Class 11 Physics — Chapter 13: Kinetic Theory Online Test

1. The escape velocity from Earth is . At what temperature would rms velocity of hydrogen molecules equal escape velocity? M = 0.002 kg/mol.

2. Reynolds number is given by: Air () flows at velocity through a pipe of diameter . Calculate Reynolds number.

3. For a cylindrical pipe of length , inner radius , outer radius , and , temperature difference is . Calculate heat transfer per second.

4. If nitrogen gas has mean free path and average molecular speed , calculate diffusion coefficient.

5. If the enthalpy of vaporization of liquid helium at 4.2 K is , calculate the entropy change per mole during vaporization.

6. A 250 g block of ice at 0 °C is converted into water at 0 °C. Find the entropy change of the system. (, )

7. The macroscopic law is derived microscopically using:

8. Entropy () connects microscopic and macroscopic descriptions by the relation:

9. The Boltzmann constant () relates:

10. According to Arrhenius equation , how does temperature affect rate constant?

11. In chemical engineering, the diffusion coefficient for gases is often estimated using kinetic theory as:

12. Why is Brownian motion critical in nanomedicine for drug delivery systems?

13. According to Einstein’s 1905 explanation, the random motion of suspended particles in Brownian motion is caused by:

14. The mean free path is inversely proportional to:

15. A gas has . If 5 moles of this gas are heated at constant volume through 40 K, how much heat is absorbed?

16. The work done by an ideal gas in an isothermal process from to is:

17. According to the law of equipartition, the average energy per molecule of a monatomic ideal gas is:

18. For a monatomic ideal gas, the total average energy per molecule according to equipartition theorem is:

19. What happens to the pressure of a gas if the rms speed of its molecules doubles at constant volume?

20. Which formula relates pressure , number density , molecular mass , and mean square speed ?

1. Thermal conductivity of gases is explained by kinetic theory as:

2. A composite wall has two layers in series: thickness of brick () and of plaster (). If area = and , calculate heat flow per second.

3. Enzymes act as catalysts in biochemical reactions because:

4. In a Boyle’s law experiment, a gas sample initially at 1 atm and 500 mL is compressed to 250 mL. What is the new pressure?

5. A vessel contains helium at 300 K and pressure . If average kinetic energy per atom = , calculate energy of 1 mole.

6. In statistical mechanics, an ensemble refers to:

7. Einstein’s expression for the diffusion coefficient of spherical particles of radius suspended in a fluid of viscosity is:

8. Which scientist proposed corrections to the ideal gas law to account for real gas behavior?

9. In the contact process for sulfuric acid production, which catalyst is used?

10. Why does the stratosphere contain a higher concentration of ozone compared to the troposphere?

11. At a liquid–gas critical point, the order parameter vanishes. If density difference between phases is , then near critical temperature:

12. The average speed of molecules in Maxwell–Boltzmann distribution is:

13. Why are catalysts widely used in chemical industries?

14. Which microscopic property determines diffusion rate of gases?

15. In nuclear emulsions, Brownian-like motion of ions can be modeled using which formula?

16. Using kinetic theory, show how viscosity relates to thermal conductivity . For monatomic gases: where is molar heat capacity at constant pressure. If for air and , calculate . (Molar volume at STP ).

17. A triatomic linear molecule like has how many degrees of freedom (ignoring vibrations)?

18. Which of the following best explains metallic luster?

19. In terms of kinetic theory, collision frequency () for two species is proportional to:

20. The Debye model describes the heat capacity of solids at low temperatures as:

21. At 100 °C, water has . Estimate the slope of liquid–vapor boundary using Clausius–Clapeyron: Given: , .

22. Which of the following does NOT affect the rate of a chemical reaction?

23. Which ensemble is used for a system at fixed temperature, volume, and number of particles?

24. For a diatomic gas (ignoring vibrations), calculate the heat required to raise 2 moles of the gas by 40 K at constant volume.

25. Which type of graph is obtained when pressure is plotted against for a fixed mass of gas at constant temperature?

26. Which statistical distribution applies to indistinguishable particles with half-integer spin (electrons, protons, neutrons)?

