Here’s a blog post with 50 MCQs for Unit 8: Behavior of Perfect Gas and Kinetic Theory, with answers and explanations:
1. The pressure exerted by a gas is due to?
A) The weight of the gas particles
B) The collision of gas molecules with the walls of the container
C) The temperature of the gas
D) The volume of the gas
Answer: B) The collision of gas molecules with the walls of the container.
Explanation: Pressure in a gas is caused by the frequent collisions of gas molecules with the walls of the container. Each collision exerts a small force, and the cumulative effect of these collisions results in pressure.
2. According to Boyle’s law, at constant temperature, the volume of a gas is?
A) Directly proportional to the pressure
B) Inversely proportional to the pressure
C) Directly proportional to the temperature
D) Inversely proportional to the temperature
Answer: B) Inversely proportional to the pressure.
Explanation: Boyle’s law states that for a given mass of gas at constant temperature, the volume of the gas is inversely proportional to the pressure: V∝1PV \propto \frac{1}{P}V∝P1.
3. The ideal gas equation is given by?
A) PV=nRTPV = nRTPV=nRT
B) PV=nRTVPV = \frac{nRT}{V}PV=VnRT
C) P=nRTVP = \frac{nRT}{V}P=VnRT
D) P=VnRTP = \frac{V}{nRT}P=nRTV
Answer: A) PV=nRTPV = nRTPV=nRT.
Explanation: The ideal gas equation PV=nRTPV = nRTPV=nRT relates pressure (P), volume (V), temperature (T), and the amount of gas (n) using the ideal gas constant (R).
4. What is the value of the universal gas constant (R)?
A) 8.31 J/mol·K
B) 1.23 J/mol·K
C) 0.0821 atm·L/mol·K
D) 3.14 J/mol·K
Answer: A) 8.31 J/mol·K.
Explanation: The universal gas constant RRR has a value of 8.31 J/mol·K when using SI units.
5. In the kinetic theory of gases, the average kinetic energy of a gas molecule is directly proportional to?
A) The pressure of the gas
B) The volume of the gas
C) The temperature of the gas
D) The number of molecules in the gas
Answer: C) The temperature of the gas.
Explanation: According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the temperature of the gas.
6. The relationship between the pressure and temperature for an ideal gas at constant volume is given by?
A) Boyle’s law
B) Charles’s law
C) Gay-Lussac’s law
D) Ideal gas law
Answer: C) Gay-Lussac’s law.
Explanation: Gay-Lussac’s law states that the pressure of a gas is directly proportional to its temperature at constant volume: P∝TP \propto TP∝T.
7. Which of the following is the correct relationship between the molar specific heat capacities for an ideal gas?
A) CP=CV+RC_P = C_V + RCP=CV+R
B) CP=CV−RC_P = C_V – RCP=CV−R
C) CP=CVC_P = C_VCP=CV
D) CV=CP+RC_V = C_P + RCV=CP+R
Answer: A) CP=CV+RC_P = C_V + RCP=CV+R.
Explanation: For an ideal gas, the relationship between the molar specific heat capacities at constant pressure CPC_PCP and constant volume CVC_VCV is given by CP=CV+RC_P = C_V + RCP=CV+R, where R is the gas constant.
8. The volume of a gas at constant pressure is increased. What happens to the temperature of the gas according to Charles’s law?
A) It increases
B) It decreases
C) It remains constant
D) It depends on the pressure
Answer: A) It increases.
Explanation: Charles’s law states that the volume of a gas is directly proportional to its temperature at constant pressure: V∝TV \propto TV∝T. Therefore, increasing the volume at constant pressure results in an increase in temperature.
9. The average kinetic energy of the molecules of an ideal gas depends on?
A) The volume of the gas
B) The pressure of the gas
C) The temperature of the gas
D) The amount of gas
Answer: C) The temperature of the gas.
Explanation: The average kinetic energy of gas molecules is directly proportional to the temperature, as given by the equation Ek=32kBTE_k = \frac{3}{2} k_B TEk=23kBT, where kBk_BkB is the Boltzmann constant.
10. What happens to the kinetic energy of gas molecules if the temperature is doubled?
A) It is halved
B) It is doubled
C) It becomes four times
D) It remains the same
Answer: B) It is doubled.
