🔹 Kinetic Theory of Gases – Stage 1 (Page 7)

1️⃣ Molecular Collisions in Gases

Gas molecules are in continuous random motion and frequently collide with each other and with container walls.

These collisions are assumed to be:

• Perfectly elastic
• Binary (only two molecules at a time)
• Short duration compared to time between 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 (molecules per unit volume)

Alternative form:

λ = kT / (√2 π d² P)

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3️⃣ Collision Frequency (Z)

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

Z = v̄ / λ

where v̄ is the mean speed.

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4️⃣ Total Number of Collisions per Unit Volume

Total collisions per unit volume per second:

Z_total = (1/2) n Z

Factor 1/2 avoids double counting of collisions.

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5️⃣ Dependence of Mean Free Path

Quantity	Effect on λ
Pressure ↑	λ decreases
Temperature ↑	λ increases
Molecular size ↑	λ decreases

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6️⃣ Transport Phenomena

Transport phenomena arise due to molecular motion and collisions.

• Viscosity – transfer of momentum
• Thermal conductivity – transfer of energy
• Diffusion – transfer of mass

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7️⃣ Key Results from Kinetic Theory

• Viscosity of gas is independent of pressure
• Viscosity increases with temperature
• Thermal conductivity increases with temperature
• Diffusion coefficient increases with temperature

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8️⃣ JEE Advanced Traps & Tricks

• Mean free path is inversely proportional to pressure
• Do not confuse collision frequency with total collisions
• Transport coefficients depend on molecular speed, not density
• Viscosity of gases ≠ viscosity of liquids (opposite trend)

✔ Stage 1 – Page 7 COMPLETE

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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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