🔥 Thermodynamics – Stage 3

Page 4 : Tough Numerical PYQs with Full Logical Solutions

This page contains calculation-heavy + concept-integrated questions exactly at JEE Advanced level.

Problem 1️⃣ : Adiabatic Expansion – Temperature Drop

An ideal gas expands adiabatically from volume V to 2V. Initial temperature = T.

Key Relation:
T·V^γ−1 = constant

Final Temperature:
T_f = T / 2^(γ−1)

❌ Do not use isothermal logic (T constant)

Problem 2️⃣ : Work Done in Adiabatic Process

Calculate work done during adiabatic expansion.

Formula:
W = (P₁V₁ − P₂V₂)/(γ − 1)

❌ Using W = nRT ln(V₂/V₁) is strictly wrong here

Problem 3️⃣ : Heat Supplied but Temperature Constant

Gas absorbs heat but temperature does not change.

ΔU = 0 ⇒ Q = W

❌ Many students think ΔT ≠ 0 whenever Q ≠ 0

Problem 4️⃣ : Cyclic Process – Net Work

Gas undergoes a closed PV cycle.

Net Work = Area enclosed in PV diagram

❌ Work is NOT zero just because initial = final state

Problem 5️⃣ : Mixing of Two Gases (Entropy)

Two gases at same T and P are mixed.

Entropy Change:
ΔS = nR ln(V_final/V_initial)

❌ Even identical gases increase entropy

Problem 6️⃣ : Refrigerator Numerical

Refrigerator operates between T₁ and T₂.

COP = T₂ / (T₁ − T₂)

❌ Students confuse COP with efficiency

Problem 7️⃣ : Free Expansion (Classic Trap)

Gas expands freely into vacuum.

Q = 0, W = 0 ⇒ ΔU = 0 ⇒ ΔT = 0

❌ Volume change does NOT imply temperature change

Problem 8️⃣ : Temperature vs Internal Energy

Same temperature, different gases.

Internal energy depends on:
✔ Temperature
✔ Degrees of freedom

Problem 9️⃣ : Concept Linking Test

Examiner checks if you can link:

First Law
PV relations
Entropy condition

✅ Stage 3 – Page 4 Completed
➡️ Next: Stage 3 – Page 5 (Extreme Traps & One-Line Kill Techniques)

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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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