STD 11 - Kinetic theory of gases PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 164 questions

51. 51. According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :- 2023 Easy
52. 52. At \(300\,K\), the rms speed of oxygen molecules is \(\sqrt{\frac{\alpha+5}{\alpha}}\) times to that of its average speed in the gas. Then, the value of \(\alpha\) will be (used \(\pi=\frac{22}{7}\) ) 2023 Medium
53. 53. For three low density gases \(A, B, C\) pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point ' \(K\) ' is \(...........\,{}^{\circ}\,C\)
    2023 Medium
54. 54. Given below are two statements: Statements \(I:\) The temperature of a gas is \(-73^{\circ}\,C\). When the gas is heated to \(527^{\circ}\,C\), the root mean square speed of the molecules is doubled. Statement \(II:\) The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below : 2023 Medium
55. 55. If the r.m.s. speed of chlorine molecule is \(490\,m / s\) at \(27^{\circ}\,C\), the r.m.s. speed of argon molecules at the same temperature will be \(......\,m/s\) (Atomic mass of argon \(=39.9\,u\), molecular mass of chlorine \(=70.9\,u )\) 2023 Easy
56. 56. Let \(\gamma_1\) be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \(\gamma_2\) be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, \(\frac{\gamma_1}{\gamma_2}\) is 2023 Medium
57. 57. Match List\(-I\) with List\(-II:\)

    List\(-I\)	List\(-II\)
    \((A)\) \(3\) Translational degrees of freedom	\((I)\) Monoatomic gases
    \((B)\) \(3\) Translational,\(2\) rotational degrees of freedoms	\((II)\) Polyatomic gases
    \((C)\) \(3\) Translational,\(2\) rotational and \(1\) vibrational degrees of freedom	\((III)\) Rigid diatomic gases
    \((D)\) \(3\) Translational,\(3\) rotational and more than one vibrational degrees of freedom	\((IV)\) Nonrigid diatomic gases

    Choose the correct answer from the options given below: 2023 Medium
58. 58. The average kinetic energy of a molecule of the gas is 2023 Easy
59. 59. The correct relation between \(\gamma=\frac{ C _p}{ c _v}\) and temperature \(T\) is : 2023 Medium
60. 60. The mean free path of molecules of a certain gas at \(STP\) is \(1500\,d\), where \(d\) is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at \(373\,K\) is approximately \(..........\,d\) 2023 Medium
61. 61. The number of air molecules per \(\mathrm{cm}^3\) increased from \(3 \times 10^{19}\) to \(12 \times 10^{19}\). The ratio of collision frequency of air molecules before and after the increase in number respectively is \(.........\) 2023 Medium
62. 62. The rms speed of oxygen molecule in a vessel at particular temperature is \(\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v\), where \(v\) is the average speed of the molecule. The value of \(x\) will be:(Take \(\pi=\frac{22}{7}\) ) 2023 Medium
63. 63. The root mean square speed of molecules of nitrogen gas at \(27^{\circ} C\) is approximately\(.......m/s\)(Given mass of a nitrogen molecule \(=4.6 \times 10^{-26}\,kg\) and take Boltzmann constant  \(k _{ B }=1.4 \times 10^{-23}\,JK ^{-1}\) ) 2023 Easy
64. 64. The root mean square velocity of molecules of gas is 2023 Easy
65. 65. The temperature at which the kinetic energy of oxygen molecules becomes double than its value at \(27^{\circ}\,C\) is \(............^{\circ}\,C\) 2023 Easy
66. 66. The temperature of an ideal gas is increased from \(200\,K\) to \(800\,K\). If r.m.s. speed of gas at \(200\,K\) is \(v_0\). Then, r.m.s. speed of the gas at \(800\,K\) will be: 2023 Easy
67. 67. Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed \(\left(v_{ ms }\right)\) and choose the correct answer from the options given below: 2023 Medium
68. 68. \(0.056 \,kg\) of Nitrogen is enclosed in a vessel at a temperature of \(127\,^{\circ} C\). The amount of heat required to double the speed of its molecules is k cal. (Take \(R =2\) \(cal \,mole\) \(^{-1} K ^{-1}\) ) 2022 Medium
69. 69. \(7\) mole of certain monoatomic ideal gas undergoes a temperature increase of \(40 K\) at constant pressure. The increase in the internal energy of the gas in this process is\(....J\) (Given \(R =8.3 JK ^{-1} mol ^{-1}\) ) 2022 Medium
