🧠 Kinetic Theory of Gases – Stage 3 (Page 7)

IIT-JEE Advanced Numericals, Traps & Smart Solving

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🔹 Problem 1 (Velocity Trap)

At temperature T, RMS speed of gas A is twice that of gas B. Find ratio of molar masses (M_A : M_B).

Solution:

v_rms ∝ 1 / √M

2 = √(M_B/M_A) ⇒ M_B/M_A = 4

Answer: M_A : M_B = 1 : 4

Trap: Many students reverse the ratio.

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🔹 Problem 2 (Pressure–Temperature)

A gas is heated so that its absolute temperature doubles. What happens to RMS speed?

v_rms ∝ √T

Answer: v_rms increases by √2 times.

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🔹 Problem 3 (Mean Free Path)

If pressure is reduced to one-third at constant temperature, mean free path becomes:

λ ∝ 1 / P

Answer: λ becomes 3 times.

IIT Tip: Pressure changes affect λ, not molecular size.

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🔹 Problem 4 (Energy Concept)

Average translational kinetic energy of a gas molecule depends on:

• A) Pressure
• B) Volume
• C) Temperature
• D) Molecular mass

Correct Answer: C

⟨KE⟩ = (3/2)kT

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🔹 Problem 5 (Gas Mixture – Advanced)

Two gases at same temperature are mixed. Which quantity becomes same for both?

• A) RMS speed
• B) Average KE
• C) Mean free path
• D) Collision frequency

Correct Answer: B

Reason:
Average KE depends only on temperature.

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🔹 Problem 6 (Speed Ordering)

Arrange speeds at same temperature:

v_mp, v_avg, v_rms

Correct Order:

v_mp < v_avg < v_rms

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🔹 Problem 7 (Pressure from Molecular View)

Pressure of gas is due to:

• A) Weight of gas
• B) Molecular attraction
• C) Momentum transfer
• D) Thermal expansion

Correct Answer: C

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⚠️ Common IIT Traps (Page 7)

• Mixing up KE with speed
• Forgetting square root relations
• Assuming pressure depends on mass
• Ignoring constant temperature condition

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💡 Smart 3-Step Strategy

1. Identify temperature dependence
2. Convert to proportional form
3. Apply square-root logic carefully

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🏆 Stage 3 – Page 7 Completed (Gold IIT Level)

📚 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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