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. The latent heat equation during condensation of a mass of vapor is:

2. Which scientist formulated the Atomic Theory in the early 19th century that laid the foundation for kinetic theory?

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

4. In an adiabatic expansion of 2 moles of a monatomic gas from 5 L to 20 L at 300 K, the final temperature is approximately:

5. If the pressure of a gas is kept constant and the temperature is doubled, what happens to the mean free path?

6. Which molecular-level property explains diffusion in gases?

7. The Maxwell–Boltzmann distribution explains that:

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

9. Which of the following compounds contains polar covalent bonds?

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

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

12. Which classical result emerges as the high-temperature limit of both Fermi–Dirac and Bose–Einstein statistics?

13. The relation between average kinetic energy per molecule and temperature is:

14. In a calorimeter experiment, 2 moles of a monatomic gas absorb 900 J of heat at constant volume. Find the rise in temperature.

15. The entropy in terms of microstates is given by Boltzmann’s formula:

16. Which molecular property is directly measured by temperature according to kinetic theory?

17. For oxygen gas at 300 K, molar mass . Calculate rms speed and then viscosity using . Given , , .

18. Why does table salt () dissolve easily in water?

19. For a gas with molecular diameter , at , and , calculate the mean free path.

20. A metal rod of length , cross-sectional area , and thermal conductivity is subjected to a temperature difference of . Calculate heat current through the rod.

21. For argon gas () at 300 K, calculate viscosity using kinetic theory. Given , .

22. Pressure affects the rate of reaction most strongly in:

23. If two gases and have molar masses and , the ratio of their rates of diffusion is:

24. How does kinetic theory explain Brownian motion?

25. Which fundamental quantity connects kinetic theory with thermodynamics?

26. What is the root mean square (rms) speed of gas molecules?

27. How does kinetic theory explain the pressure exerted by liquids in a container?

28. Brownian motion provides strong evidence for:

29. Which of the following is NOT an assumption of kinetic theory for an ideal gas?

30. Which distribution applies to indistinguishable particles with integer spin (photons, helium-4 atoms)?

1. The partition function near a phase transition becomes:

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

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

4. Why do correlation lengths diverge near second-order transitions?

5. Brownian motion cannot be observed in solids because:

6. For a diatomic gas (ignoring vibrational energy), the molar heat capacity at constant volume is:

7. Why does compressibility factor deviate from 1 for real gases?

8. Why is the factor included in the formula for mean free path?

9. Why is measuring viscosity important in engineering applications?

10. The partition function in statistical mechanics is defined as:

11. At intermediate pressures, real gases often show compressibility factor . What does this indicate?

12. In thermodynamics, free energy determines spontaneity. Which statistical mechanics quantity helps calculate free energy?

13. Calculate the mass of steam at 100 °C required to release 2,000 kJ of heat on condensation. ()

14. Which property of gases can be directly explained using the concept of mean free path?

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

16. The mean free path of a gas molecule is related to number density and molecular diameter as:

17. A 10 L container holds 0.5 mol of O at 300 K. Calculate pressure using kinetic theory:

18. What is the molar heat capacity at constant volume () of a monatomic ideal gas according to equipartition theorem?

19. Which scientist formulated the Atomic Theory in the early 19th century that laid the foundation for kinetic theory?

20. Brownian motion provides strong evidence for:

21. For a diatomic gas (no vibrations), the adiabatic index is:

22. Which of the following statements about ionic bonds is correct?

23. For an ideal gas, the relation between and is given by:

24. A steel sphere of radius falls through oil of density . The sphere density is , terminal velocity . Find viscosity of oil.

25. A diatomic gas molecule (ignoring vibrations) has how many degrees of freedom?

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

27. At 300 K, calculate fraction of nitrogen molecules with speed greater than 1000 m/s using Maxwell–Boltzmann distribution: M = 0.028 kg/mol.

28. The latent heat of fusion of aluminum is . How much energy is required to melt a block of aluminum at its melting point?

29. The latent heat equation during condensation of a mass of vapor is:

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

31. The Maxwell–Boltzmann distribution explains that:

32. For a fixed gas, what happens to the Maxwell–Boltzmann distribution when molar mass increases at constant temperature?

33. Which of the following best describes a polar covalent bond?

34. Why is statistical mechanics important in modern physics and chemistry?

35. Metallic bonds are best explained by which model?

36. Which scientist discovered the relationship now known as Charles’s law?

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

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

39. For a lubricant in a bearing, power lost due to viscous drag is: If shear stress , area , velocity , calculate power loss.

40. In kinetic theory derivation, the temperature of a gas is defined in terms of:

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

42. For a first-order phase transition, the Clausius–Clapeyron relation is:

43. For a diatomic molecule (ignoring vibrational modes), how many degrees of freedom are considered in equipartition theorem?

44. The internal energy of an ideal monatomic gas is given by:

45. The equation was used by Jean Perrin to:

46. How does kinetic theory explain the pressure exerted by liquids in a container?

47. Which catalyst is used in the Haber process for ammonia synthesis?

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

49. Which assumption of kinetic theory is violated when gases show liquefaction at high pressure?

50. The Maxwell–Boltzmann distribution provides a molecular basis for which thermodynamic law?