• Amal Augustine
• January 10, 2026

Ideal Gas and Kinetic Theory of Gases: Complete Concept Guide with MCQ Insights

The concept of an ideal gas and the kinetic theory of gases forms the backbone of thermal physics and is one of the most frequently tested areas in competitive examinations such as NEET, JEE, and engineering entrance tests. These topics provide a microscopic explanation of macroscopic properties like pressure, temperature, internal energy, and volume, helping aspirants connect observable gas behavior with molecular motion.

An ideal gas is a hypothetical model that perfectly follows the gas laws and obeys the assumptions of kinetic theory without deviation. While real gases show deviations at high pressure and low temperature, they tend to behave like ideal gases at low pressure and high temperature, making the ideal gas model extremely useful for calculations and conceptual clarity.

The kinetic theory explains gas behavior using ideas such as elastic collisions, random molecular motion, mean free path, root mean square (rms) speed, and degrees of freedom. It also provides insight into why pressure is proportional to molecular kinetic energy, why temperature measures average kinetic energy, and why internal energy of an ideal gas depends only on temperature.

What Is an Ideal Gas?

An ideal gas is defined as a gas that:

• Obeys the ideal gas equation PV=nRTPV = nRTPV=nRT

• Satisfies all assumptions of kinetic theory

• Has negligible intermolecular forces

• Undergoes perfectly elastic collisions

• Shows Maxwell–Boltzmann distribution of molecular speeds

In reality, no gas is perfectly ideal, but gases like helium and hydrogen closely approximate ideal behavior under ordinary conditions.

Kinetic Theory of Gases: Core Assumptions

The kinetic theory of gases explains gas behavior using microscopic motion of molecules. Key assumptions include:

• Gas molecules are in continuous random motion

• Collisions between molecules and container walls are elastic

• Gas pressure arises due to momentum transfer

• Mean free path depends on number density and molecular size

• Average kinetic energy is proportional to absolute temperature

• The average momentum of gas molecules is zero

These assumptions help derive results related to pressure–temperature relations, rms speed, internal energy, and gas laws.

Internal Energy and Degrees of Freedom

For an ideal gas, internal energy depends only on temperature, not on pressure or volume. This explains why:

• In isothermal processes, internal energy remains constant

• In adiabatic expansion, internal energy decreases

• In free expansion, temperature remains unchanged for ideal gases

The concept of degrees of freedom explains how energy is distributed:

• Monoatomic gases → 3 translational

• Diatomic gases → 3 translational + 2 rotational

• Vibrational modes activate at high temperatures

Each degree of freedom contributes 12kT\frac{1}{2}kT21​kT energy per molecule.

MCQs on Ideal Gas :

1. What is an ideal gas?

A) One that consists of molecules
B) A gas satisfying the assumptions of kinetic theory
C) A gas having Maxwellian distribution of speed
D) A gas having Maxwellian distribution of speed
Answer: B

2. Pressure of an ideal gas is increased by keeping temperature constant. What is the effect on kinetic energy of molecules?

A) Increase
B) Decrease
C) No change
D) Can’t be determined
Answer: C

3. A real gas behaves as an ideal gas?

A) At very low pressure and high temperature
B) High pressure and low temperature
C) High temperature and high pressure
D) Low pressure and low temperature
Answer: A

4. For a real gas (Vander Waals’ gas)

A) Boyle temperature is a/Rb
B) Triple temperature is 2a/Rb
C) Inversion temperature is a/2Rb
D) Critical temperature is a/Rb
Answer: A

5. Every gas behaves as an ideal gas at?

A) High temperature and low pressure
B) Low temperature and high pressure
C) Normal temperature and pressure
D) None of the above
Answer: A

6. Which one of the following quantities is zero on an average for the molecules of an ideal gas in equilibrium?

A) Kinetic energy
B) Density
C) Speed
D) Momentum
Answer: D

7. If the internal energy of an ideal gas decreases by the same amount as the work done by the system, then which of the following is/are correct?

1. The process must be adiabatic.

2. The process must be isothermal.

3. The temperature of the gas must decrease.
   A) 1 only
   B) 1 and 3
   C) 2 only
   D) 3 only
   Answer: B

8. The internal energy of an ideal gas depends on which of the following factors?

A) Pressure only
B) Volume only
C) Temperature only
D) Pressure, volume, and temperature
Answer: C

9. An ideal gas undergoing adiabatic expansion obeys the relation?

A) pV = RT
B) pV^γ = constant
C) (p + a/V²)(V − b) = RT
D) pV^(γ − 1) = constant
Answer: B

10. One mole of an ideal gas is heated at a constant pressure of 1 atm from 0°C to 100°C. Work done by the gas is?

A) 8.31×10³ J
B) 8.31×10⁻³ J
C) 8.31×10⁻² J
D) 8.31×10² J
Answer: D

11. When a Van der Waal’s gas undergoes free expansion, then its temperature?

A) Decreases
B) Increases
C) Does not change
D) Depends upon the nature of the gas
Answer: A

12. The pressure of a gas is proportional to?

A) The sum of kinetic and potential energies
B) Potential energy
C) Kinetic energy
D) None of the above
Answer: C

13. A cylinder contains 12 litres of oxygen at 20°C and 15 atm pressure. The temperature is raised to 35°C and volume increased to 17 litres. Final pressure?

