Kinetic Theory of Gases PYQs Set 3 (PDF)

Set 3 of 8 · Questions 61-90 of 229

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinetic Theory of Gases · Set 3 (Q61-90)
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61. $Three moles of a gas at a temperature ' T' is heated to thrice its volume by keeping the pressure constant. If ' γ' is the ratio of specific heats, then the increase in internal energy of the gas is$ (1) $\frac{3 RT}{γ - 1}$ (2) $\frac{6 RT}{γ - 1}$ (3) $\frac{8 R}{γ - 1}$ (4) $\frac{3 R}{2 ( γ - 1 )}$ 62. $If the root mean square (rms) speed of nitrogen molecules at room temperature is 100 m / s, then the rms speed of Helium molecule at the same temperature is$ (1) $1007 m / s$ (2) $350 m / s$ (3) $5014 m / s$ (4) $100 m / s$ 63. $A vessel contains 16g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the vessel in c m^{3} is :$ (1) $72 x 1 0^{5}$ (2) $32x 1 0^{5}$ (3) $27 x 1 0^{4}$ (4) $54 x 1 0^{4}$ 64. $The mean free path for a gas at temperature 300 K and pressure 600 torr is 10^{- 7} m . The mean free path of the gas at a temperature 400 K and pressure 200 torr will be$ (1) $2.5 \times 10^{- 8} m$ (2) $4.4 \times 10^{- 8} m$ (3) $3.3 \times 10^{- 8} m$ (4) $4 \times 10^{- 7} m$ 65. $The mean free path λ for a gas, with molecular diameter d and number density n can be expressed as [NEET 2020]$ (1) $\frac{1}{2 nπ d ^{2}}$ (2) $\frac{1}{2 n ^{2} π d ^{2}}$ (3) $\frac{1}{2 n ^{2} π ^{2} d ^{2}}$ (4) $\frac{1}{2 nπd}$ 66. $If 10^{22} gas molecules each of mass 10^{- 26} kg collide with a surface (perpendicular to it) elastically per second over an area 1 m^{2} with a speed 10^{4} m / s, the pressure exerted by the gas molecules will be of the order of :$ (1) $10^{4} N/m²$ (2) $2 N / m^{2}$ (3) $10^{3} N/m²$ (4) $10^{16} N/m²$ 67. $Number of molecules in a volume of 4 cm^{3} of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to ? (Given, mean kinetic energy of a molecule (at T) is 4 \times 10^{- 14} erg, g = 980 cm / s^{2} density of mercury = 13.6 g / cm^{3})$ (1) $5.8 \times 10^{18}$ (2) $4.0 \times 10^{16}$ (3) $5.8 \times 10^{16}$ (4) $4.0 \times 10^{18}$ 68. $The average kinetic energy of a monatomic molecule is 0.414 eV at temperature : (Use K_{B} = 1.38 \times 10^{- 23} J / mol - K)$ (1) $3000 K$ (2) $3200 K$ (3) $1600 K$ (4) $1500 K$ 69. $Three moles of ideal gas A with \frac{C _{P}}{C _{V}} = \frac{4}{3} is mixed with two moles of another ideal gas B with \frac{C _{P}}{C _{V}} = \frac{5}{3} The \frac{C _{P}}{C _{V}} of mixture is (Assuming temperature is constant)$ (1) $1.5$ (2) $1.42$ (3) $1.7$ (4) $1.3$ 70. $A gas mixture contains n_{1} moles of a monoatomic gas and n_{2} moles of gas of rigid diatomic molecules. Each molecule in monoatomic and diatomic gas has 3 and 5 degree of freedom respectively. If the adiabatic exponent (\frac{C _{p}}{C _{v}}) for this gas mixture is 1.5 , then the ratio \frac{n _{1}}{n _{2}} will bc$ (1) $1$ (2) $1.5$ (3) $2$ (4) $2.5$ 71. $A 25 \times 10^{- 3} m^{3} volume cylinder is filledwith 1mol of O^{2} gas at room temperature (300 K). The molecular diameter of O^{2} , and its root mean square speed, are found to be 0.3nm, and 200m/s, respectively. What is the average collision rate (per second) for an O^{2} molecule ?$ (1) $10^{12}$ (2) $10^{11}$ (3) $10^{10}$ (4) $10^{13}$ 72. $The temperature of an ideal gas is increased from 27^{\circ} C to 927^{\circ} C . The r.m.s. speed of its molecules becomes$ (1) $twice$ (2) $half$ (3) $four times$ (4) $one-fourth.