Explanation: The kinetic energy of gas molecules is directly proportional to the temperature. Doubling the temperature will double the kinetic energy.
11. In the kinetic theory of gases, the pressure exerted by the gas is a result of?
A) The random motion of gas molecules
B) The attractive forces between molecules
C) The size of the gas molecules
D) The mass of the gas molecules
Answer: A) The random motion of gas molecules.
Explanation: Pressure is caused by the random motion of gas molecules colliding with the walls of the container. Each collision exerts a force, and the total pressure is the result of these countless collisions.
12. For an ideal gas, the root mean square speed of the molecules is given by?
A) vrms=3kBTmv_{rms} = \sqrt{\frac{3k_B T}{m}}vrms=m3kBT
B) vrms=m3kBTv_{rms} = \sqrt{\frac{m}{3k_B T}}vrms=3kBTm
C) vrms=3kBTmv_{rms} = \frac{3k_B T}{m}vrms=m3kBT
D) vrms=m3kBTv_{rms} = \frac{m}{3k_B T}vrms=3kBTm
Answer: A) vrms=3kBTmv_{rms} = \sqrt{\frac{3k_B T}{m}}vrms=m3kBT.
Explanation: The root mean square speed vrmsv_{rms}vrms is given by the equation vrms=3kBTmv_{rms} = \sqrt{\frac{3k_B T}{m}}vrms=m3kBT, where kBk_BkB is the Boltzmann constant, TTT is the temperature, and mmm is the mass of a gas molecule.
13. In an ideal gas, the relationship between the pressure, volume, and temperature is?
A) PV=nRTPV = nRTPV=nRT
B) P=nRTVP = \frac{nRT}{V}P=VnRT
C) PV=nRTPV = \frac{nR}{T}PV=TnR
D) All of the above
Answer: A) PV=nRTPV = nRTPV=nRT.
Explanation: The ideal gas law is PV=nRTPV = nRTPV=nRT, where PPP is the pressure, VVV is the volume, nnn is the number of moles, RRR is the universal gas constant, and TTT is the temperature in Kelvin.
14. The average speed of gas molecules increases with?
A) Decreasing temperature
B) Increasing pressure
C) Increasing volume
D) Increasing temperature
Answer: D) Increasing temperature.
Explanation: According to the kinetic theory of gases, the average speed of gas molecules is directly proportional to the square root of the temperature, i.e., increasing temperature increases the average speed of molecules.
15. The work done in an isothermal expansion of a gas is?
A) Zero
B) Positive
C) Negative
D) The same as the change in internal energy
Answer: B) Positive.
Explanation: In an isothermal expansion, the temperature remains constant. The work done by the gas is positive because it expands against the external pressure and transfers energy to the surroundings.
16. The pressure of an ideal gas increases if?
A) The volume increases
B) The temperature decreases
C) The number of gas molecules decreases
D) The temperature increases
Answer: D) The temperature increases.
Explanation: According to Gay-Lussac’s law, the pressure of a gas is directly proportional to its temperature at constant volume. Therefore, increasing the temperature leads to an increase in pressure.
17. What does the term “perfect gas” refer to?
A) A gas with no intermolecular forces
B) A gas that obeys the ideal gas law exactly
C) A gas that condenses at high temperatures
D) A gas with very large molecules
Answer: B) A gas that obeys the ideal gas law exactly.
Explanation: A perfect or ideal gas is one that behaves exactly according to the ideal gas law, meaning it has no intermolecular forces and occupies no volume.
18. In the kinetic theory of gases, the collision between gas molecules is considered?
A) Elastic
B) Inelastic
C) Perfectly inelastic
D) Non-elastic
Answer: A) Elastic.
Explanation: In the kinetic theory of gases, it is assumed that the collisions between gas molecules are perfectly elastic, meaning there is no loss of kinetic energy during collisions.
19. The kinetic energy of an ideal gas is proportional to?
A) The volume of the gas
B) The pressure of the gas
C) The temperature of the gas
D) The number of gas molecules
Answer: C) The temperature of the gas.
Explanation: The kinetic energy of an ideal gas is directly proportional to its temperature, as described by the equation Ek=32kBTE_k = \frac{3}{2} k_B TEk=23kBT.