27. In terms of Helmholtz free energy , entropy is calculated as:

28. Einstein’s explanation of Brownian motion is considered a bridge between:

29. Calculate the increase in internal energy when 4 moles of monatomic gas are heated by 50 K at constant volume.

30. Which of the following gases is closest to ideal gas behavior under normal conditions?

1. In chemical engineering, the diffusion coefficient for gases is often estimated using kinetic theory as:

2. For a diatomic gas (ignoring vibrations), calculate the heat required to raise 2 moles of the gas by 40 K at constant volume.

3. For a gas mixture containing 1 mole of monatomic gas and 1 mole of diatomic gas (no vibrations), the effective molar is:

4. If 2 L of hydrogen and 2 L of oxygen are measured at the same temperature and pressure, then:

5. The use of catalysts in chemical kinetics primarily affects:

6. If mean free path is proportional to , what happens to when temperature doubles and pressure halves?

7. The Van der Waals constants and are determined experimentally for gases. Which of the following units are correct for and ?

8. A triatomic linear molecule like has how many degrees of freedom (ignoring vibrations)?

9. In heterogeneous catalysis, why does increasing surface area of catalyst increase reaction rate?

10. Who explained Brownian motion as evidence of molecular kinetic theory?

11. Avogadro’s law states that:

12. The Second Law of Thermodynamics states that entropy of an isolated system never decreases. How is this interpreted statistically?

13. Which equation represents the behavior of an ideal gas?

14. The Maxwell–Boltzmann distribution explains that:

15. Which physical constant can be determined from analyzing Brownian motion data?

16. In particle physics, diffusion due to Brownian motion is important in gaseous detectors. The mean square displacement after time in 3D is:

17. In aerodynamics, the drag force due to viscosity on a sphere is given by Stokes’ law: A water droplet of radius falls in air () at speed . Calculate drag force.

18. In Lee’s disc experiment, if brass disc of heat capacity cools at , calculate heat flow through the sample.

19. Thermal conductivity of copper is . A copper plate thick, area , has surfaces at and . Calculate heat current.

20. The ratio of specific heats () for a diatomic gas at moderate temperature is approximately:

21. Which ensemble is appropriate for systems with fixed energy, volume, and particle number?

22. The latent heat of fusion of ice is . How much ice at 0 °C can be melted with 100 kJ of heat?

23. If the pressure of a gas is reduced to half at constant temperature, what happens to mean free path?

24. The rate of effusion of a gas through a small hole is proportional to:

25. Which equation is derived from kinetic theory of gases?

26. Enzymes act as catalysts in biochemical reactions because:

27. A gas at 400 K has molecules with . If temperature doubles, the new most probable speed is:

28. In chemical engineering, viscosity affects mass transport. Diffusion coefficient is approximated by Stokes–Einstein relation: For a particle radius in water at 300 K (), calculate . ()

29. Which scientist is credited with formulating Avogadro’s law?

30. Which assumption of kinetic theory explains why pressure of a gas arises?

31. Which property of water is NOT directly explained by hydrogen bonding?

32. Which relation connects diffusion coefficient , mean free path , and molecular speed ?

33. Which experimental observation best supports Avogadro’s law?

34. Which term in the Van der Waals equation accounts for molecular attractions?

35. If nitrogen gas has mean free path and average molecular speed , calculate diffusion coefficient.

36. In terms of kinetic theory, collision frequency () for two species is proportional to:

37. Calculate the effusion rate ratio of hydrogen () to carbon dioxide ().

38. The Pauli Exclusion Principle states that:

39. What is the main postulate of kinetic theory of gases?

40. Why is viscosity critical in fluid engineering design?

41. Which of the following is a characteristic property of metallic bonds?

42. Which of the following correctly describes atomic orbitals?

43. Which ensemble is used for a system at fixed temperature, volume, and number of particles?

44. Einstein’s explanation of Brownian motion is considered a bridge between:

45. Which scientist first published the law of pressure-volume relationship (Boyle’s law)?

46. A slab of glass of thickness has thermal conductivity . If the two surfaces are kept at and , calculate heat flow per unit area per second.

47. The average speed of molecules in Maxwell–Boltzmann distribution is:

48. In the Van der Waals equation , what does the constant represent?

49. The head loss due to viscous flow in a circular pipe is given by Darcy–Weisbach equation: If water of viscosity flows at mean velocity through a pipe of diameter and length , calculate the head loss. ()

50. Why does ethanol () dissolve in water?