🔹 Kinetic Theory of Gases – Stage 1 (Page 6)

1️⃣ Specific Heat Capacity – Meaning

Specific heat capacity is the amount of heat required to raise the temperature of a substance by 1 K.

For gases, heat capacity depends on the process followed.

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2️⃣ Two Important Heat Capacities

(a) C_V – At Constant Volume

Heat supplied increases only the internal energy.

No work is done (W = 0)

dQ = dU

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(b) C_P – At Constant Pressure

Heat supplied increases internal energy and does work.

dQ = dU + PdV

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3️⃣ Expression for C_V (From Equipartition)

For a gas with f degrees of freedom:

C_V = (f/2) R

(Per mole)

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4️⃣ Mayer’s Relation

The relation between C_P and C_V is:

C_P − C_V = R

This relation is valid only for ideal gases.

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5️⃣ Expression for C_P

Using Mayer’s relation:

C_P = (f/2 + 1) R

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6️⃣ Ratio of Specific Heats (γ)

Important parameter in adiabatic processes:

γ = C_P / C_V

γ = (f + 2) / f

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7️⃣ Values for Different Gases (JEE MUST)

Gas	f	CV	CP	γ
Monoatomic	3	3/2 R	5/2 R	5/3
Diatomic (room temp)	5	5/2 R	7/2 R	7/5
Polyatomic (non-linear)	6	3 R	4 R	4/3

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8️⃣ JEE Advanced Traps & Tips

• Mayer’s relation works only for ideal gases
• Always check temperature before assigning f
• γ decreases as degrees of freedom increase
• C_P is always greater than C_V

✔ Stage 1 – Page 6 COMPLETE

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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
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10. KTG – Part 10
11. KTG – Part 11
12. KTG – Part 12
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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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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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