20. In an isobaric process, the volume of a gas is directly proportional to?
A) Temperature
B) Pressure
C) The number of moles of the gas
D) All of the above
Answer: A) Temperature.
Explanation: According to Charles’s law, at constant pressure, the volume of a gas is directly proportional to its temperature: V∝TV \propto TV∝T.
21. The root mean square velocity of gas molecules is dependent on?
A) Pressure
B) Volume
C) Mass of the molecules and temperature
D) All of the above
Answer: C) Mass of the molecules and temperature.
Explanation: The root mean square velocity of gas molecules is given by the formula vrms=3kBTmv_{rms} = \sqrt{\frac{3k_B T}{m}}vrms=m3kBT, where mmm is the mass of the molecule and TTT is the temperature. Hence, it depends on the mass of the molecules and temperature.
22. The equation PV=13Nmvrms2PV = \frac{1}{3} N m v_{rms}^2PV=31Nmvrms2 represents?
A) Ideal gas law
B) Kinetic theory of gases
C) Boyle’s law
D) First law of thermodynamics
Answer: B) Kinetic theory of gases.
Explanation: This equation is derived from the kinetic theory of gases and relates the pressure of the gas to the average kinetic energy of the molecules, where PPP is pressure, VVV is volume, NNN is the number of molecules, mmm is the mass of each molecule, and vrmsv_{rms}vrms is the root mean square velocity.
23. Which law states that the volume of a gas is directly proportional to its temperature at constant pressure?
A) Boyle’s law
B) Charles’s law
C) Avogadro’s law
D) Gay-Lussac’s law
Answer: B) Charles’s law.
Explanation: Charles’s law states that the volume of a gas is directly proportional to its absolute temperature at constant pressure: V∝TV \propto TV∝T.
24. The temperature of a gas is proportional to the?
A) Average velocity of the molecules
B) Square of the average velocity of the molecules
C) Cube of the average velocity of the molecules
D) Inverse square of the velocity of the molecules
Answer: B) Square of the average velocity of the molecules.
Explanation: The temperature of an ideal gas is proportional to the average kinetic energy of the molecules, which is in turn proportional to the square of their velocity.
25. The ideal gas law assumes that gas molecules?
A) Have negligible volume and no intermolecular forces
B) Are very large in size and have intermolecular forces
C) Are stationary and do not interact with each other
D) All of the above
Answer: A) Have negligible volume and no intermolecular forces.
Explanation: The ideal gas law assumes that gas molecules are point particles with no volume and do not experience intermolecular forces, which allows the gas to behave ideally.
26. The compressibility factor of a real gas is defined as?
A) Z=PVrealnRTZ = \frac{P V_{real}}{n R T}Z=nRTPVreal
B) Z=nRTPVrealZ = \frac{n R T}{P V_{real}}Z=PVrealnRT
C) Z=PVidealnRTZ = \frac{P V_{ideal}}{n R T}Z=nRTPVideal
D) Z=VrealVidealZ = \frac{V_{real}}{V_{ideal}}Z=VidealVreal
Answer: A) Z=PVrealnRTZ = \frac{P V_{real}}{n R T}Z=nRTPVreal.
Explanation: The compressibility factor ZZZ is the ratio of the pressure-volume product of a real gas to that of an ideal gas at the same temperature and volume. If Z=1Z = 1Z=1, the gas behaves ideally.
27. When the temperature of a gas is increased at constant volume, the pressure?
A) Increases
B) Decreases
C) Remains constant
D) Becomes zero
Answer: A) Increases.
Explanation: According to Gay-Lussac’s law, for a fixed volume, the pressure of a gas increases with an increase in temperature.
28. What happens to the average kinetic energy of molecules in a gas if the temperature is lowered?
A) It increases
B) It decreases
C) It remains the same
D) It becomes zero
Answer: B) It decreases.
Explanation: The average kinetic energy of molecules is directly proportional to the temperature. As the temperature decreases, the kinetic energy of the gas molecules also decreases.
29. According to the kinetic theory of gases, which of the following is true for ideal gases?
A) Gas molecules do not collide with each other.
B) The collisions between gas molecules are elastic.
C) Gas molecules have significant intermolecular forces.
D) Gas molecules occupy a finite volume.
Answer: B) The collisions between gas molecules are elastic.
Explanation: The kinetic theory assumes that the collisions between gas molecules are perfectly elastic, meaning there is no energy loss during collisions.
30. The average distance between gas molecules is called?
A) Mean free path
B) Molecular distance
C) Molecular radius
D) Effective volume
Answer: A) Mean free path.
Explanation: The mean free path is the average distance a gas molecule travels before colliding with another molecule.
31. The principle of equipartition of energy states that?
A) The total energy of a gas is equally distributed among all its particles.
B) The total energy is distributed equally among all forms of energy in the system.
C) The average kinetic energy of molecules is the same at all temperatures.
D) The total energy in a gas system is constant.
Answer: B) The total energy is distributed equally among all forms of energy in the system.
Explanation: According to the equipartition of energy principle, the total energy of a system is equally divided between all available degrees of freedom (e.g., translational, rotational, vibrational).
32. What happens to the volume of a gas when its temperature increases, provided the pressure remains constant?
A) The volume increases
B) The volume decreases
C) The volume remains constant
D) The volume becomes zero
Answer: A) The volume increases.
Explanation: According to Charles’s law, the volume of a gas increases with an increase in temperature, when the pressure is held constant.
33. The root mean square velocity of gas molecules increases when?
A) The gas is compressed
B) The gas temperature decreases
C) The gas temperature increases
D) The pressure of the gas decreases
Answer: C) The gas temperature increases.
Explanation: The root mean square velocity is proportional to the square root of the temperature. So, when the temperature of the gas increases, the velocity of the gas molecules increases.
34. The total internal energy of an ideal gas depends on?
A) The volume
B) The pressure
C) The temperature
D) Both volume and pressure
Answer: C) The temperature.
Explanation: For an ideal gas, the total internal energy depends only on the temperature, not on the volume or pressure, since there are no intermolecular forces.
35. Which of the following is a characteristic of a real gas that deviates from ideal gas behavior?
A) High temperature
B) High pressure
C) Low pressure
D) Low temperature
Answer: B) High pressure.
Explanation: Real gases deviate from ideal behavior at high pressures, where the volume of gas molecules becomes significant compared to the total volume, and intermolecular forces affect the gas behavior.
36. The van der Waals equation corrects the ideal gas law by?
A) Accounting for molecular volume and intermolecular forces
B) Only accounting for molecular volume
C) Only accounting for intermolecular forces
D) Correcting for pressure and temperature
Answer: A) Accounting for molecular volume and intermolecular forces.
Explanation: The van der Waals equation modifies the ideal gas law to include factors for the finite size of molecules and attractive forces between them, improving the accuracy for real gases.
37. The behavior of real gases can be accurately described at?
A) Low pressure and high temperature
B) High pressure and low temperature
C) Low pressure and low temperature
D) Any pressure and temperature
Answer: A) Low pressure and high temperature.
Explanation: Real gases behave more like ideal gases at low pressures and high temperatures, where the intermolecular forces and the volume of molecules are less significant.
38. In an ideal gas, the average distance between molecules increases with?
A) Decreasing temperature
B) Increasing pressure
C) Decreasing volume
D) Increasing temperature
Answer: D) Increasing temperature.
Explanation: As the temperature of the gas increases, the average kinetic energy of the molecules increases, causing them to move faster and increasing the distance between them.
39. Which of the following factors is not considered in the kinetic theory of gases?
A) Intermolecular forces
B) Molecular collisions
C) Molecular size
D) Kinetic energy
Answer: A) Intermolecular forces.
Explanation: The kinetic theory of gases assumes that gas molecules do not experience intermolecular forces. This is one of the key assumptions of ideal gas behavior.
40. Which of the following is true about the behavior of gases at extremely low temperatures?
A) Gases behave more ideally at low temperatures
B) Gases liquefy or solidify at low temperatures
C) Gases obey the ideal gas law perfectly at low temperatures
D) The volume of gases increases as temperature decreases
Answer: B) Gases liquefy or solidify at low temperatures.
Explanation: At extremely low temperatures, gases lose enough kinetic energy that intermolecular forces become significant, causing the gas to condense into a liquid or solid.