A) 9 atm
B) 11 atm
C) 15 atm
D) 17 atm
Answer: B

14. One liter of helium at 76 cm Hg and 27°C is heated till its pressure and volume are doubled. Final temperature?

A) 900°C
B) 927°C
C) 627°C
D) 327°C
Answer: B

15. The factor R/NA in an ideal gas law is

A) Celsius constant
B) Kelvin constant
C) Universal gas constant
D) Boltzmann’s constant
Answer: D

16. Match List I with List II:

A) (A)–(IV), (B)–(III), (C)–(II), (D)–(I)
B) (A)–(IV), (B)–(II), (C)–(I), (D)–(III)
C) (A)–(I), (B)–(III), (C)–(IV), (D)–(II)
D) (A)–(I), (B)–(IV), (C)–(III), (D)–(II)
Answer: C

17. The number of vibrational degrees of freedom of a diatomic molecule is

A) 0
B) 1
C) 2
D) 3
Answer: B

18. The number of rotational degrees of freedom of a diatomic molecule is

A) 1
B) 2
C) 0
D) 3
Answer: B

19. If the volume of a gas is reduced to half then the change in its mean free path is

A) Becomes half
B) Unchanged
C) Doubles
D) Depends on temperature
Answer: A

20. Given two statements:

S1: Average momentum of a molecule in ideal gas depends on temperature.
S2: If temperature doubled and O₂ dissociates into O atoms, rms speed becomes 2v.
A) Both true
B) Both false
C) S1 true, S2 false
D) S1 false, S2 true
Answer: D

21. Same gas in two vessels of equal volume and same temperature. If number of molecules ratio is 1:4:

A: rms velocity same
B: pressure ratio 1:4
C: pressure ratio 1:1
D: rms velocity ratio 1:4
A) A and C only
B) B and D only
C) A and B only
D) C only
Answer: C

22. Which statements are correct about degrees of freedom?

(A) n degrees gives n² ways of storing energy
(B) Each degree has (1/2)RT per mole
(C) Monoatomic has 1 rotational, diatomic has 2 rotational
(D) CH₄ has total 6 degrees
A) (B) and (C) only
B) (B) and (D) only
C) (A) and (B) only
D) (C) and (D) only
Answer: B

23. Effect on rms velocity of oxygen if temperature doubled and oxygen dissociates into atomic oxygen?

A) Same
B) Doubles
C) Half
D) Four times
Answer: B

24. Statements:

(1) Avg KE decreases when temperature reduced
(2) Avg KE increases with increase in volume
(3) Avg KE increases with increase in pressure at constant temperature
(4) Pressure increases with temperature at constant volume
A) (1) and (4) only
B) (1), (2), and (4) only
C) (2) and (4) only
D) (1), (2), and (5) only
Answer: A

25. Match Column I with Column II

A) 3 1 4 2
B) 2 3 4 1
C) 2 1 4 3
D) 3 2 1 4
Answer: C

26. Temperature determines the direction of net change of

A) Gross kinetic energy
B) Gross potential energy
C) Intermolecular potential energy
D) Intermolecular kinetic energy
Answer: D

27. In kinetic theory, when two gas molecules collide

A) Both KE and momentum conserved
B) Neither KE nor momentum conserved
C) Momentum conserved but KE not
D) KE conserved but momentum not
Answer: A

28. Mean free path of molecules in a polyatomic gas is independent of

A) Gas constant R
B) Volume of the molecule
C) Number density of molecules
D) Temperature of the gas
Answer: A

29. The molecular motion ceases at

A) −273°C
B) 273°C
C) −273 K
D) 273 K
Answer: A

30. The molecule of a monatomic gas has

A) Only one translational degree of freedom
B) Only two translational degrees of freedom
C) Only three translational degrees of freedom
D) No translational degrees of freedom at all
 Answer: C

Conclusion

The study of ideal gas and kinetic theory of gases bridges the gap between microscopic molecular motion and macroscopic thermodynamic behavior. By understanding how pressure originates from molecular collisions, why temperature reflects kinetic energy, and how internal energy depends solely on temperature, aspirants gain a powerful framework for solving numerical problems and conceptual MCQs.

Although ideal gases are theoretical models, they form the foundation for understanding real gases, thermodynamic processes, and advanced topics like statistical mechanics. Mastery of this chapter not only boosts exam performance but also strengthens fundamental physical intuition.

A thorough command over kinetic theory concepts, gas laws, degrees of freedom, and internal energy relations ensures confidence in tackling even the most challenging MCQs in thermal physics.