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. How does kinetic theory explain Brownian motion?

2. Which factor does NOT affect collision frequency?

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

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

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

6. In metallurgy, the Clausius–Clapeyron relation explains slope of solid–liquid equilibrium lines as:

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

8. Collision frequency between molecules is given by:

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

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

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

12. Einstein’s expression for the diffusion coefficient of spherical particles of radius suspended in a fluid of viscosity is:

13. In chemical engineering, viscosity affects mass transport. Diffusion coefficient is approximated by Stokes–Einstein relation: For a particle radius in water at 300 K (), calculate . ()

14. The partition function near a phase transition becomes:

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

16. The Boltzmann constant () relates:

17. Why does viscosity of the medium affect Brownian motion?

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

19. How does kinetic theory help explain the states of matter?

20. The equation was used by Jean Perrin to:

21. The use of catalysts in chemical kinetics primarily affects:

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

23. In nuclear emulsions, Brownian-like motion of ions can be modeled using which formula?

24. 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.

25. 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.

26. According to kinetic theory, the distribution of molecular speeds in a gas:

27. The pressure drop in laminar flow through a tube is given by: For oil of viscosity , flow rate , tube length , and radius , calculate .

28. The assumption that gas molecules move in straight lines between collisions implies:

29. The heat flux through a wall is found experimentally to be for a temperature difference of across . Calculate thermal conductivity.

30. Which fundamental quantity connects kinetic theory with thermodynamics?

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

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

3. The escape velocity from Earth is . At what temperature would rms velocity of hydrogen molecules equal escape velocity? M = 0.002 kg/mol.

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

5. Joule’s contribution to kinetic theory was primarily through:

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

7. The Boltzmann constant () relates:

8. Why must Charles’s law be expressed in Kelvin instead of Celsius?

9. If a nanoparticle of radius is suspended in water () at room temperature (), calculate its diffusion coefficient.

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

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

12. The Pauli Exclusion Principle states that:

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

14. The difference between molar heat capacities at constant pressure and volume is:

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

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

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

18. Maxwell’s contribution to kinetic theory includes:

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

20. The specific heat at constant volume of 1 mole of an ideal monatomic gas is:

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

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

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

24. The specific heat at constant pressure is greater than at constant volume because:

25. Why do polyatomic gases generally have higher specific heat capacities than monatomic gases?

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

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

28. Calculate the increase in internal energy when 4 moles of monatomic gas are heated by 50 K at constant volume.

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

30. Which scientist proposed corrections to the ideal gas law to account for real gas behavior?

31. Which equation derived by Einstein relates mean squared displacement in Brownian motion to time?

32. Show that viscosity of gases is nearly independent of pressure. For nitrogen at STP, mean free path . Using , explain why pressure cancels out.

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

34. Which of the following correctly describes atomic orbitals?

35. For a system of particles, pressure from statistical mechanics is expressed as:

36. In the Ising model, magnetization serves as:

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

38. During freezing of 1 kg of water, latent heat released is:

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

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

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

42. Which of the following explains why iodine () is solid at room temperature while chlorine () is a gas?

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

44. If air at STP has molecular diameter and number density , calculate mean free path.

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

46. The rate of most chemical reactions approximately doubles when temperature increases by:

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

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

49. For 3 moles of a diatomic gas at 300 K (ignoring vibrations), the internal energy is:

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