Kinetic Theory of Gases PYQs Set 6 (PDF)

Set 6 of 8 · Questions 151-180 of 212

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Mere Teacher · Previous Year Questions NEET Physics · Kinetic Theory of Gases · Set 6 (Q151-180)
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151. $The number of air molecules per c m^{3} is increased from 3 x 1 0^{19} to 12 x 1 0^{19} . The ratio of collision frequency of air molecules before and after the increase in number respectively is :$ (1) $0.75$ (2) $1.25$ (3) $0.50$ (4) $0.25$ 152. $If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km / s, the root mean square velocity of oxygen at the same condition in km / s is :$ (1) $2.0$ (2) $0.5$ (3) $1.5$ (4) $1.0$ 153. $The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200 K is v_{0} . Then, r.m.s. speed of the gas at 800 K will be:$ (1) $\frac{v _{0}}{4}$ (2) $v_{0}$ (3) $4 v_{0}$ (4) $2 v_{0}$ 154. $For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation \frac{d p}{d v} = - a p . If p = p_{0} at v=0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here is the gas constant)$ (1) $\frac{p _{0}}{a e R}$ (2) $\frac{a p _{0}}{e R}$ (3) $infinity$ (4) $0^{0} C$ 155. $A vessel contains 14 g of nitrogen gas at a temperature of 27°C. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be : (Take R = 8.32 J m o l^{- 1} k^{- 1})$ (1) $2229 J$ (2) $5616J$ (3) $9360J$ (4) $13104 J$ 156. $Given below are two statement: Statement - I : What μ amount of an ideal gas undergoes adiabatic change from state (P_{1}, V_{1}, T_{1}) to state (P_{2}, V_{2}, T_{2}), the work done is W = \frac{1 R ( T _{2} - T _{1} )}{1 - γ}, where γ = \frac{C _{P}}{C _{V}} and R = universal gas constant, Statement — II: In the above case, when work is done on the gas. the temperature of the gas would rise. Choose the correct answer from the options given below:$ (1) $Both statement-I and statement-II are true.$ (2) $Both statement-I and statement-II are false.$ (3) $Statement-I is true but statement-II is false.$ (4) $Statement-I is false but statement-II is true.$ 157. $A mixture of hydrogen and oxygen has volume 2000 c m^{3}, temperature 300 K, pressure 100 kPa and mass 0.76 g The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be :$ (1) $\frac{1}{3}$ (2) $\frac{3}{1}$ (3) $\frac{1}{16}$ (4) $\frac{16}{1}$ 158. $Given below are two statements : Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II: The rms speed of oxygen molecules in a gas is v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2v. In the light of the above statements, choose the correct answer from the options given below :$ (1) $Both Statement I and Statement II are true$ (2) $Both Statement I and Statement II are false$ (3) $Statement I is true but Statement II is false$ (4) $Statement I is false but Statement II is true$ 159. $The ratio of specific heats in terms of degree of freedom (f) is given by:$ (1) $(1 + \frac{f}{3})$ (2) $(1 + \frac{2}{f})$ (3) $(1 + \frac{f}{2})$ (4) $(1 + \frac{1}{f})$ 160. $Two thermodynamical process are shown in the figure. The molar heat capacity for process A and B are C_{A} and C_{B} . The molar heat capacity at constant pressure and constant volume are represented by C_{P} and C_{V}, respectively. Choose the correct statement.$ (1) $C_{B} = \infty, C_{A} = 0$ (2) $C_{A} = 0 and C_{B} = \infty$ (3) $C_{P} > C_{B} > C_{A} > C_{v}$ (4) $C_{A} > C_{P} > C_{V}$ 161. $The following graph represents the T - V curves of an ideal gas (where, T is the temperature and V is the volume) at three pressures p_{1}, p_{2} and p_{3} compared with those of charles's law represented as dotted lines. [NEET 2024] Then, the correct relation is$ (1) $p_{3} > p_{2} > p_{1}$ (2) $p_{1} > p_{3} > p_{2}$ (3) $p_{2} > p_{1} > p_{3}$ (4) $p_{1} > p_{2} > p_{3}$ 162. $Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed (v_{r m s}) and choose the correct answer from the options given below:$ (1) $v_{r m s} (mono) > v_{r m s} (dia) > v_{r m s} (poly)$ (2) $V_{r m s} (mono) = V_{r m s} (dia) = V_{r m s} (poly)$ (3) $v_{r m s} (mono) < v_{r m s} (dia) < v_{r m s} (poly)$ (4) $v_{r m s} (dia) < v_{r m s} (poly) < v_{r m s} (mono)$ 163. $The root mean square speed of molecules of nitrogen gas at 27°C is approximately: (Given mass of a nitrogen molecule = 4. 