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

1️⃣ Molecular Velocities – Components Concept

Molecular motion in a gas is random in all directions. Hence, velocity of a molecule can be resolved into three mutually perpendicular components:

v = (v_x, v_y, v_z)

Due to randomness:

• ⟨v_x⟩ = ⟨v_y⟩ = ⟨v_z⟩ = 0
• ⟨v_x²⟩ = ⟨v_y²⟩ = ⟨v_z²⟩

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2️⃣ Mean Square Speed

The average of the square of molecular speeds is called mean square speed.

⟨v²⟩ = ⟨v_x²⟩ + ⟨v_y²⟩ + ⟨v_z²⟩

Since all three components are equal:

⟨v²⟩ = 3⟨v_x²⟩

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3️⃣ Derivation of Gas Pressure (Key JEE Concept)

Consider a cubical container of side L, containing N molecules, each of mass m.

When a molecule hits the wall perpendicular to x-axis:

• Initial momentum = m v_x
• Final momentum = −m v_x
• Change in momentum = 2m v_x

Time between successive collisions with same wall:

Δt = 2L / v_x

Force exerted by one molecule:

F = (2m v_x) / (2L / v_x) = m v_x² / L

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4️⃣ Total Pressure of Gas

Pressure = Total force / Area

P = (Nm / V) ⟨v_x²⟩

Using ⟨v²⟩ = 3⟨v_x²⟩:

P = (1/3) (Nm / V) ⟨v²⟩

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5️⃣ Important Results to Remember

• Pressure is due to molecular collisions
• Only velocity component perpendicular to wall contributes
• Pressure ∝ mean square speed

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JEE Exam Notes

• This derivation is frequently tested conceptually
• Know assumptions clearly
• Pressure formula links microscopic & macroscopic physics

✔ Stage 1 – Page 2 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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🌟 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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