🔹 Kinetic Theory of Gases – Stage 1 (Page 10)

                                              

1️⃣ Collision of Gas Molecules

Gas molecules are in continuous random motion and undergo perfectly elastic collisions with each other and with the walls.

• Molecule size is very small compared to distance travelled
• No loss of kinetic energy during collisions 

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2️⃣ Mean Free Path (λ)

Mean free path is the average distance travelled by a molecule between two successive collisions.

λ = 1 / (√2 π d² n)

where,

• d = diameter of molecule
• n = number density (N/V)

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3️⃣ Mean Free Path in Terms of Pressure

λ = kT / (√2 π d² P)

• Mean free path ∝ Temperature
• Mean free path ∝ 1 / Pressure

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4️⃣ Collision Frequency (z)

Collision frequency is the number of collisions made by one molecule per second.

z = v̄ / λ

where v̄ = average speed of molecules

• Higher temperature → higher collision frequency
• Higher pressure → higher collision frequency

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5️⃣ Mean Collision Time (τ)

Time between two successive collisions:

τ = 1 / z = λ / v̄

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6️⃣ Transport Phenomena in Gases

Transport phenomena arise due to random motion of molecules.

• Viscosity
• Thermal conductivity
• Diffusion

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7️⃣ Viscosity of Gases

Viscosity is the resistance to relative motion between adjacent layers.

η = (1/3) ρ v̄ λ

• Viscosity of gases increases with temperature
• Almost independent of pressure

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8️⃣ Thermal Conductivity

Ability of gas to conduct heat due to molecular motion.

• Increases with temperature
• Independent of pressure

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9️⃣ Diffusion

Diffusion is the process by which gas molecules spread from higher concentration to lower concentration.

• Lighter gases diffuse faster
• Rate ∝ 1 / √M

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🔟 JEE Advanced Shortcuts & Traps

• Mean free path ∝ T / P
• η, K independent of pressure → common MCQ trap
• Always check proportionality, not exact formula

✔ KTG – Stage 1 COMPLETE (Pages 1–10)

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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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