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. Why does ice float on water in terms of phase transition properties?

2. Why do real gases deviate from ideal behavior at high pressure?

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

4. Why does kinetic theory correctly predict viscosity of gases but not liquids?

5. Why is effusion slower for heavy gases than for light gases?

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

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

8. The internal energy of an ideal monatomic gas is expressed microscopically as:

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

10. Why is measuring viscosity important in engineering applications?

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

12. If 3 moles of a gas occupy 67.2 L at STP, then the volume of 1 mole of the gas is:

13. In an experiment, 1 mole of an ideal monatomic gas is heated at constant volume by 25 K. How much heat is required?

14. In the upper atmosphere, mean free path of molecules is very large because:

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

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

17. What type of bond holds the atoms together in a diamond crystal?

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. In kinetic theory, what is the assumption about the size of gas molecules compared to the distance between them?

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

21. A sealed container holds water at equilibrium at 100 °C. If the pressure is suddenly reduced, what happens to the boiling point?

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

23. In Hagen–Poiseuille flow, volumetric flow rate is: A liquid of viscosity flows through a tube of radius , length , under pressure difference . Calculate flow rate.

24. Which law of thermodynamics is consistent with the conservation of molecular kinetic energy in elastic collisions?

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

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

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

28. At high temperatures, vibrational modes in molecules become active. How does this affect heat capacity?

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

30. Which type of intermolecular force is primarily responsible for the high boiling point of water?

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

2. For an ideal gas, internal energy can be expressed in terms of partition function as:

3. How does increasing concentration of reactants affect reaction rate?

4. Which law of thermodynamics is consistent with the conservation of molecular kinetic energy in elastic collisions?

5. Why does pressure of a gas increase with temperature at constant volume?

6. A balloon at constant pressure shrinks in volume when cooled. Which molecular explanation fits Charles’s law?

7. In statistical mechanics, the free energy is related to the partition function as:

8. Calculate the ratio of diffusion rates of helium (M = 4) and nitrogen (M = 28).

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

10. Graham’s law of diffusion is consistent with kinetic theory because:

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

12. What does the Maxwell-Boltzmann distribution describe in relation to thermodynamics?

13. At STP, calculate collision frequency of oxygen molecules. Take .

14. Specific heat capacity is related to microscopic states because:

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

16. In JEE-type advanced problems, pressure from kinetic theory is given by: For molecules, , , , calculate .

17. The partition function near a phase transition becomes:

18. The most probable speed of gas molecules is given by:

19. If a sealed syringe containing 30 mL of air at 1 atm is compressed to 10 mL without changing temperature, what is the final pressure?

20. A sample of gas has a volume of 250 mL at 300 K. To maintain constant pressure, what temperature is needed for the volume to expand to 500 mL?

21. For a linear triatomic molecule at high temperature where vibrational modes are active, the average energy per molecule becomes:

22. Which equation relates diffusion coefficient to mean free path?

23. Which modern field uses Brownian motion as a fundamental concept?

24. Viscosity of a gas is related to mean free path by:

25. At high temperatures, vibrational modes in molecules become active. How does this affect heat capacity?

26. Enzymes act as catalysts in biochemical reactions because:

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

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

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

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

31. 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.

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

33. Collision theory states that a chemical reaction occurs when:

34. If a copper rod of cross-sectional area , length , and conducts of heat, what is the temperature difference across its ends?

35. What happens to the Maxwell–Boltzmann distribution curve when temperature increases?

36. For 1 mole of a monatomic ideal gas at , calculate average translational kinetic energy per molecule and per mole. ()

37. Second-order (continuous) phase transitions are distinguished by:

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

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

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

41. Why are neutron stars denser than white dwarfs?

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

43. The Boltzmann constant () relates:

44. The specific heat at constant pressure near second-order transitions often diverges as:

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

46. Boyle’s law states that for a fixed mass of gas at constant temperature:

47. Which of the following is an example of an ionic bond?

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

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

50. For a monatomic ideal gas, the molar heat capacity at constant volume () is: