🔹 Kinetic Theory of Gases – Stage 2 (Page 3)

This page focuses on collisions of gas molecules — a highly conceptual and calculation-based area in IIT-JEE Advanced.

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1️⃣ What is Mean Free Path?

Mean Free Path (λ) is the average distance travelled by a gas molecule between two successive collisions.

λ = 1 / (√2 π d² n)

• d → diameter of molecule
• n → number density (molecules per unit volume)

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2️⃣ Important Dependencies of Mean Free Path

• λ ∝ 1 / Pressure
• λ ∝ Temperature
• λ ∝ 1 / (molecular size)

👉 At high altitude (low pressure), mean free path increases.

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3️⃣ Collision Frequency

Collision frequency (Z) is the number of collisions per second suffered by a molecule.

Z = v / λ

• Higher speed → more collisions
• Higher pressure → more collisions

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4️⃣ Mean Collision Time

Mean collision time (τ) is the average time between two collisions.

τ = λ / v

Relation:

Z = 1 / τ

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5️⃣ Physical Meaning (JEE Favorite)

• Dense gas → small λ → frequent collisions
• Rare gas → large λ → fewer collisions
• Liquids & solids → λ extremely small

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6️⃣ Transport Phenomena – Introduction

Molecular collisions lead to:

• Viscosity (momentum transfer)
• Thermal conductivity (energy transfer)
• Diffusion (mass transfer)

All three depend on mean free path.

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7️⃣ Viscosity – Concept Only

Viscosity in gases arises due to momentum transfer between fast and slow layers.

• Independent of pressure (at low pressure)
• Increases with temperature

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8️⃣ JEE Advanced Trap Box ⚠️

• λ decreases when pressure increases
• Collision frequency increases with temperature
• Viscosity of gas increases with temperature (opposite to liquids)

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9️⃣ Conceptual Check

If pressure doubles at constant temperature:

• Mean free path becomes half
• Collision frequency doubles
• Average kinetic energy remains same

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✔ Stage 2 – Page 3 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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