🔥 Kinetic Theory of Gases – Stage 3 (Page 9)

Numerical Problems, Graphs & Assertion–Reason (IIT-JEE)

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🔢 Numerical 1 (RMS Speed – Direct)

Find RMS speed of O₂ at 300 K. (M = 32 × 10^-3 kg/mol, R = 8.314)

v_rms = √(3RT/M)

= √(3 × 8.314 × 300 / 0.032)

Answer: ≈ 484 m/s

IIT Tip: Temperature ↑ ⇒ speed ↑ as √T

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🔢 Numerical 2 (Pressure from Molecular Data)

Gas has density ρ and RMS speed v_rms. Find pressure.

P = (1/3) ρ v_rms²

IIT Trick: Direct formula, no temperature needed

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📈 Graph Question 1

Graph of Pressure vs Mean Square Speed is:

• A) Straight line through origin
• B) Parabola
• C) Hyperbola
• D) Exponential

Correct: A

Because P ∝ ⟨c²⟩

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📈 Graph Question 2

Graph of Average Speed vs Temperature is:

• A) Linear
• B) Square root
• C) Cubic
• D) Constant

Correct: B

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⚖️ Assertion–Reason 1

Assertion (A): RMS speed of gas molecules increases with temperature.

Reason (R): Average kinetic energy of gas molecules increases with temperature.

• A) Both A and R true, R explains A
• B) Both true, R not explanation
• C) A true, R false
• D) A false, R true

Correct: A

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⚖️ Assertion–Reason 2

Assertion: At constant temperature, pressure of gas depends on molecular mass.

Reason: Heavier molecules move slower.

Correct: D

Pressure depends only on temperature and number density.

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🔍 Conceptual Numerical (Advanced)

At same temperature:

v_{rms, H₂} : v_{rms, O₂} = ?

= √(M_O₂ / M_H₂) = √(32 / 2) = 4

Answer: 4 : 1

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⚠️ IIT Exam Traps (Page 9)

• Using linear instead of √T relation
• Confusing ⟨c⟩, c_rms, c_mp
• Ignoring constant condition
• Wrong graph interpretation

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🧠 Rank Booster Strategy

• Convert word problems → formula instantly
• Memorize proportional relations
• Practice assertion–reason logic

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🏁 Stage 3 – Page 9 Completed (Almost Done!)

📚 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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