$ 73. $An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is 6 \times 10^{- 8} s . If the pressure is doubled and temperature is increased to 500K, the mean time between two successive collisions will be close to:$ (1) $2 \times 10^{- 7} s$ (2) $4 \times 10^{- 8} s$ (3) $0.5 \times 10^{- 8} s$ (4) $3 \times 10^{- 6} s$ 74. $An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true? (A) the mean free path of the molecules decreases. (B) the mean collision time between the molecules decreases. the mean free path remains unchanged (D) the mean collision time remains unchanged$ (1) $(C) and (D)$ (2) $(A) and (D)$ (3) $(B) and (C)$ (4) $(A) and (B)$ 75. $The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation P T^{2} = constant. The volume expansion coefficient of the gas will be:$ (1) $3 T^{2}$ (2) $\frac{3}{T ^{2}}$ (3) $\frac{3}{T ^{3}}$ (4) $\frac{3}{T}$ 76. $Given below are two statements: Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II : in a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below:$ (1) $Both statement I and statement II are false.$ (2) $Both statement I and statement II are true.$ (3) $Statement I is false but statement II is true$ (4) $Statement I is true but statement II is false.$ 77. $What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibriumat a temperature T (k_{B}) is Boltzmann constant)$ (1) $\frac{1}{2} k_{B} T$ (2) $\frac{2}{3} k_{B} T$ (3) $\frac{3}{2} k_{B} T$ (4) $k_{B} T$ 78. $A cylindrical container of volume 4. 0 x 1 0^{- 3} m^{3} contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400K. The pressure of the mixture of gases is : [Take gas constant as 8.3 J m o l^{- 1} K^{- 1}]$ (1) $249 \times 1 0^{1} P a$ (2) $24.9 \times 1 0^{3} P a$ (3) $24.9 \times 1 0^{5} P a$ (4) $24.9Pa$ 79. $Energy of 10 non-rigid diatomic molecules at temperature T is:$ (1) $70 K_{B} T$ (2) $35 K_{B} T$ (3) $\frac{7}{2} RT$ (4) $35 RT$ 80. $A flask contains argon and chlorine in the ratio of 2 : 1 by mass. The temperature of the mixture is 27^{\circ} C . The ratio of average kinetic energies of two gases per molecule is$ (1) $1 : 1$ (2) $2 : 1$ (3) $3 : 1$ (4) $6 : 1$ 81. $If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by:$ (1) $2 nπ d^{2}$ (2) $\frac{1}{2 nπ d ^{2}}$ (3) $\frac{1}{2 nπ d ^{2}}$ (4) $\frac{1}{2 n ^{2} π ^{2} d ^{2}}$ 82. $For a given gas at 1 atm pressure, rmsspeed of the molecule is 200m/s at 127° C . At 2 atm pressure and at 227° C, the rms speed of the molecules will be:$ (1) $100 m/s$ (2) $805 m/s$ (3) $1005 m/s$ (4) $80 m/s$ 83. $RMS velocity of oxygen molecules at NTP is 0.5 km / s . The RMS velocity for the hydrogen molecule at NTP is$ (1) $4 km / s$ (2) $2 km / s$ (3) $3 km / s$ (4) $1 km / s$ 84. $Two kg of a monoatomic gas is at a pressure of 4 \times 10^{4} N / m^{2} . The density of the gas is 8 kg / m^{3} . What is the order of energy of the gas due to its thermal motion ?$ (1) $10^{3} J$ (2) $10^{5} J$ (3) $10^{4} J$ (4) $10^{6} J$ 85. $The rms speed of oxygen and room temperature is about 500 ms^{- 1} . The rms speed of hydrogen at the same temperature is about$ (1) $125 m s^{- 1}$ (2) $2000 m s^{- 1}$ (3) $8000 m s^{- 1}$ (4) $500 m s^{- 1}$ 86. $n mole of He and 2 n mole of O_{2} is mixed in a container. Then (\frac{C _{P}}{C _{V}})_{mix} will be$ (1) $\frac{19}{13}$ (2) $\frac{40}{27}$ (3) $\frac{1}{3}$ (4) $\frac{1}{4}$ 87. $The specific heat capacity of a monatomic gas at constant volume is x % of its specific heat capacity at constant pressure. Then x =$ (1) $40$ (2) $50$ (3) $60$ (4) $75$ 88. $A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m / s . If container is suddenly stopped then change in temperature of the gas (R = gas constant ) is \frac{x}{3 R} . Value of X is$ 89. $The root mean square speed of molecules of a given mass of a gas at 27^{\circ} C and 1 atmosphere pressure is 200 ms^{- 1} . The root mean square speed of molecules of the gas at 127^{\circ} C and 2 atmosphere pressure is \frac{x}{3} ms^{- 1} . The value of x will he$ 90. $A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K . If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to$