Kinetic Theory of Gases PYQs Set 7 (PDF)

Set 7 of 8 · Questions 181-210 of 229

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinetic Theory of Gases · Set 7 (Q181-210)
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181. $A balloon carries a total load of 185kg at normal pressure and temperature 2 7^{0} C of What load will the balloon carry on rising to a height at which the barometric pressure 45cm is of Hg and the temperature is - 7^{0} C . Assuming the volume constant?$ (1) $181.46kg$ (2) $214.15kg$ (3) $219.07kg$ (4) $123.54kg$ 182. $If the r.m.s speed of chlorine molecule is 490 m s^{- 1} at 27°C, the r.m.s speed of argon molecules at the same temperature will be (Atomic mass of argon = 39.9 u, molecular mass of chlorine = 70.9 u)$ (1) $551. 7 m s^{- 1}$ (2) $651. 7 m s^{- 1}$ (3) $451. 7 m s^{- 1}$ (4) $751. 7 m s^{- 1}$ 183. $One mole of a gas expands obeying the relation as shown in P-V diagram. The maximum temperature in this process is equal to:$ (1) $\frac{P _{0} V _{0}}{R}$ (2) $\frac{3 P _{0} V _{0}}{R}$ (3) $\frac{9 P _{0} V _{0}}{8 R}$ (4) $None$ 184. $The rms speed of oxygen molecule in a vessel at particular temperature is (1 + \frac{5}{x})^{\frac{1}{2}} v, when v is the average speed of the molecule. The value of x will be: (take π = \frac{22}{7})$ (1) $27$ (2) $8$ (3) $28$ (4) $4$ 185. $A mixture of hydrogen and oxygen has volume 500 c m^{3}, temperature 300K, pressure 400kPa and mass 0.76g. The ratio of masses of oxygen to hydrogen will be :-$ (1) $3:8$ (2) $3:16$ (3) $16:3$ (4) $8:3$ 186. $The mean free path of molecules of a certain gas at STP is 1500d, where d is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 K is approximately:$ (1) $750d$ (2) $1098d$ (3) $2049d$ (4) $1500d$ 187. $Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is 1:4, then A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in these vessels will bel :4 C. The ratio of pressure will be 1 : 1 D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1 : 4$ (1) $A and C only$ (2) $B and D only$ (3) $A and B only$ (4) $C and D only$ 188. $Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B . If the collision frequency in gas B is 32 \times 1 0^{8} / s then collision frequency in gas A is ____ /s.$ (1) $2 \times 10^{8}$ (2) $8 \times 10^{8}$ (3) $4 \times 10^{8}$ (4) $32 \times 10^{8}$ 189. $If C_{p} and C_{v} are molar specific heats of an ideal gas at constant pressure and volume respectively. If γ is ratio of two specific heats and R is universal gas constant then C_{p} is equal to$ (1) $\frac{Rγ}{γ - 1}$ (2) $γR$ (3) $\frac{1 + γ}{1 - γ}$ (4) $\frac{R}{γ - 2}$ 190. $The temperature of a gas is measure of$ (1) $the average kinetic energy of gas molecules$ (2) $the average potential energy of molecules$ (3) $the average distance between the molecule of gas$ (4) $the size of the molecules of a gas.$ 191. $Which statements are correct about degrees of freedom? A. A molecule with n degrees of freedom has n^{2} different ways of storing energy. B. Each degree of freedom is associated with \frac{1}{2} R T average energy per mole. C. A monoatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom D. C H_{4} has a total to 6 degrees of freedom Choose the correct answer from the option given below:$ (1) $B and C only$ (2) $B and D only$ (3) $A and B only$ (4) $C and D only$ 192. $Following statements are given : (1) The average kinetic energy of a gas molecule decreases when the temperature is reduced. (2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. (3) The average kinetic energy of a gas molecule decreases with increases in volume. (4) Pressure of a gas increases with increase in temperature at constant pressure. (5) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below:$ (1) $(1) and (4) only$ (2) $(1), (2) and (4) only$ (3) $(2) and (4) only$ (4) $(1), (2) and (5) only$ 193. $The dimensions of Stefan's constant are$ (1) $M^{0} L^{1} T^{- 3} K^{- 4}$ (2) $M^{1} L^{1} T^{- 3} K^{- 3}$ (3) $M^{1} L^{2} T^{- 3} K^{- 4}$ (4) $M^{1} L^{0} T^{- 3} K^{- 4}$ 194. $At standard temperature and pressure the density of a gas is 1.3 kg/ m^{3} and the speed of the sound in gas is 330 m/sec. Then the degree of freedom of the gas will be$ (1) $3$ (2) $4$ (3) $5$ (4) $6$ 195. $The parameter that remains the same for molecules of all gases at a given temperature is :$ (1) $kinetic energy$ (2) $momentum$ (3) $mass$ (4) $speed$ 196. $The plot of isotherms will not be a straight line when a plot is drawn between :$ (1) $PV and V$ (2) $U and ρ (density)$ (3) $\frac{1}{P} vs \frac{1}{V}$ (4) $\frac{1}{U} and ρ$ 197. $According to kinetic theory of gases, which one of the following statements is wrong?