41. According to Graham’s law, the rate of diffusion of a gas is inversely proportional to?
A) The square root of its mass
B) Its temperature
C) The volume of the gas
D) The pressure of the gas
Answer: A) The square root of its mass.
Explanation: Graham’s law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. This means lighter gases diffuse faster than heavier gases.
42. Which of the following best describes a perfect gas?
A) A gas with significant attractive forces between molecules
B) A gas with volume occupied by molecules considered negligible
C) A gas that behaves differently at high pressures and low temperatures
D) A gas that does not obey the ideal gas law
Answer: B) A gas with volume occupied by molecules considered negligible.
Explanation: A perfect gas is one in which the volume of the gas molecules is negligible compared to the total volume of the gas, and there are no intermolecular forces.
43. The specific heat of a gas at constant pressure is always greater than that at constant volume because?
A) The gas expands doing work during heating at constant pressure
B) The gas does no work during heating at constant volume
C) The gas is in equilibrium at constant volume
D) The gas molecules collide more at constant pressure
Answer: A) The gas expands doing work during heating at constant pressure.
Explanation: At constant pressure, part of the heat energy goes into doing work as the gas expands, so the specific heat at constant pressure is greater than at constant volume, where no work is done.
44. For an ideal gas, the specific heat ratio γ\gammaγ is defined as?
A) γ=CVCP\gamma = \frac{C_V}{C_P}γ=CPCV
B) γ=CPCV\gamma = \frac{C_P}{C_V}γ=CVCP
C) γ=CV−CP\gamma = C_V – C_Pγ=CV−CP
D) γ=CP+CV\gamma = C_P + C_Vγ=CP+CV
Answer: B) γ=CPCV\gamma = \frac{C_P}{C_V}γ=CVCP.
Explanation: The specific heat ratio γ\gammaγ is the ratio of the molar specific heat at constant pressure CPC_PCP to that at constant volume CVC_VCV.
45. Which of the following laws applies to the expansion of a gas when temperature is constant?
A) Boyle’s law
B) Charles’s law
C) Avogadro’s law
D) Ideal gas law
Answer: A) Boyle’s law.
Explanation: Boyle’s law applies to the expansion of a gas at constant temperature, stating that the volume of a gas is inversely proportional to its pressure.
46. In kinetic theory, the pressure exerted by an ideal gas is proportional to?
A) The number of molecules and their velocity
B) The number of molecules and the temperature
C) The square of the velocity of the molecules
D) Both B and C
Answer: D) Both B and C.
Explanation: According to kinetic theory, pressure is proportional to the number of molecules and their velocity (which depends on temperature), and the square of the velocity.
47. The rate of effusion of a gas is inversely proportional to the square root of?
A) Its molar mass
B) Its density
C) Its temperature
D) Its volume
Answer: A) Its molar mass.
Explanation: According to Graham’s law of effusion, the rate of effusion of a gas is inversely proportional to the square root of its molar mass, meaning lighter gases effuse faster.
48. The internal energy of an ideal gas depends on?
A) Volume
B) Pressure
C) Temperature
D) Both pressure and temperature
Answer: C) Temperature.
Explanation: For an ideal gas, the internal energy is only a function of temperature, as there are no intermolecular forces and the molecules have only translational kinetic energy.
49. What is the value of RRR in SI units for one mole of an ideal gas?
A) 8.314 J/mol·K
B) 0.0821 L·atm/mol·K
C) 0.8314 J/mol·K
D) 8.314 L·atm/mol·K
Answer: A) 8.314 J/mol·K.
Explanation: The universal gas constant RRR is 8.314 J/mol·K when using SI units.
50. What is the most probable speed of molecules in a gas related to?
A) The total energy of the gas
B) The temperature of the gas
C) The number of gas molecules
D) The pressure of the gas
Answer: B) The temperature of the gas.
Explanation: The most probable speed of molecules in a gas is related to the temperature of the gas, as described by the Maxwell-Boltzmann distribution. The higher the temperature, the higher the speed of the molecules.
This concludes the 50 MCQs for Unit 8: Behavior of Perfect Gas and Kinetic Theory. These questions will help reinforce key concepts like the ideal gas law, kinetic theory, molecular behavior, and more.
Also Read : All Chapters MCQs Click Here.
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