Kinetic Theory of Gases PYQs Set 6 (PDF)

Set 6 of 8 · Questions 151-180 of 229

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinetic Theory of Gases · Set 6 (Q151-180)
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151. $An ideal gas equation can be written as p = \frac{ρRT}{M _{0}} where, ρ and M_{0} are respectively, [NEET 2020]$ (1) $mass density, mass of the gas$ (2) $number density, molar mass$ (3) $mass density, molar mass$ (4) $number density, mass of the gas$ 152. $The energy (in eV) possessed by a neon atom at 77^{\circ} C is (Blotzmann constant, K_{B} = 1.38 \times 10^{- 23} J K^{- 1})$ (1) $1.32 \times 10^{- 3}$ (2) $3.20 \times 10^{- 4}$ (3) $4.52 \times 10^{- 2}$ (4) $3.88 \times 10^{- 2}$ 153. $The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is [NEET 2022]$ (1) $5.6 \times 10^{3} m^{3}$ (2) $5.6 \times 10^{- 3} m^{3}$ (3) $5.6 m^{3}$ (4) $5.6 \times 10^{6} m^{3}$ 154. $Calculate the value of mean free path (λ) for oxygen molecules at temperature 27^{\circ} C and pressure 1.01 \times 10^{5} Pa . Assume the molecular diameter 0.3 nm and the gas is ideal.$ (1) $58 nm$ (2) $32 nm$ (3) $86 nm$ (4) $102 nm$ 155. $Two moles of helium has is mixed gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ? (R=8.3J/mol K)$ (1) $19.7 J/mol K$ (2) $15.7 J/mol K$ (3) $17.4 J/mol K$ (4) $21.6 J/mol K$ 156. $The average thermal energy for a monoatomic gas is (where, k_{B} is Boltzmann constant and T is absolute temperature.) [NEET 2020]$ (1) $\frac{3}{2} k_{B} T$ (2) $\frac{5}{2} k_{B} T$ (3) $\frac{7}{2} k_{B} T$ (4) $\frac{1}{2} k_{B} T$ 157. $At what temperature an oxygen molecule has the same r.m.s velocity as the hydrogen molecule has at 20 K ?$ (1) $160 K$ (2) $320 K$ (3) $293 K$ (4) $347 K$ 158. $One mole of the ideal gas goes through the process p = p_{0} (1 - α (\frac{V}{V _{0}})^{3}), where p and V are pressure and volume, p_{0}, V_{0} and α are constants. If the maximum attainable temperature of the gas is (\frac{3}{4}) \frac{p _{0} V _{0}}{R}, then the value of α is$ (1) $2$ (2) $\frac{1}{2}$ (3) $\frac{1}{4}$ (4) $4$ 159. $A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:$ (1) $\frac{1}{32}$ (2) $\frac{2 2}{1}$ (3) $\frac{1}{2 2}$ (4) $\frac{1}{4}$ 160. $The number of air molecules per c m^{3} is increased from 3 x 1 0^{19} to 12 x 1 0^{19} . The ratio of collision frequency of air molecules before and after the increase in number respectively is :$ (1) $0.75$ (2) $1.25$ (3) $0.50$ (4) $0.25$ 161. $If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km / s, the root mean square velocity of oxygen at the same condition in km / s is :$ (1) $2.0$ (2) $0.5$ (3) $1.5$ (4) $1.0$ 162. $The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200 K is v_{0} . Then, r.m.s. speed of the gas at 800 K will be:$ (1) $\frac{v _{0}}{4}$ (2) $v_{0}$ (3) $4 v_{0}$ (4) $2 v_{0}$ 163. $For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation \frac{d p}{d v} = - a p . If p = p_{0} at v=0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here is the gas constant)$ (1) $\frac{p _{0}}{a e R}$ (2) $\frac{a p _{0}}{e R}$ (3) $infinity$ (4) $0^{0} C$ 164. $A vessel contains 14 g of nitrogen gas at a temperature of 27°C. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be : (Take R = 8.32 J m o l^{- 1} k^{- 1})$ (1) $2229 J$ (2) $5616J$ (3) $9360J$ (4) $13104 J$ 165. $Given below are two statement: Statement - I : What μ amount of an ideal gas undergoes adiabatic change from state (P_{1}, V_{1}, T_{1}) to state (P_{2}, V_{2}, T_{2}), the work done is W = \frac{1 R ( T _{2} - T _{1} )}{1 - γ}, where γ = \frac{C _{P}}{C _{V}} and R = universal gas constant, Statement — II: In the above case, when work is done on the gas. the temperature of the gas would rise. Choose the correct answer from the options given below:$ (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) $Statement-I is false but statement-II is true.