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 a monatomic ideal gas have ?

2. If viscosity of a gas at 300 K is , predict viscosity at 600 K using Sutherland’s formula: Given .

3. The critical temperature of a gas is defined as:

4. Which of the following compounds has a purely covalent bond?

5. 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?

6. Which of the following correctly represents root mean square (rms) speed?

7. A wall of area , thickness , and conductivity separates rooms at and . Find heat loss per second.

8. An engine cylinder wall has area , thickness , and conductivity . If the inner wall is at and the outer at , calculate heat loss per second.

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

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

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

12. If a wall of thickness and conductivity separates indoors at from outdoors at , calculate heat loss per square meter per second.

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

14. Which of the following is NOT an assumption of kinetic theory?

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

16. Why is the factor of important in determining mean free path?

17. At very high altitudes, the mean free path of air molecules is extremely large because:

18. Which of the following is NOT true for covalent bonds?

19. For 1 mole of a monatomic gas at temperature , the total internal energy is:

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

21. For a reaction with high activation energy, temperature dependence of the rate is:

22. At very high pressure, which effect dominates the deviation from ideal gas behavior?

23. In nanotechnology, Brownian motion is used to estimate the diffusion coefficient of nanoparticles. Which relation is applied?

24. Why are catalysts widely used in chemical industries?

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

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

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

28. How does the presence of a catalyst affect the reaction rate?

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

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

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

2. The rate of a chemical reaction according to collision theory is directly proportional to:

3. At very high altitudes, the mean free path of air molecules is extremely large because:

4. If the volume of a gas increases three times at constant temperature, its pressure will:

5. 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?

6. From a statistical mechanics perspective, a phase transition occurs when:

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

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

9. Why does increasing temperature generally increase reaction rate?

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

11. Which of the following quantities is NOT directly needed to calculate mean free path?

12. What role did Einstein’s theory of Brownian motion play in physics history?

13. Why is the factor of important in determining mean free path?

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

15. Which microscopic property determines diffusion rate of gases?

16. 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?

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

18. For a monatomic ideal gas, what is the value of ?

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

20. The mean square displacement in one dimension according to Einstein is given by:

21. 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 .

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

23. A furnace wall of thickness , area , conductivity , has inside , outside . Calculate heat loss per second.

24. A gas mixture contains 2 moles of O and 4 moles of He at 300 K. Calculate ratio of rms speeds .

25. Why does liquefaction of gases occur in real gases but not in ideal gases?

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

27. The order of molecular speeds at a given temperature is:

28. Which of the following statements best summarizes the effect of temperature and pressure on mean free path?

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

30. Which transport property of gases is NOT directly related to mean free path?

31. The formula for mean free path is:

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

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

34. In an experiment, the time of flow of 50 ml of a liquid through an Ostwald viscometer is 120 s, while that of water (viscosity = 0.001 Pa·s) is 100 s. If densities of the liquid and water are and respectively, calculate viscosity of the liquid.

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

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

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

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

39. 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.

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

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

42. The isotherms of real gases on a - graph deviate from ideal gas isotherms because:

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

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

45. Why is viscosity critical in fluid engineering design?

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

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

48. Which of the following compounds has a purely covalent bond?

49. According to kinetic theory, pressure of a gas arises due to:

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