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. Calculate the relative rate of diffusion of nitrogen () to oxygen ().

2. Which real-world process is based on gas effusion?

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

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

5. Diffusion of gases is defined as:

6. Why does statistical mechanics predict universality near critical points?

7. The Maxwell–Boltzmann distribution explains that:

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

9. Which experiment provided evidence for the wave nature of electrons?

10. Which scientist first explained the cause of Brownian motion theoretically?

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

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

13. For a monatomic ideal gas, which degrees of freedom contribute to its energy?

14. Boyle’s Law, one of the early gas laws, relates pressure and volume as:

15. Calculate the amount of heat required to melt 500 g of ice at . Latent heat of fusion of ice .

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

17. Which of the following gases has the largest Van der Waals constant ?

18. The viscosity of a liquid can be determined using Poiseuille’s law for laminar flow through a capillary tube: If a capillary tube of radius and length allows a volume flow rate under a pressure difference of , calculate the viscosity of the liquid.

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

20. The mean free path for nitrogen at 300 K and 1 atm is . If viscosity , and is measured as , find approximate average molecular speed. Density .

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

22. In statistical mechanics, entropy is expressed as:

23. For 2 moles of a monatomic ideal gas, calculate the increase in internal energy when temperature increases by 50 K.

24. The average energy per molecule of a diatomic gas at moderate temperatures (ignoring vibrations) is:

25. A balloon filled with air has a volume of 1.5 L at 27°C. What will be its volume at 127°C, if pressure remains constant?

26. The dimension of thermal conductivity in SI units is:

27. According to Graham’s law, the rate of diffusion or effusion is:

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

29. Isotopes of an element have:

30. A 100 nm gold nanoparticle in water has . What is its root mean square displacement in 1 second?

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

2. Why does a monatomic ideal gas have ?

3. In material science, the entropy change during solid-to-liquid transition is:

4. Calculate the internal energy of 2 moles of a monatomic ideal gas at 300 K.

5. How does pressure affect the mean free path of a gas?

6. Which factor does NOT affect collision frequency?

7. What is the primary reason ionic compounds conduct electricity in molten state but not in solid state?

8. Why do reactions between ions in aqueous solution often occur very fast compared to neutral molecules?

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

10. A container has 1 mole of He gas at 300 K. Calculate total internal energy:

11. The partition function near a phase transition becomes:

12. According to kinetic theory, the volume of individual gas molecules compared to the total volume of the gas is:

13. Why does the viscosity of gases increase with temperature, unlike liquids?

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

15. If temperature rises from 300 K to 330 K, how does the rate constant typically change for a reaction with ?

16. Einstein’s theory of Brownian motion provided a way to calculate:

17. In atmospheric escape processes, lighter gases like hydrogen are lost from Earth because:

18. A glass window area, thick, with separates inside and outside . Calculate heat loss per second.

19. Why is statistical mechanics crucial for explaining phase transitions?

20. In lubrication engineering, shear stress is given by Newton’s law: If oil film of viscosity and thickness separates two plates, one moving at , calculate shear stress.

21. The specific heat ratio can be determined experimentally by:

22. A cylinder contains 4 g of O gas at STP. Calculate average translational kinetic energy of all molecules together. (Avogadro’s number ).

23. The connection between partition function and Helmholtz free energy is:

24. The Gibbs free energy change for a first-order phase transition is:

25. Which property of liquids is most influenced by intermolecular forces?

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

27. For 1 mole of an ideal gas, the total translational kinetic energy is:

28. Which of the following is the correct order of characteristic molecular speeds?

29. Which statement best describes the connection between microscopic and macroscopic views?

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

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

32. Which type of bonding explains why aluminum is both strong and a good conductor of electricity?

33. What does the steric factor in collision theory account for?

34. Why are heterogeneous catalysts often used instead of homogeneous ones in industry?

35. Why are gases highly compressible compared to solids and liquids?

36. What is the principal quantum number associated with?

37. The equipartition theorem relates directly to which thermodynamic property?

38. At the critical point of a liquid–gas transition, the order parameter is:

39. 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:

40. Which thermodynamic process involves heat transfer but no change in temperature?

41. For 1 mole of a diatomic gas (ignoring vibrations), the internal energy is:

42. Which industrial process uses finely divided platinum as a catalyst?

43. Which of the following best demonstrates Boyle’s law in real life?

44. A glycerin sample flows through a capillary of radius , length , under a pressure difference of . If volume flow rate is measured as , calculate viscosity.

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

46. In the Maxwell–Boltzmann speed distribution curve, the area under the curve represents:

47. Which law can be derived from the kinetic theory assumption that average kinetic energy is proportional to absolute temperature?

48. Which phenomenon directly validates molecular speed distribution in gases?

49. 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?

50. The root mean square displacement of a nanoparticle undergoing Brownian motion in time is given by: