🔹 Kinetic Theory of Gases – Stage 1 (Page 5)

1️⃣ Degrees of Freedom (f)

Degrees of freedom of a molecule is the number of independent ways in which it can store energy.

Main types of motion:

• Translational motion
• Rotational motion
• Vibrational motion

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2️⃣ Translational Degrees of Freedom

Motion along x, y, and z directions.

Translational DOF = 3

Applicable to all gases.

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3️⃣ Rotational Degrees of Freedom

(a) Monoatomic Gas (He, Ne, Ar)

• No rotational DOF (ideal assumption)
• Total DOF = 3

(b) Diatomic Gas (O₂, N₂, H₂)

• 2 rotational DOF (about perpendicular axes)
• Total DOF (at room temp) = 5

(c) Polyatomic Gas (CO₂, H₂O)

• 3 rotational DOF

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4️⃣ Vibrational Degrees of Freedom

Each vibrational mode contributes:

2 degrees of freedom (1 kinetic + 1 potential)

Vibrational modes become active at high temperatures.

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5️⃣ Law of Equipartition of Energy

According to this law, energy is equally distributed among all active degrees of freedom.

Energy per degree of freedom = (1/2)kT

For one mole:

Energy per DOF = (1/2)RT

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6️⃣ Total Energy of a Gas Molecule

If a molecule has f degrees of freedom:

E = (f/2)kT (per molecule)

E = (f/2)RT (per mole)

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7️⃣ Important Table (JEE Favourite)

Gas Type	Degrees of Freedom (f)	Energy per Mole
Monoatomic	3	3/2 RT
Diatomic (room temp)	5	5/2 RT
Polyatomic (non-linear)	6	3 RT

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8️⃣ JEE Advanced Traps & Tips

• Vibrational DOF ignored at low temperature
• Equipartition applies only to quadratic terms
• Monoatomic gas has no rotational energy
• Always check temperature condition

✔ Stage 1 – Page 5 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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