70. 70. A cylinder of fixed capacity of \(44.8 \,litres\) contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by \(20.0^{\circ} C\) will be ..............  \(J\)(Given gas constant \(R =8.3 \,JK ^{-1}- moI ^{-1}\) ) 2022 Medium
71. 71. A flask contains argon and oxygen in the ratio of \(3: 2\) in mass and the mixture is kept at \(27^{\circ} C\). The ratio of their average kinetic energy per molecule respectively will be ........... 2022 Medium
72. 72. A gas has \(n\) degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be. 2022 Medium
73. 73. A mixture of hydrogen and oxygen has volume \(2000 \; cm ^{3}\), temperature \(300 \; K\), pressure \(100 \; kPa\) and mass \(0.76 \; g\) The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be 2022 Medium
74. 74. A thermally insulated vessel contains an ideal gas of molecular mass \(M\) and ratio of specific heats \(1.4\). Vessel is moving with speed \(v\) and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by ... ( \(R =\) universal gas constant ) 2022 Medium
75. 75. A vessel contains \(14\,g\) of nitrogen gas at a temperature of \(27^{\circ}\,C\). The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be \(......J\) \(\left(\right.\) Take \(R =8.32\,J\,mol ^{-1} k ^{-1}\) ) 2022 Medium
76. 76. A vessel contains \(16 \,g\) of hydrogen and \(128 \,g\) of oxygen at standard temperature and pressure. The volume of the vessel in \(cm ^{3}\) is 2022 Medium
77. 77. According to kinetic theory of gases, \(A\). The motion of the gas molecules freezes at \(0^{\circ} C\) \(B\). The mean free path of gas molecules decreases if the density of molecules is increased. \(C\). The mean free path of gas molecules increases if temperature is increased keeping pressure constant. \(D\). Average kinetic energy per molecule per degree of freedom is \(\frac{3}{2} k_{B} T\) (for monoatomic gases) Choose the most appropriate answer from the options given below 2022 Medium
78. 78. Following statements are given : \((1)\) The average kinetic energy of a gas molecule decreases when the temperature is reduced. \((2)\) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. \((3)\) The average kinetic energy of a gas molecule decreases with increases in volume. \((4)\) Pressure of a gas increases with increase in temperature at constant pressure. \((5)\) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below: 2022 Medium
79. 79. One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is \(\frac{\alpha^{2}}{4} R J / mol\,K\); then the value of \(\alpha\) will be \(.......\) (Assume that the given diatomic gas has no vibrational mode.) 2022 Medium
80. 80. Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is \(1: 4\), then \(A.\) The \(r.m.s\). velocity of gas molecules in two vessels will be the same. \(B.\) The ratio of pressure in these vessels will be \(1: 4\) \(C.\) The ratio of pressure will be \(1: 1\) \(D.\) The \(r.m.s.\) velocity of gas molecules in two vessels will be in the ratio of \(1: 4\) 2022 Medium
81. 81. Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is \(\sqrt{2}\) times the speed of sound, then the value of \(n\) will be 2022 Hard
82. 82. The relation between root mean square speed \(\left( v _{ rms }\right)\) and most probable speed \(\left( v _{ p }\right)\) for the molar mass \(M\) of oxygen gas molecule at the temperature of \(300\, K\) will be 2022 Medium
83. 83. The root mean square speed of smoke particles of mass \(5 \times 10^{-17}\,kg\) in their Brownian motion in air at NTP is approximately \(.......\,mm\,s ^{-1}\) [Given \(k =1.38 \times 10^{-23}\,J\,K ^{-1}\) ] 2022 Medium
84. 84. The total internal energy of two mole monoatomic ideal gas at temperature \(T=300\,K\) will be ...........\(J\). \(\text { (Given } R =8.31\,J / mol.K )\) 2022 Easy
85. 85. What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen? 2022 Medium
86. 86. When a gas filled in a closed vessel is heated by raising the temperature by \(1^{\circ} C\), its pressure increase by \(0.4 \%\). The initial temperature of the gas is ..........\(K\) 2022 Medium
