MCQ Physics Chapter–13: Kinetic Theory, HS 1st year

 

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1. Who is credited with discovering the law that gases are made up of tiny particles?

a) Avogadro
b) Newton
c) Boyle
d) Dalton
Answer: c) Boyle

2. What is the approximate size of an atom?

a) 10 m
b) 1 nm
c) 1 Å
d) 10 Å
Answer: c) 1 Å

3. What does Avogadro's hypothesis state?

a) Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
b) All gases have the same density.
c) The mass of a gas is inversely proportional to its temperature.
d) Pressure is proportional to temperature.
Answer: a) Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.

4. What is the value of Boltzmann constant ($k_B$) in SI units?

a) $1.38 \times 10^{-23} \, \mathrm{J \, K^{-1}}$
b) $8.31 \, \mathrm{J \, mol^{-1} \, K^{-1}}$
c) $6.02 \times 10^{23} \, \mathrm{molecules/mol}$
d) $3.14 \, \mathrm{J/K}$
Answer: a) $1.38 \times 10^{-23} \, \mathrm{J \, K^{-1}}$

5. What does the equation $PV = nRT$ represent?

a) Dalton's law
b) Boyle's law
c) Charles' law
d) Ideal gas equation
Answer: d) Ideal gas equation

6. What is the temperature at standard temperature and pressure (STP)?

a) $0^\circ C$
b) $100^\circ C$
c) $273^\circ C$
d) $300 \, K$
Answer: a) $0^\circ C$

7. How is mean free path ($l$) expressed?

a) $l = \frac{k_B T}{P}$
b) $l = \frac{1}{n\pi d^2}$
c) $l = P V / T$
d) $l = \frac{3RT}{2M}$
Answer: b) $l = \frac{1}{n\pi d^2}$

8. What type of motion contributes to translational kinetic energy in a gas?

a) Rotational
b) Vibrational
c) Linear motion
d) Potential energy
Answer: c) Linear motion

9. What is the molar volume of an ideal gas at STP?

a) 22.4 L
b) 24.8 L
c) 20.2 L
d) 23.1 L
Answer: a) 22.4 L

10. What is the total pressure of a mixture of gases according to Dalton's law?

a) Equal to the average of partial pressures.
b) Sum of the partial pressures.
c) Difference between maximum and minimum pressure.
d) None of the above.
Answer: b) Sum of the partial pressures.

11. What is the root mean square (RMS) speed of a gas molecule dependent on?

a) Molecular weight
b) Temperature
c) Both molecular weight and temperature
d) Pressure
Answer: c) Both molecular weight and temperature

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11. Which of the following is an example of a monatomic gas?

a) Nitrogen
b) Helium
c) Oxygen
d) Carbon dioxide
Answer: b) Helium

12. What is the value of the universal gas constant $R$?

a) $8.314 \, \mathrm{J \, mol^{-1} \, K^{-1}}$
b) $1.38 \times 10^{-23} \, \mathrm{J \, K^{-1}}$
c) $6.02 \times 10^{23}$
d) $3.00 \times 10^{8} \, \mathrm{m/s}$
Answer: a) $8.314 \, \mathrm{J \, mol^{-1} \, K^{-1}}$

13. Which gas law states that at constant pressure, the volume of a gas is proportional to its absolute temperature?

a) Boyle’s law
b) Charles’ law
c) Avogadro’s law
d) Dalton’s law
Answer: b) Charles’ law

14. The translational kinetic energy of a gas molecule at temperature $T$ is proportional to:

a) $T^2$
b) $1/T$
c) $T$
d) $T^3$
Answer: c) $T$

15. The number of degrees of freedom for a diatomic molecule is:

a) 3
b) 5
c) 7
d) 9
Answer: b) 5

16. What is the relationship between pressure ($P$) and volume ($V$) in Boyle’s law?

a) $P \propto V$
b) $P \propto 1/V$
c) $P \propto T$
d) $P \propto n$
Answer: b) $P \propto 1/V$

17. Which scientist proposed the atomic hypothesis that “all things are made of atoms”?

a) Dalton
b) Democritus
c) Maxwell
d) Feynman
Answer: b) Democritus

18. In a polyatomic gas, vibrational modes contribute:

a) $\frac{1}{2}k_B T$
b) $k_B T$
c) $\frac{3}{2}k_B T$
d) $2k_B T$
Answer: b) $k_B T$

19. What is the main assumption of the kinetic theory of gases?

a) Gas molecules interact strongly with each other.
b) Gas molecules are in constant random motion.
c) Gas molecules move only in straight lines.
d) Gas molecules have infinite size.
Answer: b) Gas molecules are in constant random motion.

