🔹 Kinetic Theory of Gases – Stage 2 (Page 1)

Stage 2 focuses on advanced conceptual clarity, molecular-level interpretation, and exam-oriented logic required for IIT-JEE Advanced.

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1️⃣ Re-examining the Assumptions of KTG

The kinetic theory of gases is based on idealized assumptions. In Stage 2, we analyze their physical meaning and limitations.

• Molecules are point masses → valid only at low pressure
• No intermolecular forces → fails near liquefaction
• Collisions perfectly elastic → internal energy conserved
• Random, isotropic motion → no preferred direction

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2️⃣ Isotropy of Molecular Motion

Molecular velocities are equally probable in all directions.

⟨v_x²⟩ = ⟨v_y²⟩ = ⟨v_z²⟩

Hence,

⟨v²⟩ = ⟨v_x²⟩ + ⟨v_y²⟩ + ⟨v_z²⟩ = 3⟨v_x²⟩

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3️⃣ Pressure: Microscopic Interpretation

Pressure arises due to momentum transfer during molecular collisions with container walls.

P = (1/3) ρ ⟨v²⟩

• Pressure depends on mean square speed, not direction
• Independent of shape of container

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4️⃣ Root Mean Square Speed (v_rms)

RMS speed gives correct kinetic energy average.

v_rms = √(3kT / m) = √(3RT / M)

• Independent of pressure
• Depends only on temperature and molecular mass

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5️⃣ Molecular Speed Distribution (Preview)

Gas molecules do not have a single speed. Instead, speeds follow a Maxwell–Boltzmann distribution.

• Most probable speed ≠ average speed ≠ rms speed
• Distribution broadens with temperature

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6️⃣ Relation Between Different Speeds

v_mp < v̄ < v_rms

• Frequently asked conceptual question
• Independent of gas type at same temperature

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7️⃣ Translational Kinetic Energy

Average translational kinetic energy per molecule:

⟨E⟩ = (3/2) kT

• Depends only on temperature
• Same for all gases at same temperature

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8️⃣ JEE Advanced Thinking Box

• Pressure ∝ ⟨v²⟩, not v
• Velocity distribution always exists, even at constant T
• Temperature measures average KE, not speed

✔ Stage 2 – Page 1 Completed

📚 IIT–JEE Physics Complete Library (Class XI)

Curated for IIT-JEE Advanced Aspirants
Concepts • Numericals • Objective Questions • Revision Capsules

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🔥 Kinetic Theory of Gases (KTG) – Complete Library

1. KTG – Part 1
2. KTG – Part 2
3. KTG – Part 3
4. KTG – Part 4
5. KTG – Part 5
6. KTG – Part 6
7. KTG – Part 7
8. KTG – Special Notes
9. KTG – Part 9
10. KTG – Part 10
11. KTG – Part 11
12. KTG – Part 12
13. KTG – Part 13
14. KTG – Part 14
15. KTG – Part 15
16. KTG – Part 16
17. KTG – Part 17
18. KTG – Part 18
19. KTG – Part 19
20. KTG – Part 20
21. KTG – Part 21
22. KTG – Part 22
23. KTG – Part 23
24. KTG – Part 24
25. KTG – Part 25
26. KTG – Part 26
27. KTG – Part 27
28. KTG – Part 28
29. KTG – Part 29
30. KTG – Part 30

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📐 Properties of Matter – Complete IIT-JEE Library

1. Properties – Part 1
2. Properties – Part 2
3. Properties – Part 3
4. Properties – Part 4
5. Properties – Part 5
6. Properties – Part 6
7. Properties – Part 7
8. Properties – Part 8
9. Properties – Part 9
10. Properties – Part 10
11. Properties – Part 11
12. Properties – Part 12
13. Properties – Part 13
14. Properties – Part 14
15. Properties – Part 15
16. Properties – Part 16
17. Properties – Part 17
18. Properties – Part 18
19. Properties – Part 19
20. Properties – Part 20
21. Properties – Part 21
22. Properties – Part 22
23. Properties – Part 23
24. Properties – Part 24
25. Properties – Part 25

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🌟 Master & Mega Physics Libraries

• IIT-JEE Physics Master Library
• Physics Complete Mega Library
• SHM Complete Library
• Waves – JEE Advanced Library
• Gravitation Library
• Momentum & Collisions Library
• Centre of Mass Library
• Work Energy Power Library

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