87. 87. Which statements are correct about degrees of freedom? \(A.\) \(A\) molecule with \(n\) degrees of freedom has \(n^{2}\) different ways of storing energy. \(B.\) Each degree of freedom is associated with \(\frac{1}{2} RT\) average energy per mole. \(C.\) \(A\) monoatomic gas molecule has \(1\) rotational degree of freedom where as diatomic molecule has \(2\) rotational degrees of freedom \(D\) \(CH _{4}\) has a total to \(6\) degrees of freedom Choose the correct answer from the option given below: 2022 Hard
88. 88. \(1\) mole of rigid diatomic gas performs a work of \(Q / 5\) when heat \(Q\) is supplied to it. The molar heat capacity of the gas during this transformation is \(\frac{ x R }{8},\) The value of \(x\) is \(\ldots \ldots \ldots .\) \([ K =\) universal gas constant \(]\) 2021 Hard
89. 89. A balloon carries a total load of \(185\; {kg}\) at normal pressure and temperature of \(27^{\circ} {C}\). What load will the balloon carry on rising to a height at which the barometric pressure is \(45\; {cm}\) of \({Hg}\) and the temperature is \(-7^{\circ} {C}\). Assuming the volume constant? (in \({kg}\)) 2021 Hard
90. 90. A container is divided into two chambers by a partition. The volume of first chamber is \(4.5\) litre and second chamber is \(5.5\) litre. The first chamber contain \(3.0\) moles of gas at pressure \(2.0\, atm\) and second chamber contain \(4.0\) moles of gas at pressure \(3.0\, atm\) .After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is \(x \times 10^{-1} atm\). Value of \(x\) is......... 2021 Hard
91. 91. A cylindrical container of volume \(4.0 \times 10^{-3} \,{m}^{3}\) contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is \(400 \,{K}\) The pressure of the mixture of gases is: [Take gas constant as \(8.3\, {J} {mol}^{-1} {K}^{-1}\)] 2021 Medium
92. 92. A mixture of hydrogen and oxygen has volume \(500\, {cm}^{3}\), temperature \(300\, {K}\), pressure \(400\, {kPa}\) and mass \(0.76\, {g}\). The ratio of masses of oxygen to hydrogen will be :- 2021 Hard
93. 93. 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 \(\left( R =\right.\) gas constant) is \(\frac{ x }{3 R } .\) Value of \(x\) is .......... 2021 Hard
94. 94. A polyatomic ideal gas has \(24\) vibrational modes. What is the value of \(\gamma\) ? 2021 Hard
95. 95. A system consists of two types of gas molecules \(A\) and \(B\) having same number density \(2 \times\) \(10^{25}\, / {m}^{3}\). The diameter of \({A}\) and \({B}\) are \(10\, \stackrel{\circ}{{A}}\) and \(5\, \stackrel{\circ}{{A}}\) respectively. They suffer collision at room temperature. The ratio of average distance covererd by the molecule \(A\) to that of \(B\) between two successive collision is \(.....\,\times 10^{-2}\) 2021 Medium
96. 96. Calculate the value of mean free path \((\lambda)\) for oxygen molecules at temperature \(27^{\circ}\, C\) and pressure \(1.01 \times 10^{5} \,Pa\). Assume the molecular diameter \(0.3 \,nm\) and the gas is ideal. \(\left( k =1.38 \times 10^{-23}\, J\,K ^{-1}\right)\) (in \(nm\)) 2021 Hard
97. 97. Consider a mixture of gas molecule of types \(A, B\) and \(C\) having masses \(m_{A}\,<\,m_{B}\,<\,m_{C}\) ratio of their root mean square speeds at normal temperature and pressure is : 2021 Medium
98. 98. Consider a sample of oxygen behaving like an ideal gas. At \(300 \,K ,\) the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is \(32 \,g / mol\) \(\left. R =8.3 \,J K ^{-1} mol ^{-1}\right)\) 2021 Medium
99. 99. For \(a\) gas \(C_{p}-C_{V}=R\) in a state \(P\) and \(C_{p}-C_{V}=1.10 R\) in a state \(Q, T_{p}\) and \(T_{Q}\) are the temperatures in two different states \(P\) and \(Q\) respectively. Then 2021 Medium
100. 100. For an ideal gas the instantaneous change in pressure \('{p} '\) with volume \('v'\) is given by the equation \(\frac{{dp}}{{dv}}=-{ap} .\) If \({p}={p}_{0}\) at \({v}=0\) is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here \({R}\) is the gas constant) 2021 Hard

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