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

This page explains the Maxwell–Boltzmann speed distribution, one of the most tested concepts in IIT-JEE Advanced.

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1️⃣ Why Speed Distribution Exists?

In a gas, molecules continuously collide and exchange energy. Therefore, all molecules cannot have the same speed.

• Some molecules move very slowly
• Some move extremely fast
• Most move around an intermediate speed

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2️⃣ Maxwell–Boltzmann Speed Distribution

The distribution gives the number of molecules having speed between v and v + dv.

dN ∝ v² e^{(−mv² / 2kT)} dv

• v² term → number of ways to have speed v
• Exponential term → energy probability

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3️⃣ Maxwell Distribution Graph

Graph between Number of molecules (y-axis) and Speed (x-axis).

• Curve starts from zero at v = 0
• Rises to a maximum
• Gradually falls asymptotically

The area under the curve = Total number of molecules.

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4️⃣ Characteristic Speeds

Most Probable Speed:

v_mp = √(2kT / m)

Average Speed:

v̄ = √(8kT / πm)

RMS Speed:

v_rms = √(3kT / m)

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5️⃣ Ordering of Speeds (Very Important)

v_mp < v̄ < v_rms

• Always true for all gases
• Independent of temperature and gas type

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6️⃣ Effect of Temperature on Distribution

• Increase in temperature → curve shifts right
• Peak becomes lower and broader
• More high-speed molecules appear

Area under curve remains constant.

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7️⃣ Effect of Molecular Mass

• Lighter gas → curve shifts right
• Heavier gas → curve shifts left
• At same T, ⟨KE⟩ is same for all gases

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8️⃣ JEE Advanced Trap Box ⚠️

• Average speed ≠ RMS speed
• Higher speed ≠ higher kinetic energy always
• Distribution exists even at constant temperature

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9️⃣ Conceptual Check

If temperature doubles:

• v_mp, v̄, v_rms increase by √2
• Distribution widens
• Area remains same

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✔ Stage 2 – Page 2 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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