Kinetic Theory of Gases PYQs Set 2 (PDF)

Set 2 of 8 · Questions 31-60 of 229

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinetic Theory of Gases · Set 2 (Q31-60)
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31. $Two spherical black bodies have radii r_{1} and r_{2} . Their surface temperature are T_{1} and T_{2} . If they radiate same power then \frac{r _{2}}{r _{1}} is$ (1) $\frac{T _{1}}{T _{2}}$ (2) $\frac{T _{2}}{T _{1}}$ (3) $(\frac{T _{1}}{T _{2}})^{2}$ (4) $(\frac{T _{2}}{T _{1}})^{2}$ 32. $The specific heat at constant pressure of a real gas obeying P V^{2} = RT equation is:$ (1) $\frac{R}{3} + C_{V}$ (2) $C_{V} + R$ (3) $C_{V} + \frac{R}{2 V}$ (4) $R$ 33. $The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27 °C is$ (1) $927°C$ (2) $327°C$ (3) $1227 O$ (4) $627°C$ 34. $Statement (I) : Gas thermometers are less sensitive than liquid thermometers. Statement (II) : The ratio of universal gas constant and avagadro's number is called Boltzman's constant. Statement (III) : The density of a given mass of a gas at constant pressure is inversely proportional to its absolute temperature. The correct option among the following is$ (1) $Statements I, II, III are true.$ (2) $Statements I, II are true, but statement III is false.$ (3) $Statements II, III are true, but statement I is false.$ (4) $Statements I, II, III are false.$ 35. $A polyatomic ideal gas has 24 vibrational modes. What is the value of γ ?$ (1) $1.03$ (2) $3$ (3) $1.37$ (4) $10.3$ 36. $At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given: mass of oxygen molecule, m = 2.76 \times 10^{- 26} kg . Boltzmann's constant k_{B} = 1.38 \times 10^{- 23} J K^{- 1}) [NEET 2018]$ (1) $5.016 \times 10^{4} K$ (2) $8.326 \times 10^{4} K$ (3) $2.508 \times 10^{4} K$ (4) $1.254 \times 10^{4} K$ 37. $An ideal gas at pressure P is enclosed in a container that is placed in a reservoir at temperature T . If the volume of the gas is increased to two times its original value, then the new pressure P^{’} =________P$ (1) $\frac{1}{2}$ (2) $2$ (3) $1$ (4) $Cannot be determined$ 38. $When some amount of heat energy is supplied to a monatomic gas, the percentage of heat energy used for increasing the internal energy of the gas (γ = 5/3) is$ (1) $60$ (2) $40$ (3) $20$ (4) $80$ 39. $The r.m.s. speed of oxygen molecules at 47^{\circ} C is equal to that of the hydrogen molecules kept at____^{\circ} C. (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)$ (1) $-235$ (2) $-253$ (3) $-100$ (4) $-20$ 40. $A mixture of gasses consists of 16 g of Helium and 16 g of Oxygen. The ratio of specific heats of the mixture is nearly$ (1) $1.33$ (2) $1.4$ (3) $1.56$ (4) $1.62$ 41. $Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :$ (1) $\frac{9}{4} R$ (2) $\frac{7}{4} R$ (3) $\frac{3}{2} R$ (4) $\frac{5}{2} R$ 42. $The specific heats, C_{p} and C_{v} of a gas of diatomic molecules, A, are given(in units of J mol^{- 1} K^{- 1}) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then?$ (1) $A is rigid but B has a vibrational mode.$ (2) $A has a vibrational mode but B has none.$ (3) $A has one vibrational mode and B has two.$ (4) $Both A and B have a vibrational mode each.$ 43. $The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3 \times 10^{- 7} m and 600 m / s respectively. Find the frequency of its collisions.