Kinetic Theory of Gases PYQs Set 1 (PDF)

Set 1 of 8 · Questions 1-30 of 212

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Mere Teacher · Previous Year Questions NEET Physics · Kinetic Theory of Gases · Set 1 (Q1-30)
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1. $The respective speeds of the five molecules are 1, 2, 3, 4 and 5 kms^{- 1} . Then, the ratio of their rms velocity and the average velocity will be$ (1) $11 : 3$ (2) $3 : 11$ (3) $1 : 2$ (4) $3 : 4$ 2. $If for a gas \frac{R}{C _{V}} = 0.67, this gas is made up molecules which are$ (1) $Monoatomic$ (2) $Diatomic$ (3) $Polyatomic$ (4) $Mixture of diatomic and polyatomic molecules$ 3. $The temperature of a gas is - 50^{\circ} C . To what temperature the gas should be heated, so that the rms speed is increased by 3 times? [NEET 2022]$ (1) $3295^{\circ} C$ (2) $3097 K$ (3) $223 K$ (4) $669^{\circ} C$ 4. $If the absolute temperature of a gas is increased 5 times, the r.m.s. velocity of the gas molecules will be$ (1) $10 times$ (2) $5 times$ (3) $5 times$ (4) $25 times$ 5. $Consider an ideal gas in a closed container at 300 K . The container is then heated, so that the average velocity of a particles of the gas increases by a factor of 4 . What would be the final temperature?$ (1) $4500^{\circ} C$ (2) $4527^{\circ} C$ (3) $4617^{\circ} C$ (4) $4600^{\circ} C$ 6. $If the collision frequency of hydrogen molecules in a closed chamber at 27^{\circ} C is Z, then the collision frequency of the same system at 127^{\circ} C is :$ (1) $\frac{3}{2} z$ (2) $\frac{2}{3} Z$ (3) $\frac{3}{4} Z$ (4) $\frac{4}{3} Z$ 7. $The volume of an ideal gas increases 8 times and temperature becomes (1/4)^{th} of initial temperature during a reversible change. If there is no exchange of heat in this process (Δ Q = 0) then identify the gas from the following options (Assuming the gases given in the options are ideal gases):$ (1) $O_{2}$ (2) $NH_{3}$ (3) $CO_{2}$ (4) $He$ 8. $If the temperature of a gas is increased from 27^{\circ} C to 159^{\circ} C, then the percentage increase in the rms speed of the gas molecules is$ (1) $5$ (2) $10$ (3) $15$ (4) $20$ 9. $An ideal gas occupies a volume of 2 m^{3} at a pressure of 3 \times 10^{6} Pa. The energy of the gas :$ (1) $9 \times 10^{6} J$ (2) $6 \times 10^{4} J$ (3) $10^{8} J$ (4) $3 \times 10^{2} J$ 10. $Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. P_{A} and P_{B} are the pressures of the gases in A and B respectively, then \frac{P _{A}}{P _{B}} is :$ (1) $16$ (2) $8$ (3) $4$ (4) $32$ 11. $An insulating cylinder contains 4 moles of an ideal diatomic gas. When a heat Q is supplied, to it, 2 moles of the gas molecules dissociate. If the temperature of the gas remains constant, then the value of Q is (R - universal gas constant)$ (1) $2 RT$ (2) $RT$ (3) $3 RT$ (4) $4 RT$ 12. $If the average translational kinetic energy of a molecule in a gas is equal to the kinetic energy of an electron accelerating from rest through 10 V, then the temperature of the gas molecule is (Boltzmann constant = 1.38 \times 10^{- 23} JK^{- 1})$ (1) $7.73 \times 10^{3} K$ (2) $730 K$ (3) $73.7 K$ (4) $77.3 \times 10^{3} K$ 13. $During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of \frac{C _{p}}{C _{v}} for the gas is:$ (1) $\frac{5}{3}$ (2) $\frac{9}{7}$ (3) $\frac{3}{2}$ (4) $\frac{7}{5}$ 14. $The average kinetic energy of H_{2} molecules at 300 K is E . At the same temperature the average kinetic energy of O_{2} molecule is$ (1) $E$ (2) $\frac{E}{4}$ (3) $\frac{E}{16}$ (4) $16 E$ 15. $An ideal gas in a container of volume 500 c.c. is at a pressure of 2 \times 10^{+ 5} N / m^{2} . The average kinetic energy