$ (1) $All the molecules of a gas are identical.$ (2) $Collisions between the molecules of a gas and that of the molecules with the walls of the container are perfectly elastic.$ (3) $The molecules do not exert appreciable force on one another except during collision.$ (4) $The pressure exerted by a gas is due to the collision between the molecules of the gas.$ 198. $n mole of a perfect gas undergoes a cyclic process A B C A (see figure) consisting of the following processes - A \to B : Isothermal expansion at temperature T so that the volume is doubled from V_{1} to V_{2} = 2 V_{1} and pressure changes from P_{1} to P_{2} . B \to C : Isobaric compression at pressure P_{2} to initial volume V_{1} . C \to A : Isochoric change leading to change of pressure from P_{2} to P_{1} . Total work done in the complete cycle ABCA is -$ (1) $0$ (2) $nRT (ln 2 + \frac{1}{2})$ (3) $nRTIn 2$ (4) $nRT (ln 2 - \frac{1}{2})$ 199. $The plot that depicts the behavior of the mean free time T (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)$ (1) (2) (3) (4) 200. $10^{23} molecules of a gas, each having a mass of 3 \times 10^{- 27} kg strike per second per sq. cm of a rigid wall at an angle of 60^{\circ} with the normal and rebound with a velocity of 500 m / s . The pressure exerted by the gas molecules on the wall is (sin 30^{\circ} = cos 60^{\circ} = 0.5, cos 30^{\circ} = sin 60^{\circ} = 3 /2)$ (1) $500 N / m^{2}$ (2) $2000 N / m^{2}$ (3) $1500 N / m^{2}$ (4) $1000 N / m^{2}$ 201. $A cylindrical tube AB of length l, closed at both ends contains an ideal gas of 1 mol having molecular weight M . The tube is rotated in a horizontal plane with constant angular velocity ω about an axis perpendicular to AB and passing through the edge at end A, as shown in the figure. If P_{A} and P_{B} are the pressures at A and B respectively, then (Consider the temperature is same at all points in the tube)$ (1) $P_{B} = P_{A}$ (2) $P_{B} = P_{A} expMω2l2/3RT$ (3) $P_{B} = P_{A} expMω2l2/RT$ (4) $P_{B} = P_{A} expMω2l2/2RT$ 202. $Ratio of translational degrees of freedom to rotational degrees of freedom of a polyatomic linear gas molecule is$ (1) $1 : 1$ (2) $1 : 2$ (3) $2 : 3$ (4) $3 : 2$ 203. $A flask contains hydrogen and oxygen in the ratio of 2 : 1 by mass at temperature 27°C The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :$ (1) $2 : 1$ (2) $1 : 1$ (3) $1:4$ (4) $4 : 1$ 204. $The correct relation between the degrees of freedom f and the ratio of specific heat γ is :$ (1) $f = \frac{2}{γ - 1}$ (2) $f = \frac{2}{γ + 1}$ (3) $f = \frac{γ + 1}{2}$ (4) $f = \frac{1}{γ + 1}$ 205. $By what percentage should the pressure of a given mass of a gas be increased so as to decrease its volume by 10% at a constant temperature?$ (1) $8.1%$ (2) $9.1%$ (3) $10.1%$ (4) $11.1%$ 206. $The pressure P_{1} and density d_{1} of diatomic gas changes suddenly to P_{2} (> P_{1}) and d_{2} respectively during an adiabatic process. The temperature of the gas increases and becomes _________times of its initial temperature.(given \frac{d _{2}}{d _{1}} = 32)$ 207. $Initially a gas of diatomic molecules is contained in a cylinder of volume V_{1} at a pressure P_{1} and temperature 250 K . Assuming that 25 % of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature 2000 K when contained in a volume 2 V_{1} is given by P_{2} . The ratio P_{2} / P_{1} is$ 208. $A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm . Arter the partition is removed and the mixture allains equilibrium, then, the common equilibrium pressure existing in the mixture is x \times 10^{- 1} atm . Value of x is$ 209. $The change in the magnitude of the volume of an ideal gas when a small additional pressure Δ P is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity Δ T at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm. respectively. If \| Δ T \| = C ∣ Δ P then value of C in (K / atm .) is$ 210. $Starting at temperature 300 K, one mole of an ideal diatomic gas (γ = 1.4) is first compressed adiabatically from volume V_{1} to V_{2} = V_{1} /16 . it is then allowed to expand isobarically to volume 2 V_{2} . If all the processes are the quasi-static then the final temperature of the gas (in^{\circ} K) is (to the nearest integer)$