🔹 Kinetic Theory of Gases – Stage 1 (Page 8)

1️⃣ Ideal Gas vs Real Gas

An ideal gas is a hypothetical gas that strictly obeys the ideal gas equation:

PV = nRT

In reality, all gases are real gases and deviate from ideal behavior due to:

• Finite size of molecules
• Intermolecular forces

---

2️⃣ Causes of Deviation from Ideal Behavior

(a) Intermolecular Attraction

Attractive forces reduce the effective pressure exerted by gas molecules on container walls.

(b) Finite Volume of Molecules

Gas molecules occupy finite volume, reducing the free volume available for motion.

---

3️⃣ Compressibility Factor (Z)

Compressibility factor measures deviation from ideal behavior.

Z = PV / RT

• Z = 1 → Ideal gas
• Z < 1 → Attractive forces dominate
• Z > 1 → Repulsive forces dominate

---

4️⃣ Behavior of Z vs Pressure

• At low pressure: Z ≈ 1 (ideal behavior)
• At moderate pressure: Z < 1 (attraction dominant)
• At high pressure: Z > 1 (repulsion dominant)

This behavior is commonly tested in graph-based JEE questions.

---

5️⃣ van der Waals Equation (Real Gas Equation)

(P + a / V²)(V − b) = RT

where:

• a → measure of intermolecular attraction
• b → effective volume of molecules

---

6️⃣ Physical Meaning of van der Waals Constants

Constant	Meaning
a	Strength of attractive forces
b	Volume excluded by molecules

---

7️⃣ Critical Constants

The critical point is the state beyond which a gas cannot be liquefied by pressure alone.

• Critical Temperature (T_c)
• Critical Pressure (P_c)
• Critical Volume (V_c)

---

8️⃣ Relations for van der Waals Gas

V_c = 3b

P_c = a / (27 b²)

T_c = 8a / (27 R b)

---

9️⃣ Law of Corresponding States

All gases behave similarly when expressed in terms of reduced variables:

• P_r = P / P_c
• V_r = V / V_c
• T_r = T / T_c

For all gases at critical point:

Z_c = 3/8

---

🔟 JEE Advanced Traps & Key Notes

• Ideal gas is a limiting case of real gas
• Deviation increases at high pressure & low temperature
• Z vs P curve is frequently asked
• Critical constants are derived using van der Waals equation

✔ Stage 1 – Page 8 COMPLETE

📚 IIT–JEE Physics Complete Library (Class XI)

Curated for IIT-JEE Advanced Aspirants
Concepts • Numericals • Objective Questions • Revision Capsules

---

🔥 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

---

📐 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

---

🌟 Master & Mega Physics Libraries

• IIT-JEE Physics Master Library
• Physics Complete Mega Library
• SHM Complete Library
• Waves – JEE Advanced Library
• Gravitation Library
• Momentum & Collisions Library
• Centre of Mass Library
• Work Energy Power Library

---

📌 Updated regularly • Built for IIT-JEE Success