 = 44 ) (a) 3 / 88 NkT (b) 5 / 88 NkT (c) 6 / 88 NkT (d) 7 / 88 NkT 41. At standard temperature and pressure the density of a gas is 1.3 gm/ m3 and the speed of the sound in gas is 330 m/sec. Then the degree of freedom of the gas will be (a) 3 (b) 4 (c) 5 (d) 6 P T 1 3 2 4  T T + T (Temp. K)  T T + T (Temp. K)  T T + T (Temp. K)  T T + T (Temp. K) Gas a b O
42. If the mean free path of atoms is doubled then the pressure of gas will become (a) P / 4 (b) P / 2 (c) P / 8 (d) P 43. The mean free path of nitrogen molecules at a pressure of 1.0 atm and temperature 00C is m 7 0.8 10 −  . If the number of density of molecules is 25 3 2.7 10 perm , then the molecular diameter is (a) 3.2 nm (b) 3.2Å (c) 3.2m (d) 2.3mm 44. Find the ratio of specific heat at constant pressure to the specific heat constant volume for NH 3 (a) 1.33 (b) 1.44 (c) 1.28 (d) 1.67 45. For a gas = 0.67 Cv R . This gas is made up of molecules which are (a) Diatomic (b) Mixture of diatomic and polyatomic molecules (c) Monoatomic (d) Polyatomic 46. 40 calories of heat is needed to raise the temperature of 1 mole of an ideal monoatomic gas from 200C to 300C at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume ( 2 ) −1 −1 R = calorie mole K is (a) 20 calorie (b) 40 calorie (c) 60 calorie (d) 80 calorie 47. At constant volume the specific heat of a gas is , 2 3R then the value of  will be (a) 2 3 (b) 2 5 (c) 3 5 (d) None of the above 48. The density of a polyatomic gas is standard conditions is 0.795 −3 kgm . The specific heat of the gas at constant volume is (a) 1 1 930 - − − J kg K (b) 1 1 1400 - − − J kg K (c) 1 1 1120 - − − J kg K (d) 1 1 925 - − − J kg K 49. The value of Cp −Cv = 1.00 R for a gas in state A and Cp − Cv = 1.06R in another state. If PA and PB denote the pressure and TA and TB denote the temperatures in the two states, then (a) PA = PB , TA  TB (b) PA  PB , TA = TB (c) PA  PB , TA  TB (d) PA  PB , TA  TB 50. If two moles of diatomic gas and one mole of monoatomic gas are mixed with then the ratio of specific heats is (a) 3 7 (b) 4 5 (c) 13 19 (d) 19 15 51. 22 gm of CO2 at 270C is mixed with 16 gm of O2 at 370C. The temperature of the mixture is (a) 320C (b) 270C (c) 370C (d) 30.50C 52. A vessel is filled with a gas at a pressure of 76 cm of mercury at a certain temperature. The mass of the gas is increased by 50 % by introducing more gas in the vessel at the same temperature. The resultant pressure, in cm of Hg, is - (a) 76 (b) 152 (c) 114 (d) 1117 53. Container below are filled with three different gases as shown. Piston is made to oscillate in below three cases. Time Period of oscillation is TA, TB, TC. Then- N2 m He m SO2 m (a) TA>TB> TC (b) TC> TA> TB (c) TC> TB> TA (d) TB> TA> TC 54. An ideal gas is held in a container of volume V at pressure P. The average speed of a gas molecule under these conditions is v. If now the volume and pressure are changed to 2V and 2P, the average speed of a molecule will be` (a) 1/2 v (b) v (c) 2v (d) 4v 55. One kg of a diatomic gas is at a pressure of 8 × 104 N/m2 . The density of the gas is 4 kg/m3 . What is the energy of the gas due to its thermal motion ? (a) 3 × 104 J (b) 5 × 104 J (c) × 104 J (d) × 104 J 56. Maxwell's velocity distribution curve is given for two different temperatures. For the given curves - T1 T2 N V (a) T1> T2 (b) T1< T2 (c) T1 T2 (d) T1 = T2 57. Pressure versus density graph of an ideal gas is shown in figure - P  C D A B