🔹 Kinetic Theory of Gases – Stage 2 (Page 5)
This page converts theory into problem-solving power. Every numerical here reflects JEE Advanced thinking.
1️⃣ RMS Speed – Numerical Application
Formula:
vrms = √(3RT / M)
Example:
Find ratio of rms speeds of H2 and O2 at same temperature.
Solution:
v ∝ 1 / √M ⇒ vH₂ : vO₂ = √(32 / 2) = 4 : 1
2️⃣ Pressure Change with Speed
If rms speed doubles (volume constant):
- v ∝ √T ⇒ T becomes 4T
- P ∝ T ⇒ Pressure becomes 4P
⚠️ Common mistake: assuming linear relation with v
3️⃣ Mean Free Path – Numerical
Formula:
λ = 1 / (√2 π d² n)
If pressure doubles at constant temperature:
- Number density doubles
- Mean free path becomes half
4️⃣ Collision Frequency Problem
Formula:
f = v / λ
If temperature increases:
- v increases
- λ remains constant
- Collision frequency increases
5️⃣ Energy Distribution Insight
At temperature T:
- Average translational KE = (3/2) kT
- Independent of gas type
- Depends only on temperature
✔ Heavy and light gases have same average KE at same T
6️⃣ Mixed Concept – Container Expansion
A gas expands freely into vacuum:
- No work done
- No heat exchange
- Temperature remains constant (ideal gas)
⚠️ Trap: assuming cooling due to expansion
7️⃣ Conceptual Multiple Choice (JEE Type)
Which remains unchanged when temperature doubles?
- Mean free path ✔
- Collision frequency ✖
- RMS speed ✖
- Average KE ✖
8️⃣ Formula Web (Quick Recall)
- v ∝ √T
- P ∝ T (constant V)
- λ ∝ 1 / P
- f ∝ √T
9️⃣ JEE Advanced Thinking Tip 🧠
Always ask: What changes? What stays constant?
Most KTG errors come from ignoring hidden constraints.
✔ Stage 2 – Page 5 Completed
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🔥 Kinetic Theory of Gases (KTG) – Complete Library
- KTG – Part 1
- KTG – Part 2
- KTG – Part 3
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- KTG – Part 7
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- KTG – Part 12
- KTG – Part 13
- KTG – Part 14
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- KTG – Part 16
- KTG – Part 17
- KTG – Part 18
- KTG – Part 19
- KTG – Part 20
- KTG – Part 21
- KTG – Part 22
- KTG – Part 23
- KTG – Part 24
- KTG – Part 25
- KTG – Part 26
- KTG – Part 27
- KTG – Part 28
- KTG – Part 29
- KTG – Part 30
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- Properties – Part 2
- Properties – Part 3
- Properties – Part 4
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- Properties – Part 7
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- Properties – Part 24
- Properties – Part 25
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