🔹 Kinetic Theory of Gases – Stage 2 (Page 7)

This page is designed to sharpen numerical confidence and elimination speed — crucial for JEE Advanced multi-correct and integer-type questions.

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1️⃣ Advanced Numerical (JEE Pattern)

Q1. A gas has rms speed 500 m/s at temperature T. At what temperature will rms speed become 1000 m/s?

Concept Used: v_rms ∝ √T

⇒ (v₂ / v₁)² = T₂ / T₁
⇒ (1000 / 500)² = T₂ / T₁ = 4

Answer: T₂ = 4T ✅

⚡ Trick: Speed doubled → temperature becomes four times.

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2️⃣ Pressure-Based Numerical (Microscopic View)

Q2. If the rms speed of gas molecules increases by 20%, by what percentage does pressure change (volume constant)?

P ∝ v_rms²
New speed = 1.2 v

⇒ P₂ / P₁ = (1.2)² = 1.44

Answer: Pressure increases by 44% ✅

🧠 Square-law dependence is frequently tested in JEE Advanced.

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3️⃣ Mean Free Path (Elimination Concept)

Q3. Which of the following increases mean free path?

• (A) Increase in pressure
• (B) Increase in molecular diameter
• (C) Decrease in density
• (D) Increase in temperature (at constant pressure)

Formula: λ = 1 / (√2 π d² n)

Correct Options: (C) and (D) ✅

❌ Eliminate (A) and (B) immediately → both decrease λ.

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4️⃣ Collision Frequency (High-Scoring Area)

Q4. Collision frequency increases with:

• ✔ Increase in pressure
• ✔ Increase in temperature
• ❌ Increase in molecular size

Key Relation: Collision frequency ∝ n d² v

✔ Larger speed → more collisions per second.

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5️⃣ Multi-Correct Question (JEE Advanced Style)

Q5. Which statements are correct for an ideal gas?

• (A) All molecules have same speed
• (B) Average kinetic energy ∝ temperature
• (C) rms speed depends on molecular mass
• (D) Pressure arises due to collisions with walls

Correct Options: (B), (C), (D) ✅

💡 Trap Alert: Option (A) is false due to Maxwell distribution.

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6️⃣ Integer-Type Concept

Q6. Ratio of rms speeds of two gases having molar masses M and 4M at same temperature?

v_rms ∝ 1 / √M

⇒ v₁ / v₂ = √(4M / M) = 2

Answer: 2 ✅

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7️⃣ JEE Speed-Boost Rules 🚀

• Always square speed ratios
• Mass ↑ → speed ↓
• Temperature ↑ → all speeds ↑
• Pressure questions → microscopic formula first

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✔ Stage 2 – Page 7 Completed — Numericals + Elimination + Advanced Thinking.

📚 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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📌 Updated regularly • Built for IIT-JEE Success