Kinetic Theory of Gases PYQs Set 4 (PDF)

Set 4 of 8 · Questions 91-120 of 229

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinetic Theory of Gases · Set 4 (Q91-120)
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91. $A given sample of an ideal gas occupies a volume V at a pressure p and absolute temperature T . The mass of each molecule of the gas is m . Which of the following gives the density of the gas? [NEET 2016]$ (1) $p / (kT)$ (2) $pm / (kT)$ (3) $p / (kTV)$ (4) $mkT$ 92. $The ratio of vapour densities of two gases at the same temperature is \frac{4}{25}, then the ratio of r.m.s. velocities will be:$ (1) $\frac{25}{4}$ (2) $\frac{2}{5}$ (3) $\frac{5}{2}$ (4) $\frac{4}{25}$ 93. $The average translational kinetic energy of a molecule in a gas becomes equal to 0.69 eV at temperature about, [Boltzmann's constant = 1.38 \times 10^{- 23} J K^{- 1}]$ (1) $3370^{\circ} C$ (2) $3388^{\circ} C$ (3) $5333^{\circ} C$ (4) $5060^{\circ} C$ 94. $A 15 g mass of nitrogen gas is enclosed gas is enclosed in a vessel at a temperature 27° C . Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/K mole]$ (1) $0.9 kJ$ (2) $6 kJ$ (3) $10 kJ$ (4) $14 kJ$ 95. $The total kinetic energy of 1 mole of oxygen at 27^{\circ} C is : [Use universal gas constant (R) = 8.31 J / moleK]$ (1) $6845.5 J$ (2) $5942.0 J$ (3) $6232.5 J$ (4) $5670.5 J$ 96. $In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as$ (1) $T$ (2) $T$ (3) $\frac{1}{T}$ (4) $\frac{1}{T}$ 97. $A black rectangular surface of area A emits energy E per second at 27^{\circ} C . If length and breadth are reduced to 1/ 3^{rd} of initial value and temperature is raised to 327^{\circ} C then energy emitted per second becomes$ (1) $\frac{4 E}{9}$ (2) $\frac{7 E}{9}$ (3) $\frac{10 E}{9}$ (4) $\frac{16 E}{9}$ 98. $Air is filled at 60^{\circ} C in a vessel of open mouth. The vessel is heated to a temperature t^{\circ} C so that \frac{1}{4} th of the air is escaped from the vessel. Assuming air as ideal gas and the volume of the vessel remaining constant, then the value of ' t' is$ (1) $80^{\circ} C$ (2) $171^{\circ} C$ (3) $333^{\circ} C$ (4) $444^{\circ} C$ 99. $The maximum wavelength of a radiation emitted by a star is 289.8 nm . Then intensity of radiation for the star is (Given : Stefan's constant = 5.67 \times 10^{- 8} W m^{- 2} K^{- 4}, Wien's constant, b = 2898 μ mK)$ (1) $5.67 \times 10^{- 12} W m^{- 2}$ (2) $10.67 \times 10^{14} Wm^{- 2}$ (3) $5.67 \times 10^{8} W m^{- 2}$ (4) $10.67 \times 10^{7} W m^{- 2}$ 100. $Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is (32 g / mol; R = 8.3 J K^{- 1} mol^{- 1})$ (1) $\frac{3}{3}$ (2) $\frac{8}{3}$ (3) $\frac{3 π}{8}$ (4) $\frac{8 π}{3}$ 101. $The relation between the pressure (P), volume (V) and average kinetic energy (E) of a gas is$ (1) $P = \frac{E}{2 V}$ (2) $P = \frac{3}{2} \frac{E}{V}$ (3) $P = \frac{E}{3 V}$ (4) $P = \frac{2}{3} \frac{E}{V}$ 102. $A litre of dry air at STP expands adiabatically to a volume of 3 litres . If γ = 1.40, the work done by air is : (3^{1.4} = 4.6555)) [Take air to be an ideal gas]$ (1) $100.8 J$ (2) $90.5 J$ (3) $45 J$ (4) $18 J$ 103. $An ideal gas has pressure P, volume V and absolute temperature T . If m is the mass of each molecule and K is the Boltzmann constant then density of the gas is$ (1) $\frac{Pm}{KT}$ (2) $\frac{KT}{Pm}$ (3) $\frac{Km}{PT}$ (4) $\frac{PK}{Tm}$ 104. $A molecule is travelling in air at 300 K and 1 atm, and the radius of the molecule is 0.6 \times 10^{- 10} m . Calculate the approx, mean free path of the molecule. (The number density is 2.44 \times 10^{25} molecules / m^{3})$ (1) $\frac{0.2}{π} \times 1 0^{- 5} m$ (2) $\frac{0.3}{π} \times 1 0^{- 5} m$ (3) $\frac{0.4}{π} \times 1 0^{- 5} m$ (4) $\frac{0.1}{π} \times 1 0^{- 5} m$ 105. $The translational degrees of freedom (f_{t}) and rotational degrees of freedom (f_{r}) of CH_{4} molecule are:$ (1) $f_{t} = 2 and f_{r} = 2$ (2) $f_{t} = 3 and f_{r} = 3$ (3) $f_{t} = 3 and f_{r} = 2$ (4) $f_{t} = 2 and f_{r} = 3$ 106. $A thermally insulated vessel containing monoatomic gas is moving with a speed of 30 m / s . If the vessel suddenly stops, the increase in gas temperature is (Molar mass of gas = 83 g / mol and R = 8.3 J / Kmol)$ (1) $1 K$ (2) $3 K$ (3) $4 K$ (4) $6 K$ 107. $A flask contains Hydrogen and Argon in the ratio 2 : 1 by mass. The temperature of the mixture is 30 °C. The ratio of average kinetic energy per molecule of the two gases (\frac{K _{arg o n}}{K _{h ydrogen}}) is: (Given : Atomic Weight of Ar = 39.9)$ (1) $2$ (2) $1$ (3) $39 9$ (4) $\frac{39.9}{2}$ 108. $If three moles of monoatomic gas (γ = \frac{5}{3}) is mixed with two moles of a diatomic gas (γ = \frac{7}{5}), the value of adiabatic exponent γ for the mixture is:$ (1) $1.75$ (2) $1.40$ (3) $1.52$ (4) $1.35$ 109. $If the average kinetic energy of a gas molecule at 27^{\circ} C is 3.3 \times 10^{- 20} J, then the average kinetic energy of the gas molecules at 127^{\circ} C is$ (1) $15 \times 10^{- 20} J$ (2) $0.68 \times 10^{- 20} J$ (3) $4.4 \times 10^{- 20} J$ (4) $10.3 \times 10^{- 21} J$ 110. $N moles of a polyatomic gas (f = 6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is :$ (1) $6$ (2) $3$ (3) $4$ (4) $2$ 111. $Two boxes are at the same temperature. The first box contains gas with molecular mass m_{1} and rms speed v_{1} . The second box contains gas with molecular mass m_{2} and average speed v_{2} . If v_{1} = 1.5 v_{2}, then \frac{m _{1}}{m _{2}} is$ (1) $1.25$ (2) $0.74$ (3) $0.52$ (4) $0.26$ 112. $Match List I with List II: List I (A) 3 Translational degrees of freedom (B) 3 Translational, 2 rotational degrees of freedoms (C) 3 Translational, 2 rotational and 1 vibrational degrees of freedom (D) 3 Translational, 3 rotational and more than one vibrational degrees of freedom List II (I) Monoatomic gases (II) Polyatomic gases (III) Rigid diatomic gases (IV) Nonrigid diatomic gases Choose the correct answer from the options given below:$ (1) $(A)-(I), (B)-(III), (C)-(IV), (D)-(II)$ (2) $(A)-(IV), (B)-(III), (C)-(II), (D)-(I)$ (3) $(A)-(IV), (B)-(II), (C)-(I), (D)-(III)$ (4) $(A)-(I), (B)-(IV), (C)-(III), (D)-(II)$ 113. $If a gas has n degrees of freedom, then the ratio of \frac{C _{P}}{C _{V}} is$ (1) $\frac{n + 2}{n}$ (2) $\frac{2 n + 1}{n}$ (3) $\frac{n + 2}{2 n}$ (4) $\frac{n + 4}{2 n}$ 114. $At a temperature of 314 K and a pressure of 100 kPa, the speed of sound in a gas is 1380 ms^{- 1} . The radius of each gas molecule is 0.5Å . The frequency of sound at which the wavelength of sound wave in the gas becomes equal to the mean free path of the gas molecules is (Boltzmann constant = 1.38 \times 10^{- 23} JK^{- 1} .)$ (1) $1000 MHz$ (2) $10002 MHz$ (3) $\frac{1000}{2} MHz$ (4) $500 MHz$ 115. $Under standard conditions, the density of a gas is \frac{1400}{1089} kg - m^{- 3} and the speed of sound propagation in it is 330 ms^{- 1}, then the number of degrees of freedom of the gas molecules is$ (1) $2$ (2) $7$ (3) $5$ (4) $3$ 116. $What is the number of degrees of freedom for an oscillating simple pendulum?$ (1) $One$ (2) $Two$ (3) $Three$ (4) $More than three$ 117. $Two ideal polyatomic gases at temperatures T_{1} and T_{2} are mixed so that there is no loss of energy. If F_{1} and F_{2}, m_{1} and m_{2}, n_{1} and n_{2} be the degrees of freedom, masses, number of molecules of the first and second gasrespectively, the temperature of mixture ofthese two gases is :$ (1) $\frac{n _{1} T _{1} + n _{2} T _{2}}{n _{1} + n _{2}}$ (2) $\frac{n _{1} F _{1} T _{1} + n _{2} F _{2} T _{2}}{n _{1} F _{1} + n _{2} F _{2}}$ (3) $\frac{n _{1} F _{1} T _{1} + n _{2} F _{2} T _{2}}{F _{1} + F _{2}}$ (4) $\frac{n _{1} F _{1} T _{1} + n _{2} F _{2} T _{2}}{n _{1} + n _{2}}$ 118. $The temperature of a gas having 2.0 \times 10^{25} molecules per cubic meter at 1.38 atm (Given, k = (1.38 \times 10^{- 23} JK^{- 1}) is :$ (1) $500 K$ (2) $200 K$ (3) $100 K$ (4) $300 K$ 119. $A vessel of volume 10 liters is filled with H_{2} gas. The total average translational kinetic energy of its molecules is 4.5 \times 10^{5} J . The pressure of hydrogen in the vessel is$ (1) $3 \times 10^{6} Nm^{- 2}$ (2) $30 \times 10^{6} Nm^{- 2}$ (3) $30 \times 10^{4} Nm^{- 2}$ (4) $3 \times 10^{4} Nm^{- 2}$ 120. $The average translational kinetic energy of N_{2} gas molecules at ..........^{0} C becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt. (Given k_{B} = 1.38 \times 1 0^{- 23} J / K) (Fill the nearest integer).$