$ (1) $2 \times 10^{10} / s$ (2) $9 \times 10^{5} / s$ (3) $2 \times 10^{9} / s$ (4) $5 \times 10^{8} / s$ 44. $A jar ' P' is filled with gas having pressure, volume and temperature P, V, T respectively. Another gas jar Q filled with a gas having pressure 2 P . volume V /4 and temperature 2 T . The ratio of the number of molecules in jar P to those in jar Q is$ (1) $1 : 1$ (2) $1 : 2$ (3) $2 : 1$ (4) $4 : 1$ 45. $A gas mixture consists of 2 moles of O_{2} and 4 moles of Ar at temperature T . Neglecting all vibrational modes, the total internal energy of the system is [NEET 2017]$ (1) $4 RT$ (2) $15 RT$ (3) $9 RT$ (4) $11 RT$ 46. $Uranium has two isotopes of masses 235 and 238 units. If both of them are present in uranium hexafluoride gas, find the percentage ratio of difference in rms velocities of two isotopes to the rms velocity of heavier isotope.$ (1) $1.64$ (2) $0.064$ (3) $0.64$ (4) $6.4$ 47. $A gas is compressed isothermally. The r.m.s. velocity of its molecules$ (1) $increases$ (2) $decreases$ (3) $first increases and then decreases$ (4) $remains the same$ 48. $For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?$ (1) (2) (3) (4) 49. $The temperature of a gas is - 68^{\circ} C . To what temperature should it be heated, so that the r.m.s. velocity of the molecules be doubled?$ (1) $357^{\circ} C$ (2) $457^{\circ} C$ (3) $547^{\circ} C$ (4) $820^{\circ} C$ 50. $4.0 g of a gas occupies 22.4 L at NTP. The specific heat capacity of the gas at constant volume is 5.0 JK^{- 1} mol^{- 1} . If the speed of sound in this gas at NTP is 952 ms^{- 1}, then the heat capacity at constant pressure is (Take gas constant R = 8.3 JK^{- 1} mol^{- 1})$ (1) $8.0 JK^{- 1} mol^{- 1}$ (2) $7.5 JK^{- 1} mol^{- 1}$ (3) $7.0 JK^{- 1} mol^{- 1}$ (4) $8.5 JK^{- 1} mol^{- 1}$ 51. $In an ideal gas, if the masses of all molecules are doubled and their speeds are halved, then the ratio of initial and final pressure of the gas is$ (1) $2 : 1$ (2) $1 : 2$ (3) $4 : 1$ (4) $1 : 4$ 52. $One mole of an ideal monoatomic gas undergoes a process described by the equation p V^{3} = constant. The heat capacity of the gas during this process if [NEET 2016]$ (1) $\frac{3}{2} R$ (2) $\frac{5}{2} R$ (3) $2 R$ (4) $R$ 53. $A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is$ (1) $29 RT$ (2) $20 RT$ (3) $27 RT$ (4) $21 RT$ 54. $At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47^{\circ} C ?$ (1) $80 K$ (2) $- 73 K$ (3) $4 K$ (4) $20 K$ 55. $A block body radiates heat at temperature ' T_{1}' and ' T_{2}' (T_{2} > T_{1}) . The frequency corresponding to maximum energy is$ (1) $more at T_{1}$ (2) $more at T_{2}$ (3) $equal for T_{1} and T_{2}$ (4) $independent of T_{1} and T_{2}$ 56. $The mean free path of a molecule of diameter 5 \times 10^{- 10} m at the temperature 41^{\circ} C and pressure 1.38 \times 10^{5} Pa, is given as____m. (Given k_{B} = 1.38 \times 10^{- 23} J / K).$ (1) $102 \times 1 0^{- 8}$ (2) $22 \times 1 0^{- 8}$ (3) $22\times 1 0^{- 10}$ (4) $2 \times 10^{- 8}$ 57. $The kinetic energy of translation of the molecules in 50 g of CO_{2} gas at 17^{\circ} C is$ (1) $4205.5 J$ (2) $4102.8 J$ (3) $3582.7 J$ (4) $3986.3 J$ 58. $If the pressure of a gas increases by 2 % at constant volume, then its temperature$ (1) $increases by 2 %$ (2) $decreases by 2 %$ (3) $does not change$ (4) $decreases by 1 %$ 59. $Nitrogen gas is at 300^{\circ} C temperature. The temperature (in K) at which the rms speed of a H_{2} molecule would be equal to the rms speed of a nitrogen molecule, is (Molar mass of N_{2} gas 28 g).$ 60. $Gaseous cyclobutene isomerizes to butadiene in a first order process which has a ’ k ’ value of 3.3 \times 10^{- 4} s^{- 1} at 153^{\circ} C . The time in minutes it takes for the isomerization to proceed 40 % to completion at this temperature is _______(Rounded off to the nearest integer)$