🔥 Thermodynamics – Stage 1

Page 9 : Adiabatic Process & Poisson’s Equations (JEE Core)

Adiabatic Process is one of the most frequently tested concepts in JEE.

1️⃣ What is an Adiabatic Process?

ΔQ = 0

• No heat enters or leaves the system
• Change in temperature occurs due to work only

⚠ Adiabatic ≠ Isothermal
Temperature changes in adiabatic process

2️⃣ First Law Applied to Adiabatic Process

First Law:
ΔQ = ΔU + W

Since ΔQ = 0

ΔU = −W

• Expansion → Work done by gas → Temperature decreases
• Compression → Work done on gas → Temperature increases

3️⃣ Poisson’s Equation (Pressure–Volume Relation)

P V^γ = Constant

γ (gamma) = C_p / C_v

This relation is valid only for ideal gases

4️⃣ Other Important Adiabatic Relations

T V^γ−1 = Constant

T^γ P^1−γ = Constant

These relations help in fast numerical solving

5️⃣ Graphical Comparison (JEE Favourite)

P–V Graph comparison:

• Adiabatic curve is steeper than isothermal curve
• Pressure drops faster in adiabatic expansion

⚠ JEE often asks: Which curve is steeper?

6️⃣ Work Done in Adiabatic Process

W = (P₁V₁ − P₂V₂) / (γ − 1)

Derived using Poisson’s equation

7️⃣ Special Case: Free Expansion

• No work done (W = 0)
• No heat exchange (Q = 0)

ΔU = 0 → ΔT = 0 (Ideal Gas)

⚠ Looks adiabatic but behaves differently

8️⃣ JEE Advanced Traps

⚠ Do not use PV = constant for adiabatic
⚠ Gamma depends on degrees of freedom
⚠ Adiabatic does NOT mean constant temperature

👉 Next Page:
Page 10 – Cyclic Process, Heat Engine & Efficiency

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🔥 Thermodynamics – Objective Final Revision

Thermodynamics – Set 1
Set 2
Set 3
Set 4
Set 5
Set 6
Set 7
Set 8
Set 9
Set 10
Set 11
Set 12
Set 13
Set 14
Set 15
Set 16
Set 17
Set 18
Set 19
Set 20
Set 21
Set 22
Set 23
Set 24
Set 25
Set 26
Set 27
Set 28
Set 29
Set 30
Set 31
Set 32
Set 33
Set 34
Set 35
Set 36
Set 37
Set 38
Set 39
Set 40
Set 41
Set 42
Set 43
Set 44
Set 45
Set 46
Set 47
Set 48
Set 49
Set 50
Set 51
Set 52
Set 53
Set 54
Set 55
Set 56
Set 57
Set 59

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