🔹 Kinetic Theory of Gases – Stage 2 (Page 6)

This page integrates reasoning patterns, graphical understanding, and logical elimination — vital for JEE Advanced scoring beyond 90% accuracy.

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1️⃣ Assertion–Reason Practice (Conceptual Mastery)

Q1. Assertion (A): Pressure of a gas increases with temperature.
Reason (R): Average kinetic energy of molecules increases with temperature.

Answer: Both A and R are true, and R is the correct explanation of A. ✅

Concept: P ∝ ⟨KE⟩ ∝ T → linear relation under constant volume.

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Q2. Assertion (A): Mean free path increases with pressure.
Reason (R): Collision frequency increases with pressure.

Answer: A is false, R is true ❌

Logic: λ ∝ 1/P → As P ↑, λ ↓ but collision frequency ↑.

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Q3. Assertion (A): All molecules of a gas have the same energy at a given temperature.
Reason (R): Kinetic energy depends only on temperature.

Answer: A is false, R is true ❌

Explanation: Energy distribution (Maxwell-Boltzmann) → molecules have different energies.

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2️⃣ Graphical Understanding (Visual Mastery)

👉 (a) Pressure vs. Temperature (at constant V)

Linear graph: P ∝ T

📈 Straight line passing through origin

👉 (b) Mean Free Path vs. Pressure

Inverse relationship: λ ∝ 1/P

📉 Hyperbolic curve

👉 (c) Speed Distribution Curve

• As temperature increases → curve shifts right
• Area under curve = constant (total molecules)
• Peak height decreases, width increases

🔍 Insight: Even though max speed shifts, average kinetic energy depends only on T.

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3️⃣ Match the Following (Speed Relations)

Column I	Column II
(A) vrms	(p) √(3RT/M)
(B) vmean	(q) √(8RT/πM)
(C) vmp	(r) √(2RT/M)

Correct Matching: (A–p), (B–q), (C–r)

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4️⃣ Speed Ratio Results (Must Memorize)

v_rms : v_mean : v_mp = 1.085 : 1.00 : 0.921

🧠 Directly useful for comparison questions in JEE Advanced.

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5️⃣ Thermodynamic Crossover Questions

When linking KTG with Thermodynamics:

• P = (1/3) n m v² links microscopic and macroscopic levels
• For ideal gas: PV = RT → connects both interpretations

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6️⃣ JEE Concept Filter Box ⚡

• λ decreases with ↑ pressure
• RMS speed depends only on T
• Energy distribution ≠ uniform
• Transport coefficients ∝ √T

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✔ Stage 2 – Page 6 Completed — Advanced Graphs + Logical Thinking + Speed Relations.

📚 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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