$ 166. $A mixture of hydrogen and oxygen has volume 2000 c m^{3}, temperature 300 K, pressure 100 kPa and mass 0.76 g The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be :$ (1) $\frac{1}{3}$ (2) $\frac{3}{1}$ (3) $\frac{1}{16}$ (4) $\frac{16}{1}$ 167. $Given below are two statements : Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II: The rms speed of oxygen molecules in a gas is v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2v. In the light of the above statements, choose the correct answer from the options given below :$ (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) $Statement I is false but Statement II is true$ 168. $The ratio of specific heats in terms of degree of freedom (f) is given by:$ (1) $(1 + \frac{f}{3})$ (2) $(1 + \frac{2}{f})$ (3) $(1 + \frac{f}{2})$ (4) $(1 + \frac{1}{f})$ 169. $Two thermodynamical process are shown in the figure. The molar heat capacity for process A and B are C_{A} and C_{B} . The molar heat capacity at constant pressure and constant volume are represented by C_{P} and C_{V}, respectively. Choose the correct statement.$ (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) $C_{A} > C_{P} > C_{V}$ 170. $The following graph represents the T - V curves of an ideal gas (where, T is the temperature and V is the volume) at three pressures p_{1}, p_{2} and p_{3} compared with those of charles's law represented as dotted lines. [NEET 2024] Then, the correct relation is$ (1) $p_{3} > p_{2} > p_{1}$ (2) $p_{1} > p_{3} > p_{2}$ (3) $p_{2} > p_{1} > p_{3}$ (4) $p_{1} > p_{2} > p_{3}$ 171. $Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed (v_{r m s}) and choose the correct answer from the options given below:$ (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) $v_{r m s} (dia) < v_{r m s} (poly) < v_{r m s} (mono)$ 172. $The root mean square speed of molecules of nitrogen gas at 27°C is approximately: (Given mass of a nitrogen molecule = 4. 6 x 1 0^{- 26} kg and take Boltzmann constant k_{B} = 1.4x 1 0^{- 23} J K^{- 1})$ (1) $27 4 m s^{- l}$ (2) $91 m s^{- 1}$ (3) $1260 m s^{- 1}$ (4) $523 m s^{- 1}$ 173. $A gas is filled in the cylinder shown in the figure. The two pistons are joined by a string. If the gas is heated, the pistons will$ (1) $Move towards left$ (2) $Move towards right$ (3) $Remain stationary$ (4) $None of these$ 174. $For the given P - V graph for an ideal gas, chose the correct V - T graph. Process BC is adiabatic.$ (1) (2) (3) (4) 175. $Given below are two statements : Statements I : The temperature of a gas is - 73°C, When the gas is heated to 527°C, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules, In the light of the above statements, choose the correct answer from the options given below :$ (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) $Statement I is false but Statement II is true$ 176. $Consider a mixture of gas molecule of types A, B and C having masses m_{A} < m_{B} < m_{C} . The ratio of their root mean square speeds at normal temperature and pressure is :$ (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) $\frac{1}{v _{A}} < \frac{1}{v _{B}} < \frac{1}{v _{C}}$ 177. $Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B . Under such conditions, the density of A is found to be 1.5 times the density of B . The ratio of molecular weight of A and B is$ (1) $1/3$ (2) $3/4$ (3) $2$ (4) $1/2$ 178. $A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be:$ (1) $11RT$ (2) $8RT$ (3) $4RT$ (4) $16RT$ 179. $One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is \frac{α ^{2}}{4} R J/mol K; then the value of α will be_______. (Assume that the given diatomic gas has no vibrational mode.)$ 180. $0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127°C. The amount of heat required to double the speed of its molecules is_____k cal.(Take R = 2 cal m o l e^{- 1} K^{- 1})$