🔥 Thermodynamics – Stage 3

Page 2 : Hard Numerical Problems & Strategy

This page trains you to think like a JEE Advanced examiner.

Problem 1️⃣ : Variable Pressure Process

A gas expands such that pressure varies with volume as
P = kV from volume V₁ to V₂.

Strategy:

Recognize non-constant pressure
Work = ∫P dV

W = ∫ kV dV = (k/2)(V₂² − V₁²)

❌ Using W = PΔV here gives wrong answer.

Problem 2️⃣ : Zero Net Work but Heat Exchange

A gas undergoes a cyclic process. Net work = 0.

Question: Is heat exchange zero?

Key Idea:
For cycle, ΔU = 0
So Q = W

Since W = 0 ⇒ Net heat = 0
But heat absorbed ≠ heat rejected

Problem 3️⃣ : Free Expansion (Classic Trap)

Gas expands freely into vacuum.

Instant Results:

W = 0
Q = 0

From first law:
ΔU = 0

For ideal gas → Temperature remains constant

❌ This is NOT isothermal process (no heat exchange)

Problem 4️⃣ : Adiabatic Compression

Gas compressed adiabatically.

Use Relations:

PV^γ = constant
TV^γ−1 = constant

❌ Do not use ideal gas equation alone.

Problem 5️⃣ : Entropy Based Feasibility

A system absorbs heat Q at temperature T from reservoir.

ΔS(system) = Q / T
ΔS(reservoir) = −Q / T

ΔS(universe) = 0 → reversible

Any deviation ⇒ irreversible

6️⃣ Two-Process Comparison

Same initial & final states, different paths.

ΔU is same for both.

❌ Work & heat depend on path.

7️⃣ Examiner’s Favorite Trick

If pressure, volume & temperature all change:
Examiner wants you to:

Identify dominant law
Ignore useless data

8️⃣ Rank Booster Tip

When stuck:
✔ Write symbolic equations first
✔ Substitute limits later
✔ Units check saves marks

✅ Stage 3 – Page 2 Completed
➡️ Next: Stage 3 – Page 3 (Extreme JEE Advanced PYQs & Multi-Concept)

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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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