of each molecules is 6 \times 10^{- 21} J . The number of gas molecules in the container is$ (1) $5 \times 10^{25}$ (2) $25 \times 10^{23}$ (3) $5 \times 10^{23}$ (4) $2.5 \times 10^{22}$ 16. $The equation of state for 2 g of oxygen at a pressure P and temperature T, when occupying a volume V will be$ (1) $PV = 16 RT$ (2) $PV = RT$ (3) $PV = \frac{1}{16} RT$ (4) $PV = 2 RT$ 17. $The temperature, at which the root mean square mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to : [Boltzmann Constant k_{B} = 1.38 \times 10^{- 23} J/K Avogadro Number N_{A} = 6.02 \times 10^{26} / kg Radius of Earth : 6.4 \times 10^{6} m Gravitational acceleration on Earth = 10 ms^{- 2}]$ (1) $800 K$ (2) $3 \times 10^{5} K$ (3) $10^{4} K$ (4) $650 K$ 18. $If a quantity of heat 1163.4 joule is supplied to one mole of nitrogen gas, at room temperature at constant pressure, then the rise in temperature is (Given R = 8.31 J mole^{- 1} K^{- 1})$ (1) $54 K$ (2) $28 K$ (3) $65 K$ (4) $40 K$ 19. $Consider an ideal gas at pressure p, volume V and temperature T . The mean free path for molecules of the gas is L . If the radius of gas molecules, as well as pressure, volume and temperature of the gas are doubled, then the mean free path will be$ (1) $\frac{5 L}{2}$ (2) $\frac{L}{4}$ (3) $\frac{L}{8}$ (4) $2 L$ 20. $Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure is$ (1) $(\frac{1}{3})^{rd} kinetic energy per unit volume of a gas$ (2) $(\frac{2}{3})^{rd} kinetic energy per unit volume of a gas$ (3) $(\frac{3}{4})^{th} kinetic energy per unit volume of a gas$ (4) $\frac{3}{2} \times kinetic energy per unit volume of a gas$ 21. $The molecular mass of a gas having r.m.s. speed four times as that of another gas having molecular mass 32 is$ (1) $2$ (2) $4$ (3) $16$ (4) $32$ 22. $If the rms speeds of helium and oxygen are equal, then the ratio of the temperatures of helium and oxygen is$ (1) $1 : 8$ (2) $2 : 1$ (3) $1 : 4$ (4) $4 : 1$ 23. $Increase in temperature of a gas filled in a container would lead to [NEET 2019]$ (1) $increase in its kinetic energy$ (2) $decrease in its pressure$ (3) $decrease in intermolecular distance$ (4) $increase in its mass$ 24. $The mean free path l for a gas molecule depends upon diameter, d of the molecule as [NEET 2020]$ (1) $l \propto \frac{1}{d ^{2}}$ (2) $l \propto d$ (3) $l \propto d^{2}$ (4) $1 \propto \frac{1}{d}$ 25. $What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?$ (1) $\frac{2}{3} k_{B} T$ (2) $k_{B} T$ (3) $\frac{3}{2} k_{B} T$ (4) $\frac{1}{2} k_{B} T$ 26. $A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27^{\circ} C . Its density is (R = 8.3 J mol^{- 1} K^{- 1}) [NEET 2020]$ (1) $0.2 kg / m^{3}$ (2) $0.1 kg / m^{3}$ (3) $0.02 kg / m^{3}$ (4) $0.5 kg / m^{3}$ 27. $For a gas C_{P} - C_{V} = R in a state P and C_{P} - C_{V} = 1.10 R in a state Q, T_{P} and T_{Q} are the temperatures in two different states P and Q respectively. Then$ (1) $T_{P} = T_{Q}$ (2) $T_{P} < T_{Q}$ (3) $T_{P} =0. 9 T_{Q}$ (4) $T_{P} > T_{Q}$ 28. $The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U = 3 PV + 4 . The gas is$ (1) $polyatomic only$ (2) $monoatomic only$ (3) $either monoatomic or diatomic$ (4) $diatomic only.$ 29. $Two spherical black bodies have radii r_{1} and r_{2} . Their surface temperature are T_{1} and T_{2} . If they radiate same power then \frac{r _{2}}{r _{1}} is$ (1) $\frac{T _{1}}{T _{2}}$ (2) $\frac{T _{2}}{T _{1}}$ (3) $(\frac{T _{1}}{T _{2}})^{2}$ (4) $(\frac{T _{2}}{T _{1}})^{2}$ 30. $The specific heat at constant pressure of a real gas obeying P V^{2} = RT equation is:$ (1) $\frac{R}{3} + C_{V}$ (2) $C_{V} + R$ (3) $C_{V} + \frac{R}{2 V}$ (4) $R$