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

2. The Arrhenius equation relates rate constant to activation energy:

3. If the probability distribution of a quantity is sharply peaked, what does it imply about fluctuations?

4. If 2 moles of water are vaporized at 100 °C and 1 atm, how much heat is absorbed? ()

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

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

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

8. Why does Maxwell–Boltzmann distribution predict that some molecules always exceed escape velocity from Earth?

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

10. The fluctuation–dissipation relation links heat capacity to energy fluctuations:

11. For a diatomic gas at room temperature, neglecting vibrations, the molar predicted by equipartition theorem is:

12. Why is measuring viscosity important in engineering applications?

13. How does kinetic theory explain Brownian motion?

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

15. For a linear triatomic molecule at high temperature, the expected using kinetic theory is:

16. Why does Van der Waals equation reduce to the ideal gas equation at low pressure and high temperature?

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

18. Which equation links diffusion coefficient of nanoparticles to temperature, radius, and viscosity, and is used in nanotechnology research?

19. Which thermodynamic property is most directly associated with disorder in statistical mechanics?

20. Which factor does NOT affect collision frequency?

21. Why do liquids evaporate even at room temperature?

22. Temperature is directly related to which microscopic property of molecules?

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

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

25. Effusion of gases is best described as:

26. 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.

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

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

29. Why is mean free path important in determining thermal conductivity of gases?

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

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

2. Brownian motion decreases in intensity when:

3. Calculate mean free path of nitrogen at , . (Molecular diameter , ).

4. 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.

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

6. Which of the following chemical reactions demonstrates Avogadro’s law?

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

8. In engineering insulation problems, effective thermal conductivity for multilayer walls is found by:

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

10. The Ostwald process for nitric acid production uses which catalyst?

11. 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 ).

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

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

14. Which of the following conditions increases the rate of diffusion of a gas?

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

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

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

18. Calculate the molar heat capacity ratio () for a monatomic ideal gas.

19. 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?

20. Which expression relates the rms speed of molecules to pressure and density?

21. Why are catalysts widely used in chemical industries?

22. 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.

23. Calculate most probable speed of O molecules at 500 K:

24. Which type of bond explains the malleability and ductility of metals?

25. A nanoparticle of radius undergoes Brownian motion. If the viscosity of the medium is doubled, how does diffusion coefficient change?

26. Isotopes of an element have:

27. The order parameter in phase transitions represents:

28. Which of the following correctly describes atomic orbitals?

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

30. The law of equipartition of energy states that:

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

32. In molecular dynamics simulations, why is mean free path important?

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

34. In the derivation of gas pressure, why is the factor included?

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

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

37. In kinetic theory, what is assumed about the time of collision between two molecules?

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

39. The relation between pressure and volume in an adiabatic process is:

40. Which of the following explains why carbon dioxide liquefies more easily than oxygen?

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

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

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

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

45. Which of the following best explains metallic luster?

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

47. In statistical mechanics, the partition function is important because:

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

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

50. Which ensemble is used for a system at fixed temperature, volume, and chemical potential (allowing particle exchange)?