6 x 1 0^{- 26} kg and take Boltzmann constant k_{B} = 1.4x 1 0^{- 23} J K^{- 1})$ (1) $27 4 m s^{- l}$ (2) $91 m s^{- 1}$ (3) $1260 m s^{- 1}$ (4) $523 m s^{- 1}$ 164. $A gas is filled in the cylinder shown in the figure. The two pistons are joined by a string. If the gas is heated, the pistons will$ (1) $Move towards left$ (2) $Move towards right$ (3) $Remain stationary$ (4) $None of these$ 165. $For the given P - V graph for an ideal gas, chose the correct V - T graph. Process BC is adiabatic.$ (1) (2) (3) (4) 166. $Given below are two statements : Statements I : The temperature of a gas is - 73°C, When the gas is heated to 527°C, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules, In the light of the above statements, choose the correct answer from the options given below :$ (1) $Both statement I and Statement II are true$ (2) $Statement 1 is true but Statement II is false$ (3) $Both Statement I and Statement II are false$ (4) $Statement I is false but Statement II is true$ 167. $Consider a mixture of gas molecule of types A, B and C having masses m_{A} < m_{B} < m_{C} . The ratio of their root mean square speeds at normal temperature and pressure is :$ (1) $v_{A} = v_{B} = v_{C} = 0$ (2) $\frac{1}{v _{A}} > \frac{1}{v _{B}} > \frac{1}{v _{C}}$ (3) $v_{A} = v_{B} \neq = v_{C}$ (4) $\frac{1}{v _{A}} < \frac{1}{v _{B}} < \frac{1}{v _{C}}$ 168. $Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B . Under such conditions, the density of A is found to be 1.5 times the density of B . The ratio of molecular weight of A and B is$ (1) $1/3$ (2) $3/4$ (3) $2$ (4) $1/2$ 169. $A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be:$ (1) $11RT$ (2) $8RT$ (3) $4RT$ (4) $16RT$ 170. $A balloon carries a total load of 185kg at normal pressure and temperature 2 7^{0} C of What load will the balloon carry on rising to a height at which the barometric pressure 45cm is of Hg and the temperature is - 7^{0} C . Assuming the volume constant?$ (1) $181.46kg$ (2) $214.15kg$ (3) $219.07kg$ (4) $123.54kg$ 171. $If the r.m.s speed of chlorine molecule is 490 m s^{- 1} at 27°C, the r.m.s speed of argon molecules at the same temperature will be (Atomic mass of argon = 39.9 u, molecular mass of chlorine = 70.9 u)$ (1) $551. 7 m s^{- 1}$ (2) $651. 7 m s^{- 1}$ (3) $451. 7 m s^{- 1}$ (4) $751. 7 m s^{- 1}$ 172. $One mole of a gas expands obeying the relation as shown in P-V diagram. The maximum temperature in this process is equal to:$ (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) $None$ 173. $The rms speed of oxygen molecule in a vessel at particular temperature is (1 + \frac{5}{x})^{\frac{1}{2}} v, when v is the average speed of the molecule. The value of x will be: (take π = \frac{22}{7})$ (1) $27$ (2) $8$ (3) $28$ (4) $4$ 174. $A mixture of hydrogen and oxygen has volume 500 c m^{3}, temperature 300K, pressure 400kPa and mass 0.76g. The ratio of masses of oxygen to hydrogen will be :-$ (1) $3:8$ (2) $3:16$ (3) $16:3$ (4) $8:3$ 175. $The mean free path of molecules of a certain gas at STP is 1500d, where d is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 K is approximately:$ (1) $750d$ (2) $1098d$ (3) $2049d$ (4) $1500d$ 176. $Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is 1:4, then A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in these vessels will bel :4 C. The ratio of pressure will be 1 : 1 D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1 : 4$ (1) $A and C only$ (2) $B and D only$ (3) $A and B only$ (4) $C and D only$ 177. $Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B . If the collision frequency in gas B is 32 \times 1 0^{8} / s then collision frequency in gas A is ____ /s.$ (1) $2 \times 10^{8}$ (2) $8 \times 10^{8}$ (3) $4 \times 10^{8}$ (4) $32 \times 10^{8}$ 178. $If C_{p} and C_{v} are molar specific heats of an ideal gas at constant pressure and volume respectively. If γ is ratio of two specific heats and R is universal gas constant then C_{p} is equal to$ (1) $\frac{Rγ}{γ - 1}$ (2) $γR$ (3) $\frac{1 + γ}{1 - γ}$ (4) $\frac{R}{γ - 2}$ 179. $The temperature of a gas is measure of$ (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) $the size of the molecules of a gas.$ 180. $Which statements are correct about degrees of freedom? A. A molecule with n degrees of freedom has n^{2} different ways of storing energy. B. Each degree of freedom is associated with \frac{1}{2} R T average energy per mole. C. A monoatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom D. C H_{4} has a total to 6 degrees of freedom Choose the correct answer from the option given below:$ (1) $B and C only$ (2) $B and D only$ (3) $A and B only$ (4) $C and D only$