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

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

3. If the diameter of molecules is halved while keeping pressure and temperature constant, the mean free path will:

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

5. How does kinetic theory explain Brownian motion?

6. Diffusion of gases is defined as:

7. Why do reactions between ions in aqueous solution usually occur very fast?

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

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

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

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

12. The macroscopic quantity pressure in a gas arises microscopically from:

13. Who was the first scientist to propose that matter is made up of indivisible particles called “atoms”?

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

15. A gas effuses 1.414 times faster than oxygen. What is its molar mass?

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

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

18. What is the root mean square (rms) speed of gas molecules?

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

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

21. Why does ice float on water, considering kinetic theory and molecular structure?

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

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

24. The ratio of rates of effusion of hydrogen and oxygen is:

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

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

27. The ratio of specific heats () for a diatomic gas at moderate temperature is approximately:

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

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

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

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

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

3. The mean free path of air molecules at 1 atm is . What will it be at pressure of , at same temperature?

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

5. Which scientist experimentally verified Einstein’s theory of Brownian motion?

6. The enthalpy change during melting (fusion) is given by:

7. According to kinetic theory, the pressure exerted by a gas in a container is due to:

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

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

10. The order parameter in phase transitions represents:

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

12. Calculate the effusion rate ratio of hydrogen () to carbon dioxide ().

13. A gas has a pressure of 5 atm when its volume is 10 L. What will be the pressure if the gas is compressed to 2 L at constant temperature?

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

15. Which factor most strongly determines whether a bond is ionic or covalent?

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

17. In statistical mechanics, ensemble averages correspond experimentally to:

18. Which compound is held together by covalent bonding?

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

20. Which experimental observation validates the Maxwell–Boltzmann distribution of molecular speeds?

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

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

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

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

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. For a diatomic gas (ignoring vibrational energy), the molar heat capacity at constant volume is:

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

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

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

30. Calculate the entropy change when 1 mole of water vapor condenses at 373 K. ()

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

32. For oxygen gas at 300 K, molar mass . Calculate rms speed and then viscosity using . Given , , .

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

34. Which of the following best explains metallic luster?

35. In probability distributions, the normalization condition requires:

36. Which statistical mechanics relation connects fluctuations to heat capacity near a phase transition?

37. Calculate the heat required to raise the temperature of 3 moles of a diatomic gas (ignoring vibrations) by 50 K at constant pressure.

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

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

40. How much heat is released when 200 g of water at 100 °C condenses into liquid? ()

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

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

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

44. Which of the following liquids has the highest surface tension?

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

46. 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 ).

47. The molecular speed distribution widens when:

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

49. Calculate the mass of steam at 100 °C required to release 2,000 kJ of heat on condensation. ()

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