20. The mean free path in a gas increases if:

a) Pressure increases
b) Number density increases
c) Temperature decreases
d) Molecular size decreases
Answer: d) Molecular size decreases

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21. What does the kinetic theory explain?

a) Properties of solids
b) Behavior of gases
c) Formation of liquids
d) Properties of metals
Answer: b) Behavior of gases

22. What is the internal energy of an ideal monatomic gas dependent on?

a) Pressure only
b) Volume only
c) Temperature only
d) Both pressure and volume
Answer: c) Temperature only

23. What is the molar specific heat ($C_v$) for a diatomic gas?

a) $3/2 R$
b) $5/2 R$
c) $7/2 R$
d) $9/2 R$
Answer: b) $5/2 R$

24. What does the term “dynamic equilibrium” refer to in gases?

a) Molecules remain stationary.
b) Molecules move uniformly without collision.
c) Molecules collide but average properties remain constant.
d) Pressure and temperature decrease simultaneously.
Answer: c) Molecules collide but average properties remain constant.

25. Which molecule has higher average speed at the same temperature?

a) Oxygen
b) Carbon dioxide
c) Helium
d) Nitrogen
Answer: c) Helium

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26. What is the definition of a mole in terms of Avogadro's number?

a) The mass of 6.02 $\times$ $10^{23}$ atoms.
b) The number of atoms in 1 liter of gas.
c) 6.02 $\times$ $10^{23}$ particles.
d) The volume of one molecule of gas.
Answer: c) 6.02 $\times$ $10^{23}$ particles.

27. Which quantity is not part of the ideal gas equation?

a) Volume
b) Temperature
c) Density
d) Pressure
Answer: c) Density

28. What is the specific heat ratio ($\gamma$) for a monatomic gas?

a) $5/2$
b) $3/2$
c) $7/5$
d) $5/3$
Answer: d) $5/3$

29. In thermal equilibrium, the distribution of energy in various modes follows:

a) Law of conservation of energy
b) Law of equipartition of energy
c) Dalton’s law
d) Boyle’s law
Answer: b) Law of equipartition of energy

30. Which parameter is not considered in calculating the mean free path?

a) Number density of molecules
b) Diameter of molecules
c) Speed of molecules
d) Pressure of the gas
Answer: d) Pressure of the gas

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31. What is the primary reason gases expand to fill a container?

a) Strong intermolecular forces
b) Negligible intermolecular forces
c) Molecular weight of gas
d) High molecular density
Answer: b) Negligible intermolecular forces

32. What is the number density ($n$) in the ideal gas equation?

a) Volume per molecule
b) Number of molecules per unit volume
c) Mass per unit volume
d) Pressure per unit volume
Answer: b) Number of molecules per unit volume

33. Which factor primarily determines the speed of gas molecules?

a) Pressure
b) Temperature
c) Volume
d) Number density
Answer: b) Temperature

34. A gas behaves ideally at:

a) High pressures and low temperatures
b) Low pressures and high temperatures
c) High pressures and high temperatures
d) Low pressures and low temperatures
Answer: b) Low pressures and high temperatures

35. What is the average translational kinetic energy per molecule of a gas at temperature $T$?

a) $(3/2)RT$
b) $k_BT$
c) $(3/2)k_BT$
d) $(1/2)RT$
Answer: c) $(3/2)k_BT$

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36. How many translational degrees of freedom do monatomic gases have?

a) 1
b) 2
c) 3
d) 5
Answer: c) 3

37. What happens to the velocity of a gas molecule after an elastic collision with a wall?

a) Velocity increases.
b) Velocity decreases.
c) Velocity remains the same in magnitude.
d) Velocity becomes zero.
Answer: c) Velocity remains the same in magnitude.

38. What is the ratio of $C_p$ to $C_v$ for a diatomic gas?

a) $5/3$
b) $3/2$
c) $7/5$
d) $1.67$
Answer: c) $7/5$

39. The kinetic energy of gas molecules is directly related to:

a) Volume
b) Mass
c) Pressure
d) Temperature
Answer: d) Temperature

40. What type of collisions occur between gas molecules?

a) Inelastic
b) Elastic
c) Constant
d) None of the above
Answer: b) Elastic

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