🔹 Kinetic Theory of Gases – Stage 1 (Page 4)

1️⃣ Three Important Molecular Speeds

In a gas, molecules do not move with the same speed. Instead, their speeds are distributed over a range.

The three important speeds are:

• Most Probable Speed (v_mp)
• Average Speed (v_avg)
• Root Mean Square Speed (v_rms)

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2️⃣ Most Probable Speed (v_mp)

The speed possessed by the maximum number of molecules at a given temperature.

v_mp = √(2kT / m)

In molar form:

v_mp = √(2RT / M)

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3️⃣ Average Speed (v_avg)

Arithmetic mean of the speeds of all molecules.

v_avg = √(8kT / πm)

In molar form:

v_avg = √(8RT / πM)

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4️⃣ RMS Speed (v_rms)

Defined as the square root of the mean of the squares of speeds.

v_rms = √(3kT / m)

In molar form:

v_rms = √(3RT / M)

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5️⃣ Relation Between Speeds (VERY IMPORTANT)

v_mp : v_avg : v_rms = √2 : √(8/π) : √3

Numerically:

v_mp < v_avg < v_rms

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6️⃣ Maxwell–Boltzmann Speed Distribution

The Maxwell distribution curve shows how molecular speeds are distributed at a given temperature.

• Curve is asymmetric
• Peak corresponds to v_mp
• Area under curve = total molecules

Effect of temperature:

• Increase in T → curve flattens
• Peak shifts to right
• More high-speed molecules

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7️⃣ JEE Exam Traps

• Speeds depend on √T, not T
• At same T, lighter gas moves faster
• KE depends on T, speed depends on mass
• Never confuse speed with kinetic energy

✔ Stage 1 – Page 4 COMPLETE

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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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